A quantum computing view on unitary coupled cluster theory

Walking through Hilbert Space with Quantum Computers

Computations of chemical systems' equilibrium properties and nonequilibrium dynamics have been suspected of being a "killer app" for quantum computers. This review highlights the recent advancements of quantum algorithms tackling complex sampling tasks in the key areas of computational chemistry: ground state, thermal state properties, and quantum dynamics calculations. We review a broad range of quantum algorithms, from hybrid quantum-classical to fully quantum, focusing on the traditional Monte Carlo family, including Markov chain Monte Carlo, variational Monte Carlo, projector Monte Carlo, path integral Monte Carlo, etc. We also cover other relevant techniques involving complex sampling tasks, such as quantum-selected configuration interaction, minimally entangled typical thermal states, entanglement forging, and Monte Carlo-flavored Lindbladian dynamics. We provide a comprehensive overview of these algorithms' classical and quantum counterparts, detailing their theoretical frameworks and discussing the potentials and challenges in achieving quantum computational advantages.

Many-body approach to projective solution of generalized operators: Formulation and application to quantum computing

In this paper, we propose a novel many-body approach for determining the amplitudes of generalized operators in a projection-based formalism. To implicitly account for the effects of higher-order excitations, we begin with the well-established double-exponential coupled-cluster (CC) ansatz, parametrized by both one- and two-body excitation operators, complemented by a set of vacuum-annihilating two-body generalized operators with effective excitation rank of one. A systematic formalism is developed that effectively bypasses the constraints due to the vacuum-annihilation property of the generalized operators toward a set of closed-form residual equations for their optimization. Such a strategy requires the removal of the underlying redundancy in high-rank excited determinants, generated due to the presence of the generalized operators in the ansatz, by projecting them onto an internally contracted lower-dimensional manifold. This many-body formalism is integrated with the near-term projective quantum eigensolver (PQE) framework that leverages the conventional CC-like residual minimization to iteratively decouple the excited manifold from the reference. With the application of several molecular systems within PQE architecture, we demonstrate that the developed methodology enables us to achieve similar accuracy to the disentangled unitary coupled cluster with singles, doubles, and triples ansatz while utilizing an order of magnitude fewer quantum resources. Furthermore, when simulated under stochastic Gaussian noise or depolarizing hardware noise, our method shows significantly improved noise resilience compared to the other members of PQE family and the state-of-the-art variational quantum eigensolver.

SHARC-VQE: Simplified Hamiltonian approach with refinement and correction enabled variational quantum eigensolver for molecular simulation

Quantum computing is finding increasingly more applications in quantum chemistry, particularly to simulate electronic structure and molecular properties of simple systems. The transformation of a molecular Hamiltonian from the fermionic space to the qubit space results in a series of Pauli strings. Calculating the energy then involves evaluating the expectation values of each of these strings, which presents a significant bottleneck for applying variational quantum eigensolvers (VQEs) in quantum chemistry. Unlike fermionic Hamiltonians, the terms in a qubit Hamiltonian are additive. This work leverages this property to introduce a novel method for extracting information from the partial qubit Hamiltonian, thereby enhancing the efficiency of VQEs. This work introduces the SHARC-VQE (Simplified Hamiltonian Approximation, Refinement, and Correction-VQE) method, where the full molecular Hamiltonian is partitioned into two parts based on the ease of quantum execution. The easy-to-execute part constitutes the partial Hamiltonian, and the remaining part, while more complex to execute, is generally less significant. The latter is approximated by a refined operator and added up as a correction into the partial Hamiltonian. SHARC-VQE significantly reduces computational costs for molecular simulations. The cost of a single energy measurement can be reduced from O(N4ϵ2) to O(1ϵ2) for a system of N qubits and accuracy ϵ, while the overall cost of VQE can be reduced from O(N7ϵ2) to O(N3ϵ2). Furthermore, measurement outcomes using SHARC-VQE are less prone to errors induced by noise from quantum circuits, reducing the errors from 20%-40% to 5%-10% without any additional error correction or mitigation technique. In addition, the SHARC-VQE is demonstrated as an initialization technique, where the simplified partial Hamiltonian is used to identify an optimal starting point for a complex problem. Overall, this method improves the efficiency of VQEs and enhances the accuracy and reliability of quantum simulations by mitigating noise and overcoming computational challenges.

Evaluating Ground State Energies of Chemical Systems with Low-Depth Quantum Circuits and High Accuracy

Quantum computers have the potential to efficiently solve the electronic structure problem but are currently limited by noise and shallow circuits. We present an enhanced Variational Quantum Eigensolver (VQE) ansatz based on the Qubit Coupled Cluster (QCC) approach that requires optimization of only n parameters, where n is the number of Pauli string generators, rather than the typical n + 2m parameters, where m is the number of qubits. We evaluate the ground state energies and molecular dissociation curves of strongly correlated molecules, namely O3 and Li4, using active spaces of varying sizes in conjunction with our enhanced QCC ansatz, Unitary Coupled Cluster Single-Double (UCCSD) ansatz, and the classical Coupled Cluster Singles and Doubles (CCSD) method. Compared to UCCSD, our approach significantly reduces the number of parameters while maintaining high accuracy. Numerical simulations demonstrate the effectiveness of our approach, and experiments on superconducting and trapped-ion quantum computers showcase its practicality on real hardware. By eliminating the need for symmetry-restoring gates and reducing the number of parameters, our enhanced QCC ansatz enables accurate quantum chemistry calculations on near-term quantum devices for strongly correlated systems.

Unitary vibrational coupled cluster: General theory and implementation

Along with the surge in interest in quantum computing, interest in the unitary coupled cluster (UCC) Ansatz has reemerged. Although extensively studied within electronic structure theory, the UCC Ansatz remains relatively unexplored for the problem of molecular vibrations. In this contribution, working equations for the unitary vibrational coupled cluster (UVCC) Ansatz are derived, implemented, and benchmarked. Accuracy and convergence of state-specific excitation energies toward the full vibrational configuration interaction (FVCI) limit are observed to be comparable to vibrational coupled cluster theory. In addition, the overlap of a truncated UVCC state with the FVCI state is shown to exhibit some interesting properties from the perspective of fault-tolerant quantum computing.

