Quantum coherence in a one-electron semiconductor charge qubit

Quantum coherence and interference of a single moiré exciton in nano-fabricated twisted monolayer semiconductor heterobilayers

The moiré potential serves as a periodic quantum confinement for optically generated excitons, creating spatially ordered zero-dimensional quantum systems. However, a broad emission spectrum resulting from inhomogeneity among moiré potentials hinders the investigation of their intrinsic properties. In this study, we demonstrated a method for the optical observation of quantum coherence and interference of a single moiré exciton in a twisted semiconducting heterobilayer beyond the diffraction limit of light. We observed a single and sharp photoluminescence peak from a single moiré exciton following nanofabrication. Our findings revealed the extended duration of quantum coherence in a single moiré exciton, persisting beyond 10 ps, and an accelerated decoherence process with increasing temperature and excitation power density. Moreover, quantum interference experiments revealed the coupling between moiré excitons in different moiré potential minima. The observed quantum coherence and interference of moiré exciton will facilitate potential applications of moiré quantum systems in quantum technologies.

Photonic Which-Path Entangler Based on Longitudinal Cavity-Qubit Coupling

We show that a modulated longitudinal cavity-qubit coupling can be used to control the path taken by a multiphoton coherent-state wave packet conditioned on the state of a qubit, resulting in a qubit-which-path (QWP) entangled state. QWP states can generate long-range multipartite entanglement using strategies for interfacing discrete- and continuous-variable degrees of freedom. Using the approach presented here, entanglement can be distributed in a quantum network without the need for single-photon sources or detectors.

Pulse-controlled qubit in semiconductor double quantum dots

We present a numerically-optimized multipulse framework for the quantum control of a single-electron double quantum dot qubit. Our framework defines a set of pulse sequences, necessary for the manipulation of the ideal qubit basis, that avoids errors associated with excitations outside the computational subspace. A novel control scheme manipulates the qubit adiabatically, while also retaining high speed and ability to perform a general single-qubit rotation. This basis generates spatially localized logical qubit states, making readout straightforward. We consider experimentally realistic semiconductor qubits with finite pulse rise and fall times and determine the fastest pulse sequence yielding the highest fidelity. We show that our protocol leads to improved control of a qubit. We present simulations of a double quantum dot in a semiconductor device to visualize and verify our protocol. These results can be generalized to other physical systems since they depend only on pulse rise and fall times and the energy gap between the two lowest eigenstates.

Coherent charge oscillations in a bilayer graphene double quantum dot

The coherent dynamics of a quantum mechanical two-level system passing through an anti-crossing of two energy levels can give rise to Landau-Zener-Stückelberg-Majorana (LZSM) interference. LZSM interference spectroscopy has proven to be a fruitful tool to investigate charge noise and charge decoherence in semiconductor quantum dots (QDs). Recently, bilayer graphene has developed as a promising platform to host highly tunable QDs potentially useful for hosting spin and valley qubits. So far, in this system no coherent oscillations have been observed and little is known about charge noise in this material. Here, we report coherent charge oscillations and [Formula: see text] charge decoherence times in a bilayer graphene double QD. The charge decoherence times are measured independently using LZSM interference and photon assisted tunneling. Both techniques yield [Formula: see text] average values in the range of 400-500 ps. The observation of charge coherence allows to study the origin and spectral distribution of charge noise in future experiments.

Wigner-molecularization-enabled dynamic nuclear polarization

Multielectron semiconductor quantum dots (QDs) provide a novel platform to study the Coulomb interaction-driven, spatially localized electron states of Wigner molecules (WMs). Although Wigner-molecularization has been confirmed by real-space imaging and coherent spectroscopy, the open system dynamics of the strongly correlated states with the environment are not yet well understood. Here, we demonstrate efficient control of spin transfer between an artificial three-electron WM and the nuclear environment in a GaAs double QD. A Landau-Zener sweep-based polarization sequence and low-lying anticrossings of spin multiplet states enabled by Wigner-molecularization are utilized. Combined with coherent control of spin states, we achieve control of magnitude, polarity, and site dependence of the nuclear field. We demonstrate that the same level of control cannot be achieved in the non-interacting regime. Thus, we confirm the spin structure of a WM, paving the way for active control of correlated electron states for application in mesoscopic environment engineering.

Colloquium: Advances in automation of quantum dot devices control

Arrays of quantum dots (QDs) are a promising candidate system to realize scalable, coupled qubit systems and serve as a fundamental building block for quantum computers. In such semiconductor quantum systems, devices now have tens of individual electrostatic and dynamical voltages that must be carefully set to localize the system into the single-electron regime and to realize good qubit operational performance. The mapping of requisite QD locations and charges to gate voltages presents a challenging classical control problem. With an increasing number of QD qubits, the relevant parameter space grows sufficiently to make heuristic control unfeasible. In recent years, there has been considerable effort to automate device control that combines script-based algorithms with machine learning (ML) techniques. In this Colloquium, a comprehensive overview of the recent progress in the automation of QD device control is presented, with a particular emphasis on silicon- and GaAs-based QDs formed in two-dimensional electron gases. Combining physics-based modeling with modern numerical optimization and ML has proven effective in yielding efficient, scalable control. Further integration of theoretical, computational, and experimental efforts with computer science and ML holds vast potential in advancing semiconductor and other platforms for quantum computing.

