Single-Loop Realization of Arbitrary Nonadiabatic Holonomic Single-Qubit Quantum Gates in a Superconducting Circuit

Effective non-adiabatic holonomic quantum computation of cavity modes via invariant-based reverse engineering

In this paper, we propose a protocol to realize non-adiabatic holonomic quantum computation (NHQC) of cavity modes via invariant-based reverse engineering. Coupling cavity modes with an auxiliary atom trapped in a cavity, we derive effective Hamiltonians with the help of laser pulses. Based on the derived Hamiltonians, invariant-based reverse engineering is used to find proper evolution paths for NHQC. Moreover, the systematic-error-sensitivity nullified optimal control method is considered in the parameter selections, making the protocol insensitive to the influence of systematic errors of pulses. We also estimate the imperfections induced by random noise and decoherence. Numerical results show that the protocol holds robustness against these imperfections. Therefore, the protocol may provide useful perspectives to quantum computation with optical qubits in cavity quantum electrodynamics systems. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.

Single-Atom Verification of the Noise-Resilient and Fast Characteristics of Universal Nonadiabatic Noncyclic Geometric Quantum Gates

Quantum gates induced by geometric phases are intrinsically robust against noise due to the global properties of their evolution paths. Compared to conventional nonadiabatic geometric quantum computation, the recently proposed nonadiabatic noncyclic geometric quantum computation (NNGQC) works in a faster fashion while still remaining the robust feature of the geometric operations. Here, we experimentally implement the NNGQC in a single trapped ultracold ^{40}Ca^{+} ion to verify the noise-resilient and fast feature. By performing unitary operations under imperfect conditions, we witness the advantages of the NNGQC with measured fidelities by quantum process tomography in comparison to other two quantum gates by conventional nonadiabatic geometric quantum computation and by straightforward dynamical evolution. Our results provide the first evidence confirming the possibility of accelerated quantum information processing with limited systematic errors even in an imperfect situation.

Distributed geometric quantum computation based on the optimized-control-technique in a cavity-atom system via exchanging virtual photons

We propose a scheme for quantum geometric computation on a fiber-cavity-fiber system, in which two atoms are located in two single-mode cavities, respectively, connected with each other by optical fiber. This scheme not only has the feature of virtual excitation of photons in the cavity quantum electrodynamics (CQED) that can reduce the effect of decay effectively but also has the advantage of geometric phase to withstand noises due to its built-in noise-resilience feature and robust merit. Specifically, our proposal combined with optimized-control-technology (OCT) can reduce gate operation error by adjusting the time-dependent amplitude and phase of the resonant field which further enhances the robustness of the quantum operation. The robustness against decoherence is demonstrated numerically and the scheme may be applied in the remote quantum information processing tasks and quantum computation.

Experimental Implementation of Universal Nonadiabatic Geometric Quantum Gates in a Superconducting Circuit

Using geometric phases to realize noise-resilient quantum computing is an important method to enhance the control fidelity. In this work, we experimentally realize a universal nonadiabatic geometric quantum gate set in a superconducting qubit chain. We characterize the realized single- and two-qubit geometric gates with both quantum process tomography and randomized benchmarking methods. The measured average fidelities for the single-qubit rotation gates and two-qubit controlled-Z gate are 0.9977(1) and 0.977(9), respectively. Besides, we also experimentally demonstrate the noise-resilient feature of the realized single-qubit geometric gates by comparing their performance with the conventional dynamical gates with different types of errors in the control field. Thus, our experiment proves a way to achieve high-fidelity geometric quantum gates for robust quantum computation.

Quantum walks in periodically kicked circuit QED lattice

We investigate the quantum walks of a single particle in a one-dimensional periodically kicked circuit quantum electrodynamics lattice. It is found that the dynamic process of the quantum walker is affected by the strength of incommensurate potentials and the driven periods of the system. We calculate the mean square displacement to illustrate the dynamic properties of the quantum walks, which shows that the localized process of the quantum walker presents the zero power-law index distribution. By calculating the mean information entropy, we find that the next-nearest-neighbor interactions have a remarkable deviation effects on the quantum walks and make a more stricter parameter condition for the localization of the quantum walker. Moreover, assisted by the lattice-based cavity input-output process, the localized features of circuit quantum electrodynamics lattice can be observed by measuring the average photon number of the cavity field in the steady state.