SHARC meets TEQUILA: mixed quantum-classical dynamics on a quantum computer using a hybrid quantum-classical algorithm

Recent developments in quantum computing are highly promising, particularly in the realm of quantum chemistry. Due to the noisy nature of currently available quantum hardware, hybrid quantum-classical algorithms have emerged as a reliable option for near-term simulations. Mixed quantum-classical dynamics methods effectively capture nonadiabatic effects by integrating classical nuclear dynamics with quantum chemical computations of the electronic properties. However, these methods face challenges due to the high computational cost of the quantum chemistry part. To mitigate the computational demand, we propose a method where the required electronic properties are computed through a hybrid quantum-classical approach that combines classical and quantum hardware. This framework employs the variational quantum eigensolver and variational quantum deflation algorithms to obtain ground and excited state energies, gradients, nonadiabatic coupling vectors, and transition dipole moments. These quantities are used to propagate the nonadiabatic molecular dynamics using the Tully's fewest switches surface hopping method, although the implementation is also compatible with other molecular dynamics approaches. The approach, implemented by integrating the molecular dynamics program package SHARC with the TEQUILA quantum computing framework, is validated by studying the cis-trans photoisomerization of methanimine and the electronic relaxation of ethylene. The results show qualitatively accurate molecular dynamics that align with experimental findings and other computational studies. This work is expected to mark a significant step towards achieving a "quantum advantage" for realistic chemical simulations.

Nonunitary Coupled Cluster Enabled by Midcircuit Measurements on Quantum Computers

Many quantum algorithms rely on a quality initial state for optimal performance. Preparing an initial state for specific applications can considerably reduce the cost of probabilistic algorithms such as the well studied quantum phase estimation (QPE). Fortunately, in the application space of quantum chemistry, generating approximate wave functions for molecular systems is well studied, and quantum computing algorithms stand to benefit from importing these classical methods directly into a quantum circuit. In this work, we propose a state preparation method based on coupled cluster (CC) theory, which is a pillar of quantum chemistry on classical computers, by incorporating midcircuit measurements into the circuit construction. Currently, the most well studied state preparation method for quantum chemistry on quantum computers is the variational quantum eigensolver (VQE) with a unitary-CC with single- and double-electron excitation terms (UCCSD) ansatz whose operations are limited to unitary gates. We verify the accuracy of our state preparation protocol using midcircuit measurements by performing energy evaluation and state overlap computation for a set of small chemical systems. We further demonstrate that our approach leads to a reduction of the classical computation overhead, and the number of CNOT and T gates by 28 and 57% on average when compared against the standard VQE-UCCSD protocol.

Tiled unitary product states for strongly correlated Hamiltonians

Approximating the electronic wave function for strongly correlated systems remains a major theoretical challenge. Emerging quantum computers can enable new types of wave-function ansatz to be considered, with the potential to overcome the exponential memory storage for strong correlation. I have recently introduced the tiled Unitary Product States (tUPS) ansatz, which successfully combines the preservation of particle-number and spin symmetry with shallow quantum circuits and local qubit connectivity [H. G. A. Burton, Phys. Rev. Res., 2024, 6, 023300]. In this contribution, I investigate the accuracy of this tUPS hierarchy for strongly-correlated Hamiltonians. I consider the picket-fence pairing Hamiltonian and the two-dimensional Hubbard lattice, which collectively describe a range of strong correlation mechanisms found in molecules. Numerical results demonstrate that highly accurate energies can be achieved with a compact approximation for both weak and strong correlation in the Hubbard model, and the repulsive pairing regime. These data provide valuable insights into the applicability of the tUPS hierarchy for strong electron correlation.

Towards efficient quantum computing for quantum chemistry: reducing circuit complexity with transcorrelated and adaptive ansatz techniques

The near-term utility of quantum computers is hindered by hardware constraints in the form of noise. One path to achieving noise resilience in hybrid quantum algorithms is to decrease the required circuit depth - the number of applied gates - to solve a given problem. This work demonstrates how to reduce circuit depth by combining the transcorrelated (TC) approach with adaptive quantum ansätze and their implementations in the context of variational quantum imaginary time evolution (AVQITE). The combined TC-AVQITE method is used to calculate ground state energies across the potential energy surfaces of H4, LiH, and H2O. In particular, H4 is a notoriously difficult case where unitary coupled cluster theory, including singles and doubles excitations, fails to provide accurate results. Adding TC yields energies close to the complete basis set (CBS) limit while reducing the number of necessary operators - and thus circuit depth - in the adaptive ansätze. The reduced circuit depth furthermore makes our algorithm more noise-resilient and accelerates convergence. Our study demonstrates that combining the TC method with adaptive ansätze yields compact, noise-resilient, and easy-to-optimize quantum circuits that yield accurate quantum chemistry results close to the CBS limit.

Classification of dynamical Lie algebras of 2-local spin systems on linear, circular and fully connected topologies

Much is understood about 1-dimensional spin chains in terms of entanglement properties, physical phases, and integrability. However, the Lie algebraic properties of the Hamiltonians describing these systems remain largely unexplored. In this work, we provide a classification of all Lie algebras generated by the terms of 2-local spin chain Hamiltonians, or so-called dynamical Lie algebras, on 1-dimensional linear and circular lattice structures. We find 17 unique dynamical Lie algebras. Our classification includes some well-known models such as the transverse-field Ising model and the Heisenberg chain, and we also find more exotic classes of Hamiltonians that appear new. In addition to the closed and open spin chains, we consider systems with a fully connected topology, which may be relevant for quantum machine learning approaches. We discuss the practical implications of our work in the context of variational quantum computing, quantum control and the spin chain literature.

Variational quantum imaginary time evolution for matrix product state Ansatz with tests on transcorrelated Hamiltonians

The matrix product state (MPS) Ansatz offers a promising approach for finding the ground state of molecular Hamiltonians and solving quantum chemistry problems. Building on this concept, the proposed technique of quantum circuit MPS (QCMPS) enables the simulation of chemical systems using a relatively small number of qubits. In this study, we enhance the optimization performance of the QCMPS Ansatz by employing the variational quantum imaginary time evolution (VarQITE) approach. Guided by McLachlan's variational principle, the VarQITE method provides analytical metrics and gradients, resulting in improved convergence efficiency and robustness of the QCMPS. We validate these improvements numerically through simulations of H2, H4, and LiH molecules. In addition, given that VarQITE is applicable to non-Hermitian Hamiltonians, we evaluate its effectiveness in preparing the ground state of transcorrelated Hamiltonians. This approach yields energy estimates comparable to the complete basis set (CBS) limit while using even fewer qubits. In particular, we perform simulations of the beryllium atom and LiH molecule using only three qubits, maintaining high fidelity with the CBS ground state energy of these systems. This qubit reduction is achieved through the combined advantages of both the QCMPS Ansatz and transcorrelation. Our findings demonstrate the potential practicality of this quantum chemistry algorithm on near-term quantum devices.