Dynamical Behavior of Two Interacting Double Quantum Dots in 2D Materials for Feasibility of Controlled-NOT Operation

Two interacting double quantum dots (DQDs) can be suitable candidates for operation in the applications of quantum information processing and computation. In this work, DQDs are modeled by the heterostructure of two-dimensional (2D) MoS₂ having 1T-phase embedded in 2H-phase with the aim to investigate the feasibility of controlled-NOT (CNOT) gate operation with the Coulomb interaction. The Hamiltonian of the system is constructed by two models, namely the 2D electronic potential model and the 4×4 matrix model whose matrix elements are computed from the approximated two-level systems interaction. The dynamics of states are carried out by the Crank-Nicolson method in the potential model and by the fourth order Runge-Kutta method in the matrix model. Model parameters are analyzed to optimize the CNOT operation feasibility and fidelity, and investigate the behaviors of DQDs in different regimes. Results from both models are in excellent agreement, indicating that the constructed matrix model can be used to simulate dynamical behaviors of two interacting DQDs with lower computational resources. For CNOT operation, the two DQD systems with the Coulomb interaction are feasible, though optimization of engineering parameters is needed to achieve optimal fidelity.

Microwave-Frequency Scanning Gate Microscopy of a Si/SiGe Double Quantum Dot

Conventional transport methods provide quantitative information on spin, orbital, and valley states in quantum dots but lack spatial resolution. Scanning tunneling microscopy, on the other hand, provides exquisite spatial resolution at the expense of speed. Working to combine the spatial resolution and energy sensitivity of scanning probe microscopy with the speed of microwave measurements, we couple a metallic tip to a Si/SiGe double quantum dot (DQD) that is integrated with a charge detector. We first demonstrate that the dc-biased tip can be used to change the occupancy of the DQD. We then apply microwaves through the tip to drive photon-assisted tunneling (PAT). We infer the DQD level diagram from the frequency and detuning dependence of the tunneling resonances. These measurements allow the resolution of ∼65 μeV excited states, an energy consistent with valley splittings in Si/SiGe. This work demonstrates the feasibility of scanning gate experiments with Si/SiGe devices.

Charge-Noise Resilience of Two-Electron Quantum Dots in Si/SiGe Heterostructures

The valley degree of freedom presents challenges and opportunities for silicon spin qubits. An important consideration for singlet-triplet states is the presence of two distinct triplets, composed of valley vs orbital excitations. Here, we show that both of these triplets are present in the typical operating regime, but that only the valley-excited triplet offers intrinsic protection against charge noise. We further show that this protection arises naturally in dots with stronger confinement. These results reveal an inherent advantage for silicon-based multielectron qubits.

Fingerprints of Qubit Noise in Transient Cavity Transmission

Noise affects the coherence of qubits and thereby places a bound on the performance of quantum computers. We theoretically study a generic two-level system with fluctuating control parameters in a photonic cavity and find that basic features of the noise spectral density are imprinted in the transient transmission through the cavity. We obtain analytical expressions for generic noise and proceed to study the cases of quasistatic, white and 1/f^{α} noise in more detail. Additionally, we propose a way of extracting the noise power spectral density in a frequency band only bounded by the range of the qubit-cavity detuning and with an exponentially decaying error due to finite measurement times. Our results suggest that measurements of the time-dependent transmission probability represent a novel way of extracting noise characteristics.

A silicon singlet-triplet qubit driven by spin-valley coupling

Spin–orbit effects, inherent to electrons confined in quantum dots at a silicon heterointerface, provide a means to control electron spin qubits without the added complexity of on-chip, nanofabricated micromagnets or nearby coplanar striplines. Here, we demonstrate a singlet–triplet qubit operating mode that can drive qubit evolution at frequencies in excess of 200 MHz. This approach offers a means to electrically turn on and off fast control, while providing high logic gate orthogonality and long qubit dephasing times. We utilize this operational mode for dynamical decoupling experiments to probe the charge noise power spectrum in a silicon metal-oxide-semiconductor double quantum dot. In addition, we assess qubit frequency drift over longer timescales to capture low-frequency noise. We present the charge noise power spectral density up to 3 MHz, which exhibits a 1/f^α dependence consistent with α ~ 0.7, over 9 orders of magnitude in noise frequency.

Spin-orbit coupling in gate-defined quantum dots in silicon metal-oxide semiconductors provides a promising route for electrical control of spin qubits. Here, the authors demonstrate that intervalley spin–orbit interaction enables fast singlet–triplet qubit rotations in this platform, at frequencies exceeding 200MHz.

Evaluation of synthetic and experimental training data in supervised machine learning applied to charge-state detection of quantum dots

Automated tuning of gate-defined quantum dots is a requirement for large-scale semiconductor-based qubit initialisation. An essential step of these tuning procedures is charge-state detection based on charge stability diagrams. Using supervised machine learning to perform this task requires a large dataset for models to train on. In order to avoid hand labelling experimental data, synthetic data has been explored as an alternative. While providing a significant increase in the size of the training dataset compared to using experimental data, using synthetic data means that classifiers are trained on data sourced from a different distribution than the experimental data that is part of the tuning process. Here we evaluate the prediction accuracy of a range of machine learning models trained on simulated and experimental data, and their ability to generalise to experimental charge stability diagrams in two-dimensional electron gas and nanowire devices. We find that classifiers perform best on either purely experimental or a combination of synthetic and experimental training data, and that adding common experimental noise signatures to the synthetic data does not dramatically improve the classification accuracy. These results suggest that experimental training data as well as realistic quantum dot simulations and noise models are essential in charge-state detection using supervised machine learning.