Demonstration of Controlled-Phase Gates between Two Error-Correctable Photonic Qubits

To realize fault-tolerant quantum computing, it is necessary to store quantum information in logical qubits with error correction functions, realized by distributing a logical state among multiple physical qubits or by encoding it in the Hilbert space of a high-dimensional system. Quantum gate operations between these error-correctable logical qubits, which are essential for implementation of any practical quantum computational task, have not been experimentally demonstrated yet. Here we demonstrate a geometric method for realizing controlled-phase gates between two logical qubits encoded in photonic fields stored in cavities. The gates are realized by dispersively coupling an ancillary superconducting qubit to these cavities and driving it to make a cyclic evolution depending on the joint photonic state of the cavities, which produces a conditional geometric phase. We first realize phase gates for photonic qubits with the logical basis states encoded in two quasiorthogonal coherent states, which have important implications for continuous-variable-based quantum computation. Then we use this geometric method to implement a controlled-phase gate between two binomially encoded logical qubits, which have an error-correctable function.

Hybrid superconductor-atom quantum interface with Raman chirped shortcut to adiabatic passage

Realization of the highly efficient hybrid atom-photon gates is vital to the quantum interface that integrates atoms and superconducting resonators. Here we propose a scheme to realize the hybrid state transfer and controlled-PHASE gate based on Raman chirped shortcut to adiabatic passage. The scheme is fast to protect the quantum state from the decoherence effects in the hybrid interface, as well as is robust due to the geometric phase. We show that this two-qubit gate is more resilient than the Raman pulse and Raman chirped adiabatic passage against the variations in the vacuum coupling strength and two-photon detuning. Its fast and robust features make it especially suitable for long-term storage and optical readout of superconducting qubits, and moreover, entanglement swapping between two disparate components.

Plug-and-Play Approach to Nonadiabatic Geometric Quantum Gates

Nonadiabatic holonomic quantum computation (NHQC) has been developed to shorten the construction times of geometric quantum gates. However, previous NHQC gates require the driving Hamiltonian to satisfy a set of rather restrictive conditions, reducing the robustness of the resulting geometric gates against control errors. Here we show that nonadiabatic geometric gates can be constructed in an extensible way, called NHQC+, for maintaining both flexibility and robustness against certain types of noises. Consequently, this approach makes it possible to incorporate most of the existing optimal control methods, such as dynamical decoupling, composite pulses, and a shortcut to adiabaticity, into the construction of single-looped geometric gates. Furthermore, this extensible approach of geometric quantum computation can be applied to various physical platforms such as superconducting qubits and nitrogen-vacancy centers. Specifically, we performed numerical simulation to show how the noise robustness in recent experimental implementations [Phys. Rev. Lett. 119, 140503 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.140503; Nat. Photonics 11, 309 (2017)NPAHBY1749-488510.1038/nphoton.2017.40] can be significantly improved by our NHQC+.approach. These results cover a large class of new techniques combing the noise robustness of both geometric phase and optimal control theory.

Environment-Assisted Holonomic Quantum Maps

Holonomic quantum computation uses non-Abelian geometric phases to realize error resilient quantum gates. Nonadiabatic holonomic gates are particularly suitable to avoid unwanted decoherence effects, as they can be performed at high speed. By letting the computational system interact with a structured environment, we show that the scope of error resilience of nonadiabatic holonomic gates can be widened to include systematic parameter errors. Our scheme maintains the geometric properties of the evolution and results in an environment-assisted holonomic quantum map that can mimic the effect of a holonomic gate. We demonstrate that the sensitivity to systematic errors can be reduced in a proof-of-concept spin-bath model.

Experimental Realization of Nonadiabatic Shortcut to Non-Abelian Geometric Gates

When a quantum system is driven slowly through a parametric cycle in a degenerate Hilbert space, the state would acquire a non-Abelian geometric phase, which is stable and forms the foundation for holonomic quantum computation (HQC). However, in the adiabatic limit, the environmental decoherence becomes a significant source of errors. Recently, various nonadiabatic holonomic quantum computation (NHQC) schemes have been proposed, but all at the price of increased sensitivity to control errors. Alternatively, there exist theoretical proposals for speeding up HQC by the technique of "shortcut to adiabaticity" (STA), but no experimental demonstration has been reported so far, as these proposals involve a complicated control of four energy levels simultaneously. Here, we propose and experimentally demonstrate that HQC via shortcut to adiabaticity can be constructed with only three energy levels, using a superconducting qubit in a scalable architecture. With this scheme, all holonomic single-qubit operations can be realized nonadiabatically through a single cycle of state evolution. As a result, we are able to experimentally benchmark the stability of STA+HQC against NHQC in the same platform. The flexibility and simplicity of our scheme makes it also implementable on other systems, such as nitrogen-vacancy center, quantum dots, and nuclear magnetic resonance. Finally, our scheme can be extended to construct two-qubit holonomic entangling gates, leading to a universal set of STAHQC gates.