Quantum Algorithms for the Variational Optimization of Correlated Electronic States with Stochastic Reconfiguration and the Linear Method

Solving the electronic Schrodinger equation for strongly correlated ground states is a long-standing challenge. We present quantum algorithms for the variational optimization of wave functions correlated by products of unitary operators, such as Local Unitary Cluster Jastrow (LUCJ) ansatzes, using stochastic reconfiguration (SR) and the linear method (LM). While an implementation on classical computing hardware would require exponentially growing compute cost, the cost (number of circuits and shots) of our quantum algorithms is polynomial in system size. We find that classical simulations of optimization with the linear method consistently find lower energy solutions than with the L-BFGS-B optimizer across the dissociation curves of the notoriously difficult N2 and C2 dimers; LUCJ predictions of the ground-state energies deviate from exact diagonalization by 1 kcal/mol or less at all points on the potential energy curve. While we do characterize the effect of shot noise on the LM optimization, these noiseless results highlight the critical but often overlooked role that optimization techniques must play in attacking the electronic structure problem (on both classical and quantum hardware), for which even mean-field optimization is formally NP hard. We also discuss the challenge of obtaining smooth curves in these strongly correlated regimes, and propose a number of quantum-friendly solutions ranging from symmetry-projected ansatz forms to a symmetry-constrained optimization algorithm.

Size-consistency and orbital-invariance issues revealed by VQE-UCCSD calculations with the FMO scheme

The fragment molecular orbital (FMO) scheme is one of the popular fragmentation-based methods and has the potential advantage of making the circuit shallow for quantum chemical calculations on quantum computers. In this study, we used a GPU-accelerated quantum simulator (cuQuantum) to perform the electron correlation part of the FMO calculation as unitary coupled-cluster singles and doubles (UCCSD) with the variational quantum eigensolver (VQE) for hydrogen-bonded (FH)  3 and (FH)  2 -H  2 O systems with the STO-3G basis set. VQE-UCCSD calculations were performed using both canonical and localized MO sets, and the results were examined from the point of view of size-consistency and orbital-invariance affected by the Trotter error. It was found that the use of localized MO leads to better results, especially for (FH)  2 -H  2 O. The GPU acceleration was substantial for the simulations with larger numbers of qubits, and was about a factor of 6.7-7.7 for 18 qubit systems.

Divergences in classical and quantum linear response and equation of motion formulations

Calculating molecular properties using quantum devices can be performed through the quantum linear response (qLR) or, equivalently, the quantum equation of motion (qEOM) formulations. Different parameterizations of qLR and qEOM are available, namely naïve, projected, self-consistent, and state-transfer. In the naïve and projected parameterizations, the metric is not the identity, and we show that it depends on redundant orbital rotations. This dependency may lead to divergences in the excitation energies for certain choices of the redundant orbital rotation parameters in an idealized noiseless setting. Furthermore, this leads to a significant variance when calculations include statistical noise from finite quantum sampling.

An Attractive Way to Correct for Missing Singles Excitations in Unitary Coupled Cluster Doubles Theory

Coupled cluster methods based exclusively on double excitations are comparatively "cheap" and interesting model chemistries, as they are typically able to capture the bulk of the dynamic electron correlation effects. The trade-off in such approximations is that the effect of neglected excitations, particularly single excitations, can be considerable. Using standard and electron-pair-restricted T2 operators to define two flavors of unitary coupled cluster doubles (UCCD) methods, we investigate the extent to which missing single excitations can be recovered from low-order corrections in many-body perturbation theory (MBPT) within the unitary coupled cluster (UCC) formalism. Our analysis includes the derivations of finite-order UCC energy functionals, which are used as a basis to define perturbative estimates of missed single excitations. This leads to the novel UCCD[4S] and UCCD[6S] methods, which consider energy corrections for missing single excitations through fourth- and sixth-order in MBPT, respectively. We also apply the same methodology to the electron-pair-restricted ansatz, but the improvements are only marginal. Our findings show that augmenting UCCD with these post hoc perturbative corrections can lead to UCCSD-quality results.

A hybrid quantum computing pipeline for real world drug discovery

Quantum computing, with its superior computational capabilities compared to classical approaches, holds the potential to revolutionize numerous scientific domains, including pharmaceuticals. However, the application of quantum computing for drug discovery has primarily been limited to proof-of-concept studies, which often fail to capture the intricacies of real-world drug development challenges. In this study, we diverge from conventional investigations by developing a hybrid quantum computing pipeline tailored to address genuine drug design problems. Our approach underscores the application of quantum computation in drug discovery and propels it towards more scalable system. We specifically construct our versatile quantum computing pipeline to address two critical tasks in drug discovery: the precise determination of Gibbs free energy profiles for prodrug activation involving covalent bond cleavage, and the accurate simulation of covalent bond interactions. This work serves as a pioneering effort in benchmarking quantum computing against veritable scenarios encountered in drug design, especially the covalent bonding issue present in both of the case studies, thereby transitioning from theoretical models to tangible applications. Our results demonstrate the potential of a quantum computing pipeline for integration into real world drug design workflows.

Probing Quantum Efficiency: Exploring System Hardness in Electronic Ground State Energy Estimation

We consider the question of how correlated the system hardness is between classical algorithms of electronic structure theory in ground state estimation and quantum algorithms. To define the system hardness for classical algorithms, we employ empirical criterion based on the deviation of electronic energies produced by coupled cluster and configuration interaction methods from the exact ones along multiple bonds dissociation in a set of molecular systems. For quantum algorithms, we have selected the Variational Quantum Eigensolver (VQE) and Quantum Phase Estimation (QPE) methods. As characteristics of the system hardness for quantum methods, we analyzed circuit depths for the state preparation, the number of quantum measurements needed for the energy expectation value, and various cost characteristics for the Hamiltonian encodings via Trotter approximation and linear combination of unitaries (LCU). Our results show that the quantum resource requirements are mostly unaffected by classical hardness, with the only exception being the state preparation part, which contributes to both VQE and QPE algorithm costs. However, there are clear indications that constructing the initial state with a significant overlap with the true ground state is easier than obtaining the state with an energy expectation value within chemical precision. These results support optimism regarding the identification of a molecular system where a quantum algorithm excels over its classical counterpart, as quantum methods can maintain efficiency in classically challenging systems.