Universal separability criterion for arbitrary density matrices from causal properties of separable and entangled quantum states

General physical background of famous Peres-Horodecki positive partial transpose (PH- or PPT-) separability criterion is revealed. Especially, the physical sense of partial transpose operation is shown to be equivalent to what one could call as the "local causality reversal" (LCR-) procedure for all separable quantum systems or to the uncertainty in a global time arrow direction in all entangled cases. Using these universal causal considerations brand new general relations for the heuristic causal separability criterion have been proposed for arbitrary [Formula: see text] density matrices acting in [Formula: see text] Hilbert spaces which describe the ensembles of N quantum systems of D eigenstates each. Resulting general formulas have been then analyzed for the widest special type of one-parametric density matrices of arbitrary dimensionality, which model a number of equivalent quantum subsystems being equally connected (EC-) with each other to arbitrary degree by means of a single entanglement parameter p. In particular, for the family of such EC-density matrices it has been found that there exists a number of N- and D-dependent separability (or entanglement) thresholds [Formula: see text] for the values of the corresponded entanglement parameter p, which in the simplest case of a qubit-pair density matrix in [Formula: see text] Hilbert space are shown to reduce to well-known results obtained earlier independently by Peres (Phys Rev Lett 77:1413-1415, 1996) and Horodecki (Phys Lett A 223(1-2):1-8, 1996). As the result, a number of remarkable features of the entanglement thresholds for EC-density matrices has been described for the first time. All novel results being obtained for the family of arbitrary EC-density matrices are shown to be applicable to a wide range of both interacting and non-interacting (at the moment of measurement) multi-partite quantum systems, such as arrays of qubits, spin chains, ensembles of quantum oscillators, strongly correlated quantum many-body systems with the possibility of many-body localization, etc.

Materials challenges and opportunities for quantum computing hardware

Quantum computing hardware technologies have advanced during the past two decades, with the goal of building systems that can solve problems that are intractable on classical computers. The ability to realize large-scale systems depends on major advances in materials science, materials engineering, and new fabrication techniques. We identify key materials challenges that currently limit progress in five quantum computing hardware platforms, propose how to tackle these problems, and discuss some new areas for exploration. Addressing these materials challenges will require scientists and engineers to work together to create new, interdisciplinary approaches beyond the current boundaries of the quantum computing field.

Correlated spectrum of distant semiconductor qubits coupled by microwave photons

We develop a new spectroscopic method to quickly and intuitively characterize the coupling of two microwave-photon-coupled semiconductor qubits via a high-impedance resonator. Highly distinctive and unique geometric patterns are revealed as we tune the qubit tunnel couplings relative to the frequency of the mediating photons. These patterns are in excellent agreement with a simulation using the Tavis-Cummings model, and allow us to readily identify different parameter regimes for both qubits in the detuning space. This method could potentially be an important component in the overall spectroscopic toolbox for quickly characterizing certain collective properties of multiple cavity quantum electrodynamics (QED) coupled qubits.

Exploiting a Single-Crystal Environment to Minimize the Charge Noise on Qubits in Silicon

Electron spins in silicon offer a competitive, scalable quantum-computing platform with excellent single-qubit properties. However, the two-qubit gate fidelities achieved so far have fallen short of the 99% threshold required for large-scale error-corrected quantum computing architectures. In the past few years, there has been a growing realization that the critical obstacle in meeting this threshold in semiconductor qubits is charge noise arising from the qubit environment. In this work, a notably low level of charge noise of S₀  = 0.0088 ± 0.0004 μeV² Hz^-1 is demonstrated using atom qubits in crystalline silicon, achieved by separating the qubits from surfaces and interface states. The charge noise is measured using both a single electron transistor and an exchange-coupled qubit pair that collectively provide a consistent charge noise spectrum over four frequency decades, with the noise level S₀ being an order of magnitude lower than previously reported. Low-frequency detuning noise, set by the total measurement time, is shown to be the dominant dephasing source of two-qubit exchange oscillations. With recent advances in fast (≈μs) single-shot readout, it is shown that by reducing the total measurement time to ≈1 s, 99.99% two-qubit S W A P gate fidelities can be achieved in single-crystal atom qubits in silicon.

Microwave Photon Detectors Based on Semiconducting Double Quantum Dots

Detectors of microwave photons find applications in different fields ranging from security to cosmology. Due to the intrinsic difficulties related to the detection of vanishingly small energy quanta ℏ ω , significant portions of the microwave electromagnetic spectrum are still uncovered by suitable techniques. No prevailing technology has clearly emerged yet, although different solutions have been tested in different contexts. Here, we focus on semiconductor quantum dots, which feature wide tunability by external gate voltages and scalability for large architectures. We discuss possible pathways for the development of microwave photon detectors based on photon-assisted tunneling in semiconducting double quantum dot circuits. In particular, we consider implementations based on either broadband transmission lines or resonant cavities, and we discuss how developments in charge sensing techniques and hybrid architectures may be beneficial for the development of efficient photon detectors in the microwave range.

Charge noise induced spin dephasing in a nanowire double quantum dot with spin-orbit coupling

Unexpected fluctuating charge field near a semiconductor quantum dot has severely limited the coherence time of the localized spin qubit. It is the interplay between the spin-orbit coupling and the asymmetrical confining potential in a quantum dot, that mediates the longitudinal interaction between the spin qubit and the fluctuating charge field. Here, we study the 1/f  charge noise induced spin dephasing in a nanowire double quantum dot via exactly solving its eigen-energies and eigenfunctions. Our calculations demonstrate that the spin dephasing has a nonmonotonic dependence on the asymmetry of the double quantum dot confining potential. With the increase of the potential asymmetry, the dephasing rate first becomes stronger very sharply before reaching to a maximum, after that it becomes weaker softly. Also, we find that the applied external magnetic field contributes to the spin dephasing, the dephasing rate is strongest at the anti-crossing point B ₀ in the double quantum dot.

Simulation Methodology for Electron Transfer in CMOS Quantum Dots

The construction of quantum computer simulators requires advanced software which can capture the most significant characteristics of the quantum behavior and quantum states of qubits in such systems. Additionally, one needs to provide valid models for the description of the interface between classical circuitry and quantum core hardware. In this study, we model electron transport in semiconductor qubits based on an advanced CMOS technology. Starting from 3D simulations, we demonstrate an order reduction and the steps necessary to obtain ordinary differential equations on probability amplitudes in a multi-particle system. We compare numerical and semi-analytical techniques concluding this paper by examining two case studies: the electron transfer through multiple quantum dots and the construction of a Hadamard gate simulated using a numerical method to solve the time-dependent Schrödinger equation and the tight-binding formalism for a time-dependent Hamiltonian.

Picosecond coherent electron motion in a silicon single-electron source

An advanced understanding of ultrafast coherent electron dynamics is necessary for the application of submicrometre devices under a non-equilibrium drive to quantum technology, including on-demand single-electron sources¹, electron quantum optics^2-4, qubit control^5-7, quantum sensing^8,9 and quantum metrology¹⁰. Although electron dynamics along an extended channel has been studied extensively^2-4,11, it is hard to capture the electron motion inside submicrometre devices. The frequency of the internal, coherent dynamics is typically higher than 100 GHz, beyond the state-of-the-art experimental bandwidth of less than 10 GHz (refs. ^6,12,13). Although the dynamics can be detected by means of a surface-acoustic-wave quantum dot¹⁴, this method does not allow for a time-resolved detection. Here we theoretically and experimentally demonstrate how we can observe the internal dynamics in a silicon single-electron source that comprises a dynamic quantum dot in an effective time-resolved fashion with picosecond resolution using a resonant level as a detector. The experimental observations and the simulations with realistic parameters show that a non-adiabatically excited electron wave packet¹⁵ spatially oscillates quantum coherently at ~250 GHz inside the source at 4.2 K. The developed technique may, in future, enable the detection of fast dynamics in cavities, the control of non-adiabatic excitations¹⁵ or a single-electron source that emits engineered wave packets¹⁶. With such achievements, high-fidelity initialization of flying qubits⁵, high-resolution and high-speed electromagnetic-field sensing⁸ and high-accuracy current sources¹⁷ may become possible.

Sound-driven single-electron transfer in a circuit of coupled quantum rails

Surface acoustic waves (SAWs) strongly modulate the shallow electric potential in piezoelectric materials. In semiconductor heterostructures such as GaAs/AlGaAs, SAWs can thus be employed to transfer individual electrons between distant quantum dots. This transfer mechanism makes SAW technologies a promising candidate to convey quantum information through a circuit of quantum logic gates. Here we present two essential building blocks of such a SAW-driven quantum circuit. First, we implement a directional coupler allowing to partition a flying electron arbitrarily into two paths of transportation. Second, we demonstrate a triggered single-electron source enabling synchronisation of the SAW-driven sending process. Exceeding a single-shot transfer efficiency of 99%, we show that a SAW-driven integrated circuit is feasible with single electrons on a large scale. Our results pave the way to perform quantum logic operations with flying electron qubits.

Simulation of 1D Topological Phases in Driven Quantum Dot Arrays

We propose a driving protocol which allows us to use quantum dot arrays as quantum simulators for 1D topological phases. We show that by driving the system out of equilibrium, one can imprint bond order in the lattice (producing structures such as dimers, trimers, etc.) and selectively modify the hopping amplitudes at will. Our driving protocol also allows for the simultaneous suppression of all the undesired hopping processes and the enhancement of the necessary ones, enforcing certain key symmetries which provide topological protection. In addition, we have discussed its implementation in a 12-QD array with two interacting electrons and found correlation effects in their dynamics, when configurations with different number of edge states are considered.

All-Microwave Control and Dispersive Readout of Gate-Defined Quantum Dot Qubits in Circuit Quantum Electrodynamics

Developing fast and accurate control and readout techniques is an important challenge in quantum information processing with semiconductor qubits. Here, we study the dynamics and the coherence properties of a GaAs/AlGaAs double quantum dot charge qubit strongly coupled to a frequency-tunable high-impedance resonator. We drive qubit transitions with synthesized microwave pulses and perform qubit readout through the state-dependent frequency shift imparted by the qubit on the dispersively coupled resonator. We perform Rabi oscillation, Ramsey fringe, energy relaxation, and Hahn-echo measurements and find significantly reduced decoherence rates down to γ_{2}/2π∼3  MHz corresponding to coherence times of up to T_{2}∼50  ns for charge states in gate-defined quantum dot qubits. We realize Rabi π pulses of width down to σ∼0.25  ns.

Semiconductor quantum computation

Semiconductors, a significant type of material in the information era, are becoming more and more powerful in the field of quantum information. In recent decades, semiconductor quantum computation was investigated thoroughly across the world and developed with a dramatically fast speed. The research varied from initialization, control and readout of qubits, to the architecture of fault-tolerant quantum computing. Here, we first introduce the basic ideas for quantum computing, and then discuss the developments of single- and two-qubit gate control in semiconductors. Up to now, the qubit initialization, control and readout can be realized with relatively high fidelity and a programmable two-qubit quantum processor has even been demonstrated. However, to further improve the qubit quality and scale it up, there are still some challenges to resolve such as the improvement of the readout method, material development and scalable designs. We discuss these issues and introduce the forefronts of progress. Finally, considering the positive trend of the research on semiconductor quantum devices and recent theoretical work on the applications of quantum computation, we anticipate that semiconductor quantum computation may develop fast and will have a huge impact on our lives in the near future.