A reduced cost four-component relativistic unitary coupled cluster method for atoms and molecules

We present a four-component relativistic unitary coupled cluster method for atoms and molecules. We have used commutator-based non-perturbative approximation using the "Bernoulli expansion" to derive an approximation to the relativistic unitary coupled cluster method. The performance of the full quadratic unitary coupled-cluster singles and doubles method (qUCCSD), as well as a perturbative approximation variant (UCC3), has been reported for both energies and properties. It can be seen that both methods give results comparable to those of the standard relativistic coupled cluster method. The qUCCSD method shows better agreement with experimental results due to the better inclusion of relaxation effects. The relativistic UCC3 and qUCCSD methods can simulate the spin-forbidden transition with easy access to transition properties. A natural spinor-based scheme to reduce the computational cost of relativistic UCC3 and qUCCSD methods has been discussed.

Toward Accurate Calculation of Excitation Energies on Quantum Computers with ΔADAPT-VQE: A Case Study of BODIPY Derivatives

Quantum chemistry simulations offer a cost-effective way to computationally design BODIPY photosensitizers. However, accurate predictions of excitation energies pose a challenge for time-dependent density functional theory and equation-of-motion coupled-cluster singles and doubles methods. By contrast, reliable predictions can be achieved by multireference quantum chemistry methods; unfortunately, their computational cost increases exponentially with the number of electrons. Alternatively, quantum computing holds potential for an exact simulation of the photophysical properties in a computationally more efficient way. Herein, we introduce the state-specific ΔUCCSD-VQE (unitary coupled-cluster singles and doubles-variational quantum eigensolver) and ΔADAPT-VQE methods in which the electronically excited state is calculated via a non-Aufbau configuration. We show for six BODIPY derivatives that the proposed methods predict accurate excitation energies that are in good agreement with those from experiments. Due to its performance and simplicity, we believe that ΔADAPT will become a useful approach for the simulation of BODIPY photosensitizers on near-term quantum devices.

Machine Learning Accelerates Precise Excited-State Potential Energy Surface Calculations on a Quantum Computer

Electronically excited-state problems represent a crucial research field in quantum chemistry, closely related to numerous practical applications in photophysics and photochemistry. The emerging of quantum computing provides a promising computational paradigm to solve the Schrödinger equation for predicting potential energy surfaces (PESs). Here, we present a deep neural network model to predict parameters of the quantum circuits within the framework of variational quantum deflation and subspace search variational quantum eigensolver, which are two popular excited-state algorithms to implement on a quantum computer. The new machine learning-assisted algorithm is employed to study the excited-state PESs of small molecules, achieving highly accurate predictions. We then apply this algorithm to study the excited-state properties of the ArF system, which is essential to a gas laser. Through this study, we believe that with future advancements in hardware capabilities, quantum computing could be harnessed to solve excited-state problems for a broad range of systems.

A new "gold standard": Perturbative triples corrections in unitary coupled cluster theory and prospects for quantum computing

A major difficulty in quantum simulation is the adequate treatment of a large collection of entangled particles, synonymous with electron correlation in electronic structure theory, with coupled cluster (CC) theory being the leading framework for dealing with this problem. Augmenting computationally affordable low-rank approximations in CC theory with a perturbative account of higher-rank excitations is a tractable and effective way of accounting for the missing electron correlation in those approximations. This is perhaps best exemplified by the "gold standard" CCSD(T) method, which bolsters the baseline CCSD with the effects of triple excitations using considerations from many-body perturbation theory (MBPT). Despite this established success, such a synergy between MBPT and the unitary analog of CC theory (UCC) has not been explored. In this work, we propose a similar approach wherein converged UCCSD amplitudes are leveraged to evaluate energy corrections associated with triple excitations, leading to the UCCSD[T] method. In terms of quantum computing, this correction represents an entirely classical post-processing step that improves the energy estimate by accounting for triple excitation effects without necessitating new quantum algorithm developments or increasing demand for quantum resources. The rationale behind this choice is shown to be rigorous by studying the properties of finite-order UCC energy functionals, and our efforts do not support the addition of the fifth-order contributions as in the (T) correction. We assess the performance of these approaches on a collection of small molecules and demonstrate the benefits of harnessing the inherent synergy between MBPT and UCC theories.

Quantum-centric high performance computing for quantum chemistry

High performance computing (HPC) is renowned for its capacity to tackle complex problems. Meanwhile, quantum computing (QC) provides a potential way to accurately and efficiently solve quantum chemistry problems. The emerging field of quantum-centric high performance computing (QCHPC), which merges these two powerful technologies, is anticipated to enhance computational capabilities for solving challenging problems in quantum chemistry. The implementation of QCHPC for quantum chemistry requires interdisciplinary research and collaboration across multiple fields, including quantum chemistry, quantum physics, computer science and so on. This perspective provides an introduction to the quantum algorithms that are suitable for deployment in QCHPC, focusing on conceptual insights rather than technical details. Parallel strategies to implement these algorithms on quantum-centric supercomputers are discussed. We also summarize high performance quantum emulating simulators, which are considered a viable tool to explore QCHPC. We conclude with challenges and outlooks in this field.

Toward Real Chemical Accuracy on Current Quantum Hardware Through the Transcorrelated Method

Quantum computing is emerging as a new computational paradigm with the potential to transform several research fields including quantum chemistry. However, current hardware limitations (including limited coherence times, gate infidelities, and connectivity) hamper the implementation of most quantum algorithms and call for more noise-resilient solutions. We propose an explicitly correlated Ansatz based on the transcorrelated (TC) approach to target these major roadblocks directly. This method transfers, without any approximation, correlations from the wave function directly into the Hamiltonian, thus reducing the resources needed to achieve accurate results with noisy quantum devices. We show that the TC approach allows for shallower circuits and improves the convergence toward the complete basis set limit, providing energies within chemical accuracy to experiment with smaller basis sets and, thus, fewer qubits. We demonstrate our method by computing bond lengths, dissociation energies, and vibrational frequencies close to experimental results for the hydrogen dimer and lithium hydride using two and four qubits, respectively. To demonstrate our approach's current and near-term potential, we perform hardware experiments, where our results confirm that the TC method paves the way toward accurate quantum chemistry calculations already on today's quantum hardware.