A spin dephasing mechanism mediated by the interplay between the spin-orbit coupling and the asymmetrical confining potential in a semiconductor quantum dot

Understanding the spin dephasing mechanism is of fundamental importance in all potential applications of the spin qubit. Here we demonstrate a spin dephasing mechanism in a semiconductor quantum dot due to the 1/f charge noise. The spin-charge interaction is mediated by the interplay between the spin-orbit coupling and the asymmetrical quantum dot confining potential. The dephasing rate is proportional to both the strength of the spin-orbit coupling and the degree of the asymmetry of the confining potential. For parameters typical of the InSb, InAs, and GaAs quantum dots with a moderate well-height [Formula: see text] meV, we find the spin dephasing times are [Formula: see text] μs, 275 μs, and 55 ms, respectively. In particular, the spin dephasing can be enhanced by lowering the well-height. When the well-height is as small as [Formula: see text] meV, the spin depahsing times in the InSb, InAs, and GaAs quantum dots are decreased to [Formula: see text] μs, 18 μs, and 9 ms, respectively.

A Rout to Protect Quantum Gates constructed via quantum walks from Noises

The continuous-time quantum walk on a one-dimensional graph of odd number of sites with an on-site potential at the center is studied. We show that such a quantum-walk system can construct an X-gate of a single qubit as well as a control gate for two qubits, when the potential is much larger than the hopping strength. We investigate the decoherence effect and find that the coherence time can be enhanced by either increasing the number of sites on the graph or the ratio of the potential to the hopping strength, which is expected to motivate the design of the quantum gate with long coherence time. We also suggest several experimental proposals to realize such a system.

A silicon metal-oxide-semiconductor electron spin-orbit qubit

The silicon metal-oxide-semiconductor (MOS) material system is a technologically important implementation of spin-based quantum information processing. However, the MOS interface is imperfect leading to concerns about 1/f trap noise and variability in the electron g-factor due to spin-orbit (SO) effects. Here we advantageously use interface-SO coupling for a critical control axis in a double-quantum-dot singlet-triplet qubit. The magnetic field-orientation dependence of the g-factors is consistent with Rashba and Dresselhaus interface-SO contributions. The resulting all-electrical, two-axis control is also used to probe the MOS interface noise. The measured inhomogeneous dephasing time, [Formula: see text], of 1.6 μs is consistent with 99.95% ²⁸Si enrichment. Furthermore, when tuned to be sensitive to exchange fluctuations, a quasi-static charge noise detuning variance of 2 μeV is observed, competitive with low-noise reports in other semiconductor qubits. This work, therefore, demonstrates that the MOS interface inherently provides properties for two-axis qubit control, while not increasing noise relative to other material choices.

Landau-Zener-Stückelberg interference in coherent charge oscillations of a one-electron double quantum dot

Landau-Zener (LZ) transition has received renewed interest as an alternative approach to control single-qubit states. An LZ transition occurs when a system passes through an avoided crossing that arises from quantum mechanical coupling of two levels, taking the system to a coherent superposition of the two states. Then, multiple LZ transitions induce interference known as Landau-Zener-Stückelberg (LZS) interference whose amplitude strongly depends on the velocity or adiabaticity of the passage. Here, we study the roles of LZ transitions and LZS interference in coherent charge oscillations of a one-electron semiconductor double quantum dot by time-domain experiments using standard rectangular voltage pulses. By employing density matrix simulations, we show that, in the standard setup using rectangular pulses, even a small distortion of the pulse can give rise to LZ transitions and hence LZS interference, which significantly enhances the measured oscillation amplitude. We further show experimentally that the nature of the coherent charge oscillations changes from Rabi-type to LZS oscillations with increasing pulse distortion. Our results thus demonstrate that it is essential to take into account LZS interference for both precise control of charge qubits and correct interpretation of measurement results.

Temperature dependence of long coherence times of oxide charge qubits

The ability to maintain coherence and control in a qubit is a major requirement for quantum computation. We show theoretically that long coherence times can be achieved at easily accessible temperatures (such as boiling point of liquid helium) in small (i.e., ~10 nanometers) charge qubits of oxide double quantum dots when only optical phonons are the source of decoherence. In the regime of strong electron-phonon coupling and in the non-adiabatic region, we employ a duality transformation to make the problem tractable and analyze the dynamics through a non-Markovian quantum master equation. We find that the system decoheres after a long time, despite the fact that no energy is exchanged with the bath. Detuning the dots to a fraction of the optical phonon energy, increasing the electron-phonon coupling, reducing the adiabaticity, or decreasing the temperature enhances the coherence time.

Cavity QED with hybrid nanocircuits: from atomic-like physics to condensed matter phenomena

Circuit QED techniques have been instrumental in manipulating and probing with exquisite sensitivity the quantum state of superconducting quantum bits coupled to microwave cavities. Recently, it has become possible to fabricate new devices in which the superconducting quantum bits are replaced by hybrid mesoscopic circuits combining nanoconductors and metallic reservoirs. This mesoscopic QED provides a new experimental playground to study the light-matter interaction in electronic circuits. Here, we present the experimental state of the art of mesoscopic QED and its theoretical description. A first class of experiments focuses on the artificial atom limit, where some quasiparticles are trapped in nanocircuit bound states. In this limit, the circuit QED techniques can be used to manipulate and probe electronic degrees of freedom such as confined charges, spins, or Andreev pairs. A second class of experiments uses cavity photons to reveal the dynamics of electron tunneling between a nanoconductor and fermionic reservoirs. For instance, the Kondo effect, the charge relaxation caused by grounded metallic contacts, and the photo-emission caused by voltage-biased reservoirs have been studied. The tunnel coupling between nanoconductors and fermionic reservoirs also enable one to obtain split Cooper pairs, or Majorana bound states. Cavity photons represent a qualitatively new tool to study these exotic condensed matter states.

Quantum simulation of a Fermi-Hubbard model using a semiconductor quantum dot array

Interacting fermions on a lattice can develop strong quantum correlations, which are the cause of the classical intractability of many exotic phases of matter. Current efforts are directed towards the control of artificial quantum systems that can be made to emulate the underlying Fermi-Hubbard models. Electrostatically confined conduction-band electrons define interacting quantum coherent spin and charge degrees of freedom that allow all-electrical initialization of low-entropy states and readily adhere to the Fermi-Hubbard Hamiltonian. Until now, however, the substantial electrostatic disorder of the solid state has meant that only a few attempts at emulating Fermi-Hubbard physics on solid-state platforms have been made. Here we show that for gate-defined quantum dots this disorder can be suppressed in a controlled manner. Using a semi-automated and scalable set of experimental tools, we homogeneously and independently set up the electron filling and nearest-neighbour tunnel coupling in a semiconductor quantum dot array so as to simulate a Fermi-Hubbard system. With this set-up, we realize a detailed characterization of the collective Coulomb blockade transition, which is the finite-size analogue of the interaction-driven Mott metal-to-insulator transition. As automation and device fabrication of semiconductor quantum dots continue to improve, the ideas presented here will enable the investigation of the physics of ever more complex many-body states using quantum dots.

Coherent coupling between a quantum dot and a donor in silicon

Individual donors in silicon chips are used as quantum bits with extremely low error rates. However, physical realizations have been limited to one donor because their atomic size causes fabrication challenges. Quantum dot qubits, in contrast, are highly adjustable using electrical gate voltages. This adjustability could be leveraged to deterministically couple donors to quantum dots in arrays of qubits. In this work, we demonstrate the coherent interaction of a ³¹P donor electron with the electron of a metal-oxide-semiconductor quantum dot. We form a logical qubit encoded in the spin singlet and triplet states of the two-electron system. We show that the donor nuclear spin drives coherent rotations between the electronic qubit states through the contact hyperfine interaction. This provides every key element for compact two-electron spin qubits requiring only a single dot and no additional magnetic field gradients, as well as a means to interact with the nuclear spin qubit.

In silicon, quantum information can be stored in donors or quantum dots, each with its advantages and limitations—particularly in terms of fabrication. Here the authors coherently couple a phosphorous donor’s electron spin to a quantum dot, encoding information in the hybrid two-electron system’s state.

Three-electron spin qubits

The goal of this article is to review the progress of three-electron spin qubits from their inception to the state of the art. We direct the main focus towards the exchange-only qubit (Bacon et al 2000 Phys. Rev. Lett. 85 1758-61, DiVincenzo et al 2000 Nature 408 339) and its derived versions, e.g. the resonant exchange (RX) qubit, but we also discuss other qubit implementations using three electron spins. For each three-spin qubit we describe the qubit model, the envisioned physical realization, the implementations of single-qubit operations, as well as the read-out and initialization schemes. Two-qubit gates and decoherence properties are discussed for the RX qubit and the exchange-only qubit, thereby completing the list of requirements for quantum computation for a viable candidate qubit implementation. We start by describing the full system of three electrons in a triple quantum dot, then discuss the charge-stability diagram, restricting ourselves to the relevant subsystem, introduce the qubit states, and discuss important transitions to other charge states (Russ et al 2016 Phys. Rev. B 94 165411). Introducing the various qubit implementations, we begin with the exchange-only qubit (DiVincenzo et al 2000 Nature 408 339, Laird et al 2010 Phys. Rev. B 82 075403), followed by the RX qubit (Medford et al 2013 Phys. Rev. Lett. 111 050501, Taylor et al 2013 Phys. Rev. Lett. 111 050502), the spin-charge qubit (Kyriakidis and Burkard 2007 Phys. Rev. B 75 115324), and the hybrid qubit (Shi et al 2012 Phys. Rev. Lett. 108 140503, Koh et al 2012 Phys. Rev. Lett. 109 250503, Cao et al 2016 Phys. Rev. Lett. 116 086801, Thorgrimsson et al 2016 arXiv:1611.04945). The main focus will be on the exchange-only qubit and its modification, the RX qubit, whose single-qubit operations are realized by driving the qubit at its resonant frequency in the microwave range similar to electron spin resonance. Two different types of two-qubit operations are presented for the exchange-only qubits which can be divided into short-ranged and long-ranged interactions. Both of these interaction types are expected to be necessary in a large-scale quantum computer. The short-ranged interactions use the exchange coupling by placing qubits next to each other and applying exchange-pulses (DiVincenzo et al 2000 Nature 408 339, Fong and Wandzura 2011 Quantum Inf. Comput. 11 1003, Setiawan et al 2014 Phys. Rev. B 89 085314, Zeuch et al 2014 Phys. Rev. B 90 045306, Doherty and Wardrop 2013 Phys. Rev. Lett. 111 050503, Shim and Tahan 2016 Phys. Rev. B 93 121410), while the long-ranged interactions use the photons of a superconducting microwave cavity as a mediator in order to couple two qubits over long distances (Russ and Burkard 2015 Phys. Rev. B 92 205412, Srinivasa et al 2016 Phys. Rev. B 94 205421). The nature of the three-electron qubit states each having the same total spin and total spin in z-direction (same Zeeman energy) provides a natural protection against several sources of noise (DiVincenzo et al 2000 Nature 408 339, Taylor et al 2013 Phys. Rev. Lett. 111 050502, Kempe et al 2001 Phys. Rev. A 63 042307, Russ and Burkard 2015 Phys. Rev. B 91 235411). The price to pay for this advantage is an increase in gate complexity. We also take into account the decoherence of the qubit through the influence of magnetic noise (Ladd 2012 Phys. Rev. B 86 125408, Mehl and DiVincenzo 2013 Phys. Rev. B 87 195309, Hung et al 2014 Phys. Rev. B 90 045308), in particular dephasing due to the presence of nuclear spins, as well as dephasing due to charge noise (Medford et al 2013 Phys. Rev. Lett. 111 050501, Taylor et al 2013 Phys. Rev. Lett. 111 050502, Shim and Tahan 2016 Phys. Rev. B 93 121410, Russ and Burkard 2015 Phys. Rev. B 91 235411, Fei et al 2015 Phys. Rev. B 91 205434), fluctuations of the energy levels on each dot due to noisy gate voltages or the environment. Several techniques are discussed which partly decouple the qubit from magnetic noise (Setiawan et al 2014 Phys. Rev. B 89 085314, West and Fong 2012 New J. Phys. 14 083002, Rohling and Burkard 2016 Phys. Rev. B 93 205434) while for charge noise it is shown that it is favorable to operate the qubit on the so-called '(double) sweet spots' (Taylor et al 2013 Phys. Rev. Lett. 111 050502, Shim and Tahan 2016 Phys. Rev. B 93 121410, Russ and Burkard 2015 Phys. Rev. B 91 235411, Fei et al 2015 Phys. Rev. B 91 205434, Malinowski et al 2017 arXiv: 1704.01298), which are least susceptible to noise, thus providing a longer lifetime of the qubit.