Efficient and Robust Parameter Optimization of the Unitary Coupled-Cluster Ansatz

The variational quantum eigensolver (VQE) framework has been instrumental in advancing near-term quantum algorithms. However, parameter optimization remains a significant bottleneck for VQE, requiring a large number of measurements for successful algorithm execution. In this paper, we propose sequential optimization with approximate parabola (SOAP) as an efficient and robust optimizer specifically designed for parameter optimization of the unitary coupled-cluster ansatz on quantum computers. SOAP leverages sequential optimization and approximates the energy landscape as quadratic functions, minimizing the number of energy evaluations required to optimize each parameter. To capture parameter correlations, SOAP incorporates the average direction from previous iterations into the optimization direction set. Numerical benchmark studies on molecular systems demonstrate that SOAP achieves significantly faster convergence and greater robustness to noise compared with traditional optimization methods. Furthermore, numerical simulations of up to 20 qubits reveal that SOAP scales well with the number of parameters in the ansatz. The exceptional performance of SOAP is further validated through experiments on a superconducting quantum computer using a 2-qubit model system.

Quantum Algorithmic Approach to Multiconfigurational Valence Bond Theory: Insights from Interpretable Circuit Design

Efficient ways to prepare Fermionic ground states on quantum computers are in high demand, and different techniques have been developed over the past few years. Despite having a vast set of methods, it is still unclear which method performs well for which system. In this work, we combine interpretable circuit designs with an effective basis approach in order to optimize a multiconfigurational valence bond wave function. Based on selected model systems, we show how this leads to an explainable performance. We demonstrate that the developed methodology outperforms related methods in terms of the size of the effective basis, as well as individual quantum resources for the involved circuits.

Quantum Equation of Motion with Orbital Optimization for Computing Molecular Properties in Near-Term Quantum Computing

Determining the properties of molecules and materials is one of the premier applications of quantum computing. A major question in the field is how to use imperfect near-term quantum computers to solve problems of practical value. Inspired by the recently developed variants of the quantum counterpart of the equation-of-motion (qEOM) approach and the orbital-optimized variational quantum eigensolver (oo-VQE), we present a quantum algorithm (oo-VQE-qEOM) for the calculation of molecular properties by computing expectation values on a quantum computer. We perform noise-free quantum simulations of BeH2 in the series of STO-3G/6-31G/6-31G* basis sets and of H4 and H2O in 6-31G using an active space of four electrons and four spatial orbitals (8 qubits) to evaluate excitation energies, electronic absorption, and, for twisted H4, circular dichroism spectra. We demonstrate that the proposed algorithm can reproduce the results of conventional classical CASSCF calculations for these molecular systems.

Vibrational ADAPT-VQE: Critical points lead to problematic convergence

Quantum chemistry is one of the most promising applications for which quantum computing is expected to have a significant impact. Despite considerable research in the field of electronic structure, calculating the vibrational properties of molecules on quantum computers remains a relatively unexplored field. In this work, we develop a vibrational Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum Eigensolver (vADAPT-VQE) formalism based on an infinite product representation (IPR) of anti-Hermitian excitation operators of the Full Vibrational Configuration Interaction (FVCI) wavefunction, which allows for preparing eigenstates of vibrational Hamiltonians on quantum computers. In order to establish the vADAPT-VQE algorithm using the IPR, we study the exactness of disentangled Unitary Vibrational Coupled Cluster (dUVCC) theory and show that dUVCC can formally represent the FVCI wavefunction in an infinite expansion. To investigate the performance of the vADAPT-VQE algorithm, we numerically study whether the vADAPT-VQE algorithm generates a sequence of operators that may represent the FVCI wavefunction. Our numerical results indicate frequent appearance of critical points in the wavefunction preparation using vADAPT-VQE. These results imply that one may encounter diminishing usefulness when preparing vibrational wavefunctions on quantum computers using vADAPT-VQE and that additional studies are required to find methods that can circumvent this behavior.

Quantum simulation of conical intersections

We explore the simulation of conical intersections (CIs) on quantum devices, setting the groundwork for potential applications in nonadiabatic quantum dynamics within molecular systems. The intersecting potential energy surfaces of H3+ are computed from a variance-based contracted quantum eigensolver. We show how the CIs can be correctly described on quantum devices using wavefunctions generated by the anti-Hermitian contracted Schrödinger equation ansatz, which is a unitary transformation of wavefunctions that preserves the topography of CIs. A hybrid quantum-classical procedure is used to locate the seam of CIs. Additionally, we discuss the quantum implementation of the adiabatic to diabatic transformation and its relation to the geometric phase effect. Results on noisy intermediate-scale quantum devices showcase the potential of quantum computers in dealing with problems in nonadiabatic chemistry.

Noise-independent route toward the genesis of a COMPACT ansatz for molecular energetics: A dynamic approach

Recent advances in quantum information and quantum science have inspired the development of various compact, dynamically structured ansätze that are expected to be realizable in Noisy Intermediate-Scale Quantum (NISQ) devices. However, such ansätze construction strategies hitherto developed involve considerable measurements, and thus, they deviate significantly in the NISQ platform from their ideal structures. Therefore, it is imperative that the usage of quantum resources be minimized while retaining the expressivity and dynamical structure of the ansatz that can adapt itself depending on the degree of correlation. We propose a novel ansatz construction strategy based on the ab initio many-body perturbation theory that requires no pre-circuit measurement and, thus, remains structurally unaffected by any hardware noise. The accuracy and quantum complexity associated with the ansatz are solely dictated by a pre-defined perturbative order, as desired, and, hence, are tunable. Furthermore, the underlying perturbative structure of the ansatz construction pipeline enables us to decompose any high-rank excitation that appears in higher perturbative orders into the product of various low-rank operators, and it thus keeps the execution gate-depth to its minimum. With a number of challenging applications on strongly correlated systems, we demonstrate that our ansatz performs significantly better, both in terms of accuracy, parameter count, and circuit depth, in comparison to the allied unitary coupled cluster based ansätze.

Folded Spectrum VQE: A Quantum Computing Method for the Calculation of Molecular Excited States

The recent developments of quantum computing present novel potential pathways for quantum chemistry as the scaling of the computational power of quantum computers could be harnessed to naturally encode and solve electronic structure problems. Theoretically exact quantum algorithms for chemistry have been proposed (e.g., quantum phase estimation), but the limited capabilities of current noisy intermediate-scale quantum devices motivated the development of less demanding hybrid algorithms. In this context, the variational quantum eigensolver (VQE) algorithm was successfully introduced as an effective method to compute the ground-state energies of small molecules. This study investigates the folded spectrum (FS) method as an extension of the VQE algorithm for the computation of molecular excited states. It provides the possibility of directly computing excited states around a selected target energy using the same quantum circuit as for the ground-state calculation. Inspired by the variance-based methods from the quantum Monte Carlo literature, the FS method minimizes the energy variance, thus, in principle, requiring a computationally expensive squared Hamiltonian to be applied. We alleviate this potentially poor scaling by employing a Pauli grouping procedure to identify sets of commuting Pauli strings that can be evaluated simultaneously. This allows for a significant reduction in the computational cost. We applied the FS-VQE method to small molecules (H2, LiH), obtaining all electronic excited states with chemical accuracy on ideal quantum simulators. Furthermore, we explore the application of quantum error mitigation techniques, demonstrating improved energy accuracy on noisy simulators compared with simulations without mitigation.