Environmental noise spectroscopy with qubits subjected to dynamical decoupling

A qubit subjected to pure dephasing due to classical Gaussian noise can be turned into a spectrometer of this noise by utilizing its readout under properly chosen dynamical decoupling (DD) sequences to reconstruct the power spectral density of the noise. We review the theory behind this DD-based noise spectroscopy technique, paying special attention to issues that arise when the environmental noise is non-Gaussian and/or it has truly quantum properties. While we focus on the theoretical basis of the method, we connect the discussed concepts with specific experiments, and provide an overview of environmental noise models relevant for solid-state based qubits, including quantum-dot based spin qubits, superconducting qubits, and NV centers in diamond.

A decoherence-free subspace in a charge quadrupole qubit

Quantum computing promises significant speed-up for certain types of computational problems. However, robust implementations of semiconducting qubits must overcome the effects of charge noise that currently limit coherence during gate operations. Here we describe a scheme for protecting solid-state qubits from uniform electric field fluctuations by generalizing the concept of a decoherence-free subspace for spins, and we propose a specific physical implementation: a quadrupole charge qubit formed in a triple quantum dot. The unique design of the quadrupole qubit enables a particularly simple pulse sequence for suppressing the effects of noise during gate operations. Simulations yield gate fidelities 10-1,000 times better than traditional charge qubits, depending on the magnitude of the environmental noise. Our results suggest that any qubit scheme employing Coulomb interactions (for example, encoded spin qubits or two-qubit gates) could benefit from such a quadrupolar design.

Markovian quantum master equation beyond adiabatic regime

By introducing a temporal change time scale τ_{A}(t) for the time-dependent system Hamiltonian, a general formulation of the Markovian quantum master equation is given to go well beyond the adiabatic regime. In appropriate situations, the framework is well justified even if τ_{A}(t) is faster than the decay time scale of the bath correlation function. An application to the dissipative Landau-Zener model demonstrates this general result. The findings are applicable to a wide range of fields, providing a basis for quantum control beyond the adiabatic regime.

Signatures of Hyperfine, Spin-Orbit, and Decoherence Effects in a Pauli Spin Blockade

We detect in real time interdot tunneling events in a weakly coupled two-electron double quantum dot in GaAs. At finite magnetic fields, we observe two characteristic tunneling times T_{d} and T_{b}, belonging to, respectively, a direct and a blocked (spin-flip-assisted) tunneling. The latter corresponds to the lifting of a Pauli spin blockade, and the tunneling times ratio η=T_{b}/T_{d} characterizes the blockade efficiency. We find pronounced changes in the behavior of η upon increasing the magnetic field, with η increasing, saturating, and increasing again. We explain this behavior as due to the crossover of the dominant blockade-lifting mechanism from the hyperfine to spin-orbit interactions and due to a change in the contribution of the charge decoherence.

Tunable capacitive coupling between two semiconductor charge qubits

Strong coupling between two qubits is one of the main requirements for high fidelity two-qubit logic operations. Here we experimentally investigate the capacitive coupling between two double quantum dots. A pair of open slot confinement gates is used to enhance the coupling. We find that the coupling energy J can be conveniently tuned in a broad range. Through numerical simulations, we study the effect of J on two-qubit operations. The analysis shows that our experimentally obtained J is adequate to achieve high fidelity two-qubit entanglement and logic gates.

Quantum computing with acceptor spins in silicon

The states of a boron acceptor near a Si/SiO2 interface, which bind two low-energy Kramers pairs, have exceptional properties for encoding quantum information and, with the aid of strain, both heavy hole and light hole-based spin qubits can be designed. Whereas a light-hole spin qubit was introduced recently (arXiv:1508.04259), here we present analytical and numerical results proving that a heavy-hole spin qubit can be reliably initialised, rotated and entangled by electrical means alone. This is due to strong Rashba-like spin-orbit interaction terms enabled by the interface inversion asymmetry. Single qubit rotations rely on electric-dipole spin resonance (EDSR), which is strongly enhanced by interface-induced spin-orbit terms. Entanglement can be accomplished by Coulomb exchange, coupling to a resonator, or spin-orbit induced dipole-dipole interactions. By analysing the qubit sensitivity to charge noise, we demonstrate that interface-induced spin-orbit terms are responsible for sweet spots in the dephasing time [Formula: see text] as a function of the top gate electric field, which are close to maxima in the EDSR strength, where the EDSR gate has high fidelity. We show that both qubits can be described using the same starting Hamiltonian, and by comparing their properties we show that the complex interplay of bulk and interface-induced spin-orbit terms allows a high degree of electrical control and makes acceptors potential candidates for scalable quantum computation in Si.