Optimizing Shot Assignment in Variational Quantum Eigensolver Measurement

Variational quantum eigensolvers (VQEs) show promise for tackling complex quantum chemistry challenges and realizing quantum advantages. However, in VQE, the measurement step encounters difficulties due to errors in objective function evaluation, e.g., the energy of a quantum state. While increasing the number of measurement shots can mitigate measurement errors, this approach leads to higher costs. Strategies for shot assignment have been investigated, allowing for the allocation of varying shot numbers to different Hamiltonian terms and reducing measurement variance through term-specific insights. In this paper, we introduce a dynamic approach, the Variance-Preserved Shot Reduction (VPSR) method. This technique strives to minimize the total number of measurement shots while preserving the variance of measurements throughout the VQE process. Our numerical experiments on H2 and LiH molecular ground states demonstrate the effectiveness of VPSR in achieving VQE convergence with a notably lower shot count.

Physics-Constrained Hardware-Efficient Ansatz on Quantum Computers That Is Universal, Systematically Improvable, and Size-Consistent

Variational wave function ansätze are at the heart of solving quantum many-body problems in physics and chemistry. Previous designs of hardware-efficient ansatz (HEA) on quantum computers are largely based on heuristics and lack rigorous theoretical foundations. In this work, we introduce a physics-constrained approach for designing HEA with rigorous theoretical guarantees by imposing a few fundamental constraints. Specifically, we require that the target HEA to be universal, systematically improvable, and size-consistent, which is an important concept in quantum many-body theories for scalability but has been overlooked in previous designs of HEA. We extend the notion of size-consistency to HEA and present a concrete realization of HEA that satisfies all these fundamental constraints while only requiring linear qubit connectivity. The developed physics-constrained HEA is superior to other heuristically designed HEA in terms of both accuracy and scalability, as demonstrated numerically for the Heisenberg model and some typical molecules. In particular, we find that restoring size-consistency can significantly reduce the number of layers needed to reach a certain accuracy. In contrast, the failure of other HEA to satisfy these constraints severely limits their scalability to larger systems with more than 10 qubits. Our work highlights the importance of incorporating physical constraints into the design of HEA for efficiently solving many-body problems on quantum computers.

Applications of noisy quantum computing and quantum error mitigation to "adamantaneland": a benchmarking study for quantum chemistry

The field of quantum computing has the potential to transform quantum chemistry. The variational quantum eigensolver (VQE) algorithm has allowed quantum computing to be applied to chemical problems in the noisy intermediate-scale quantum (NISQ) era. Applications of VQE have generally focused on predicting absolute energies instead of chemical properties that are relative energy differences and that are most interesting to chemists studying a chemical problem. We address this shortcoming by constructing a molecular benchmark data set in this work containing isomers of C10H16 and carbocationic rearrangements of C10H15+, calculated at a high-level of theory. Using the data set, we compared noiseless VQE simulations to conventionally performed density functional and wavefunction theory-based methods to understand the quality of results. We also investigated the effectiveness of a quantum state tomography-based error mitigation technique in applications of VQE under noise (simulated and real). Our findings reveal that the use of quantum error mitigation is crucial in the NISQ era and advantageous to yield almost noiseless quality results.

Variational Quantum Eigensolver Boosted by Adiabatic Connection

In this work, we integrate the variational quantum eigensolver (VQE) with the adiabatic connection (AC) method for efficient simulations of chemical problems on near-term quantum computers. Orbital-optimized VQE methods are employed to capture the strong correlation within an active space, and classical AC corrections recover the dynamical correlation effects comprising electrons outside of the active space. On two challenging strongly correlated problems, namely, the dissociation of N2 and the electronic structure of the tetramethyleneethane biradical, we show that the combined VQE-AC approach enhances the performance of VQE dramatically. Moreover, since the AC corrections do not bring any additional requirements on quantum resources or measurements, they can actually boost the VQE algorithms. Our work paves the way toward quantum simulations of real-life problems on near-term quantum computers.

Toward Chemical Accuracy with Shallow Quantum Circuits: A Clifford-Based Hamiltonian Engineering Approach

Achieving chemical accuracy with shallow quantum circuits is a significant challenge in quantum computational chemistry, particularly for near-term quantum devices. In this work, we present a Clifford-based Hamiltonian engineering algorithm, namely CHEM, that addresses the trade-off between circuit depth and accuracy. Based on a variational quantum eigensolver and hardware-efficient ansatz, our method designs the Clifford-based Hamiltonian transformation that (1) ensures a set of initial circuit parameters corresponding to the Hartree-Fock energy can be generated, (2) effectively maximizes the initial energy gradient with respect to circuit parameters, (3) imposes negligible overhead for classical processing and does not require additional quantum resources, and (4) is compatible with any circuit topology. We demonstrate the efficacy of our approach using a quantum hardware emulator, achieving chemical accuracy for systems as large as 12 qubits with fewer than 30 two-qubit gates. Our Clifford-based Hamiltonian engineering approach offers a promising avenue for practical quantum computational chemistry on near-term quantum devices.

Quantum Neural Network Inspired Hardware Adaptable Ansatz for Efficient Quantum Simulation of Chemical Systems

The variational quantum eigensolver is a promising way to solve the Schrödinger equation on a noisy intermediate-scale quantum (NISQ) computer, while its success relies on a well-designed wave function ansatz. Inspired by the quantum neural network, we propose a new hardware heuristic ansatz where its expressibility can be improved by increasing either the depth or the width of the circuit. Such a character makes this ansatz adaptable to different hardware environments. More importantly, it provides a general framework to improve the efficiency of the quantum resource utilization. For example, on a superconducting quantum computer where circuit depth is usually the bottleneck and the qubits thus cannot be fully used, circuit depth can be significantly reduced by introducing ancilla qubits. Ancilla qubits also make the circuit less sensitive to noises in practical application. These results open a new avenue to develop practical applications of quantum computation in the NISQ era.

Block-Invariant Symmetry Shift: Preprocessing Technique for Second-Quantized Hamiltonians to Improve Their Decompositions to Linear Combination of Unitaries

Computational cost of energy estimation for molecular electronic Hamiltonians via quantum phase estimation (QPE) grows with the difference between the largest and smallest eigenvalues of the Hamiltonian. In this work, we propose a preprocessing procedure that reduces the norm of the Hamiltonian without changing its eigenspectrum for the target states of a particular symmetry. The new procedure, block-invariant symmetry shift (BLISS), builds an operator T̂ such that the cost of implementing H ^ - T ^ is reduced compared to that of Ĥ, yet H ^ - T ^ acts on the subspaces of interest the same way as Ĥ does. BLISS performance is demonstrated for a linear combination of unitaries (LCU)-based QPE approaches on a set of small molecules. Using the number of electrons as the symmetry specifying the target set of states, BLISS provided a factor of 2 reduction of 1-norm for several LCU decompositions compared to their unshifted versions.

Basis Set Generation and Optimization in the NISQ Era with Quiqbox.jl

In the noisy intermediate-scale quantum era, ab initio computation of electronic structure problems has become one of the major benchmarks for identifying the boundary between classical and quantum computational power. Basis sets play a key role in the electronic structure methods implemented on both classical and quantum devices. To investigate the consequences of single-particle basis sets, we propose a framework for more customizable basis set generation and optimization. This framework allows composite basis sets to go beyond typical basis set frameworks, such as atomic basis sets, by introducing the concept of mixed-contracted Gaussian-type orbitals. These basis set generations set the stage for more flexible variational optimization of basis set parameters. To realize this framework, we have developed an open-source software package named "Quiqbox" in the Julia programming language. We demonstrate various examples of using Quiqbox for basis set optimization and generation, ranging from optimizing atomic basis sets on the Hartree-Fock level, preparing the initial state for variational quantum eigensolver computation, and constructing basis sets with completely delocalized orbitals. We also include various benchmarks of Quiqbox for basis set optimization and ab initial electronic structure computation.

Bridging physical intuition and hardware efficiency for correlated electronic states: the local unitary cluster Jastrow ansatz for electronic structure

A prominent goal in quantum chemistry is to solve the molecular electronic structure problem for ground state energy with high accuracy. While classical quantum chemistry is a relatively mature field, the accurate and scalable prediction of strongly correlated states found, e.g., in bond breaking and polynuclear transition metal compounds remains an open problem. Within the context of a variational quantum eigensolver, we propose a new family of ansatzes which provides a more physically appropriate description of strongly correlated electrons than a unitary coupled cluster with single and double excitations (qUCCSD), with vastly reduced quantum resource requirements. Specifically, we present a set of local approximations to the unitary cluster Jastrow wavefunction motivated by Hubbard physics. As in the case of qUCCSD, exactly computing the energy scales factorially with system size on classical computers but polynomially on quantum devices. The local unitary cluster Jastrow ansatz removes the need for SWAP gates, can be tailored to arbitrary qubit topologies (e.g., square, hex, and heavy-hex), and is well-suited to take advantage of continuous sets of quantum gates recently realized on superconducting devices with tunable couplers. The proposed family of ansatzes demonstrates that hardware efficiency and physical transparency are not mutually exclusive; indeed, chemical and physical intuition regarding electron correlation can illuminate a useful path towards hardware-friendly quantum circuits.

Growth Reduction of Similarity-Transformed Electronic Hamiltonians in Qubit Space

Accurately solving the electronic structure problem through the variational quantum eigensolver (VQE) is hindered by the available quantum resources of current and near-term devices. One approach to relieving the circuit depth requirements for VQE is to "pre-process" the electronic Hamiltonian by a similarity transformation incorporating some degree of electronic correlation, with the remaining correlation left to be addressed by the circuit ansatz. This often comes at the price of a substantial increase in the number of terms to measure in the similarity-transformed Hamiltonian. In this work, we propose an efficient approach to sampling elements from the complete Pauli group for N qubits which minimizes the onset of new terms in the transformed Hamiltonian while facilitating substantial energy lowering. We benchmark the growth-mitigating generator selection technique for ground state energy estimations applied to models of the H4, N2, and H2O molecular systems. It is found that utilizing a selection procedure which obtains the growth-minimizing generator from the set of operators with the maximal energy gradient is the most competitive approach to reducing the onset of Hamiltonian terms while achieving systematic energy lowering of the reference state.

Unitary Coupled Cluster: Seizing the Quantum Moment

Shallow, CNOT-efficient quantum circuits are crucial for performing accurate computational chemistry simulations on current noisy quantum hardware. Here, we explore the usefulness of noniterative energy corrections, based on the method of moments of coupled-cluster theory, for accelerating convergence toward full configuration interaction. Our preliminary numerical results relying on iteratively constructed ansätze suggest that chemically accurate energies can be obtained with substantially more compact circuits, implying enhanced resilience to gate and decoherence noise.

Linear-Scaling Quantum Circuits for Computational Chemistry

We have recently constructed compact, CNOT-efficient, quantum circuits for Fermionic and qubit excitations of arbitrary many-body rank [Magoulas, I.; Evangelista, F. A. J. Chem. Theory Comput. 2023, 19, 822]. Here, we present approximations of these circuits that substantially reduce the CNOT counts even further. Our preliminary numerical data, using the selected projective quantum eigensolver approach, show up to a 4-fold reduction in CNOTs. At the same time, there is practically no loss of accuracy in the energies compared to the parent implementation, while the ensuing symmetry breaking is essentially negligible.

Quantum computing for near-term applications in generative chemistry and drug discovery

In recent years, drug discovery and life sciences have been revolutionized with machine learning and artificial intelligence (AI) methods. Quantum computing is touted to be the next most significant leap in technology; one of the main early practical applications for quantum computing solutions is predicted to be in quantum chemistry simulations. Here, we review the near-term applications of quantum computing and their advantages for generative chemistry and highlight the challenges that can be addressed with noisy intermediate-scale quantum (NISQ) devices. We also discuss the possible integration of generative systems running on quantum computers into established generative AI platforms.

Nuclear shell-model simulation in digital quantum computers

The nuclear shell model is one of the prime many-body methods to study the structure of atomic nuclei, but it is hampered by an exponential scaling on the basis size as the number of particles increases. We present a shell-model quantum circuit design strategy to find nuclear ground states by exploiting an adaptive variational quantum eigensolver algorithm. Our circuit implementation is in excellent agreement with classical shell-model simulations for a dozen of light and medium-mass nuclei, including neon and calcium isotopes. We quantify the circuit depth, width and number of gates to encode realistic shell-model wavefunctions. Our strategy also addresses explicitly energy measurements and the required number of circuits to perform them. Our simulated circuits approach the benchmark results exponentially with a polynomial scaling in quantum resources for each nucleus. This work paves the way for quantum computing shell-model studies across the nuclear chart and our quantum resource quantification may be used in configuration-interaction calculations of other fermionic systems.

Partitioning Quantum Chemistry Simulations with Clifford Circuits

Current quantum computing hardware is restricted by the availability of only few, noisy qubits which limits the investigation of larger, more complex molecules in quantum chemistry calculations on quantum computers in the near term. In this work, we investigate the limits of their classical and near-classical treatment while staying within the framework of quantum circuits and the variational quantum eigensolver. To this end, we consider naive and physically motivated, classically efficient product ansatz for the parametrized wavefunction adapting the separable-pair ansatz form. We combine it with post-treatment to account for interactions between subsystems originating from this ansatz. The classical treatment is given by another quantum circuit that has support between the enforced subsystems and is folded into the Hamiltonian. To avoid an exponential increase in the number of Hamiltonian terms, the entangling operations are constructed from purely Clifford or near-Clifford circuits. While Clifford circuits can be simulated efficiently classically, they are not universal. In order to account for missing expressibility, near-Clifford circuits with only few, selected non-Clifford gates are employed. The exact circuit structure to achieve this objective is molecule-dependent and is constructed using simulated annealing and genetic algorithms. We demonstrate our approach on a set of molecules of interest and investigate the extent of our methodology's reach.

Optimizing the number of measurements for vibrational structure on quantum computers: coordinates and measurement schemes

One of the primary challenges prohibiting demonstrations of practical quantum advantages for near-term devices amounts to excessive measurement overheads for estimating relevant physical quantities such as ground state energies. However, with major differences between the electronic and vibrational structures of molecules, the question of how the resource requirements of computing anharmonic, vibrational states can be reduced remains relatively unexplored compared to its electronic counterpart. Importantly, bosonic commutation relations, distinguishable Hilbert spaces and vibrational coordinates allow manipulations of the vibrational system that can be exploited to minimize resource requirements. In this work, we investigate the impact of different coordinate systems and measurement schemes on the number of measurements needed to estimate anharmonic, vibrational states for a variety of three-mode (six-mode) molecules. We demonstrate an average of 3-fold (1.5-fold), with up to 7-fold (2.5-fold), reduction in the number of measurements required by employing appropriate coordinate transformations, based on an automized construction of qubit Hamiltonians from a conventional vibrational structure program.

TenCirChem: An Efficient Quantum Computational Chemistry Package for the NISQ Era

TenCirChem is an open-source Python library for simulating variational quantum algorithms for quantum computational chemistry. TenCirChem shows high-performance in the simulation of unitary coupled-cluster circuits, using compact representations of quantum states and excitation operators. Additionally, TenCirChem supports noisy circuit simulation and provides algorithms for variational quantum dynamics. TenCirChem's capabilities are demonstrated through various examples, such as the calculation of the potential energy curve of H₂O with a 6-31G(d) basis set using a 34-qubit quantum circuit, the examination of the impact of quantum gate errors on the variational energy of the H₂ molecule, and the exploration of the Marcus inverted region for charge transfer rate based on variational quantum dynamics. Furthermore, TenCirChem is capable of running real quantum hardware experiments, making it a versatile tool for both simulation and experimentation in the field of quantum computational chemistry.

Measurement Optimization Techniques for Excited Electronic States in Near-Term Quantum Computing Algorithms

The variational quantum eigensolver (VQE) remains one of the most popular near-term quantum algorithms for solving the electronic structure problem. Yet, for its practicality, the main challenge to overcome is improving the quantum measurement efficiency. Numerous quantum measurement techniques have been developed recently, but it is unclear how these state-of-the-art measurement techniques will perform in extensions of VQE for obtaining excited electronic states. Assessing the measurement techniques' performance in the excited state VQE is crucial because the measurement requirements in these extensions are typically much greater than in the ground state VQE, as one must measure the expectation value of multiple observables in addition to that of the electronic Hamiltonian. Here, we adapt various measurement techniques to two widely used excited state VQE algorithms: multistate contraction and quantum subspace expansion. Then, the measurement requirements of each measurement technique are numerically compared. We find that the best methods for multistate contraction are ones utilizing Hamiltonian data and wave function information to minimize the number of measurements. In contrast, randomized measurement techniques are more appropriate for quantum subspace expansion, with many more observables of vastly different energy scales to measure. Nevertheless, when the best possible measurement technique for each excited state VQE algorithm is considered, significantly fewer measurements are required in multistate contraction than in quantum subspace expansion.

Exploring Parameter Redundancy in the Unitary Coupled-Cluster Ansätze for Hybrid Variational Quantum Computing

One of the commonly used chemically inspired approaches in variational quantum computing is the unitary coupled-cluster (UCC) ansätze. Despite being a systematic way of approaching the exact limit, the number of parameters in the standard UCC ansätze exhibits unfavorable scaling with respect to the system size, hindering its practical use on near-term quantum devices. Efforts have been taken to propose some variants of the UCC ansätze with better scaling. In this paper, we explore the parameter redundancy in the preparation of unitary coupled-cluster singles and doubles (UCCSD) ansätze employing spin-adapted formulation, small amplitude filtration, and entropy-based orbital selection approaches. Numerical results of using our approach on some small molecules have exhibited a significant cost reduction in the number of parameters to be optimized and in the time to convergence compared with conventional UCCSD-VQE simulations. We also discuss the potential application of some machine learning techniques in further exploring the parameter redundancy, providing a possible direction for future studies.

State Preparation of Antisymmetrized Geminal Power on a Quantum Computer without Number Projection

The antisymmetrized geminal power (AGP) is equivalent to the number projected Bardeen-Cooper-Schrieffer (PBCS) wave function. It is also an elementary symmetric polynomial (ESP) state. We generalize previous research on deterministically implementing the Dicke state to a state preparation algorithm for an ESP state, or equivalently AGP, on a quantum computer. Our method is deterministic and has polynomial cost, and it does not rely on number symmetry breaking and restoration. We also show that our circuit is equivalent to a disentangled unitary paired coupled cluster operator and a layer of unitary Jastrow operator acting on a single Slater determinant. The method presented herein highlights the ability of disentangled unitary coupled cluster to capture nontrivial entanglement properties that are hardly accessible with traditional Hartree-Fock based electronic structure methods.