Gatemon Benchmarking and Two-Qubit Operations

Recent experiments have demonstrated superconducting transmon qubits with semiconductor nanowire Josephson junctions. These hybrid gatemon qubits utilize field effect tunability characteristic of semiconductors to allow complete qubit control using gate voltages, potentially a technological advantage over conventional flux-controlled transmons. Here, we present experiments with a two-qubit gatemon circuit. We characterize qubit coherence and stability and use randomized benchmarking to demonstrate single-qubit gate errors below 0.7% for all gates, including voltage-controlled Z rotations. We show coherent capacitive coupling between two gatemons and coherent swap operations. Finally, we perform a two-qubit controlled-phase gate with an estimated fidelity of 91%, demonstrating the potential of gatemon qubits for building scalable quantum processors.

Tunable Hybrid Qubit in a GaAs Double Quantum Dot

We experimentally demonstrate a tunable hybrid qubit in a five-electron GaAs double quantum dot. The qubit is encoded in the (1,4) charge regime of the double dot and can be manipulated completely electrically. More importantly, dot anharmonicity leads to quasiparallel energy levels and a new anticrossing, which help preserve quantum coherence of the qubit and yield a useful working point. We have performed Larmor precession and Ramsey fringe experiments near the new working point and find that the qubit decoherence time is significantly improved over a charge qubit. This work shows a new way to encode a semiconductor qubit that is controllable and coherent.

Quantum gates by periodic driving

Topological quantum computation has been extensively studied in the past decades due to its robustness against decoherence. One way to realize the topological quantum computation is by adiabatic evolutions—it requires relatively long time to complete a gate, so the speed of quantum computation slows down. In this work, we present a method to realize single qubit quantum gates by periodic driving. Compared to adiabatic evolution, the single qubit gates can be realized at a fixed time much shorter than that by adiabatic evolution. The driving fields can be sinusoidal or square-well field. With the sinusoidal driving field, we derive an expression for the total operation time in the high-frequency limit, and an exact analytical expression for the evolution operator without any approximations is given for the square well driving. This study suggests that the period driving could provide us with a new direction in regulations of the operation time in topological quantum computation.

Experimental realization of non-adiabatic universal quantum gates using geometric Landau-Zener-Stückelberg interferometry

High fidelity universal gates for quantum bits form an essential ingredient of quantum information processing. In particular, geometric gates have attracted attention because they have a higher intrinsic resistance to certain errors. However, their realization remains a challenge because of the need for complicated quantum control on a multi-level structure as well as meeting the adiabatic condition within a short decoherence time. Here, we demonstrate non-adiabatic quantum operations for a two-level system by applying a well-controlled geometric Landau-Zener-Stückelberg interferometry. By characterizing the gate quality, we also investigate the operation in the presence of realistic dephasing. Furthermore, the result provides an essential model suitable for understanding an interplay of geometric phase and Landau-Zener-Stückelberg process which are well explored separately.

Lissajous Rocking Ratchet: Realization in a Semiconductor Quantum Dot

Breaking time-reversal symmetry (TRS) in the absence of a net bias can give rise to directed steady-state nonequilibrium transport phenomena such as ratchet effects. Here we present, theoretically and experimentally, the concept of a Lissajous rocking ratchet based on breaking TRS. Our system is a semiconductor quantum dot with periodically modulated dot-lead tunnel barriers. Broken TRS gives rise to single electron tunneling current. Its direction is fully controlled by exploring frequency and phase relations between the two barrier modulations. The concept of Lissajous ratchets can be realized in a large variety of different systems, including nanoelectrical, nanoelectromechanical, or superconducting circuits. It promises applications based on a detailed on-chip comparison of radio-frequency signals.

Conditional rotation of two strongly coupled semiconductor charge qubits

Universal multiple-qubit gates can be implemented by a set of universal single-qubit gates and any one kind of entangling two-qubit gate, such as a controlled-NOT gate. For semiconductor quantum dot qubits, two-qubit gate operations have so far only been demonstrated in individual electron spin-based quantum dot systems. Here we demonstrate the conditional rotation of two capacitively coupled charge qubits, each consisting of an electron confined in a GaAs/AlGaAs double quantum dot. Owing to the strong inter-qubit coupling strength, gate operations with a clock speed up to 6 GHz have been realized. A truth table measurement for controlled-NOT operation shows comparable fidelities to that of spin-based two-qubit gates, although phase coherence is not explicitly measured. Our results suggest that semiconductor charge qubits have a considerable potential for scalable quantum computing and may stimulate the use of long-range Coulomb interaction for coherent quantum control in other devices.

Viewing Majorana Bound States by Rabi Oscillations

We propose to use Rabi oscillation as a probe to view the fractional Josepshon relation (FJR) associated with Majorana bound states (MBSs) expected in one-dimensional topological superconductors. The system consists of a quantum dot (QD) and an rf-SQUID with MBSs at the Josephson junction. Rabi oscillations between energy levels formed by MBSs are induced by ac gate voltage controlling the coupling between QD and MBS when the photon energy proportional to the ac frequency matches gap between quantum levels formed by MBSs and QD. As a manifestation of the Rabi oscillation in the whole system involving MBSs, the electron occupation on QD oscillates with time, which can be measured by charge sensing techniques. With Floquet theorem and numerical analysis we reveal that from the resonant driving frequency for coherent Rabi oscillation one can directly map out the FJR cos(πΦ/Φ0) as a signature of MBSs, with Φ the magnetic flux through SQUID and Φ0 = hc/2e the flux quantum. The present scheme is expected to provide a clear evidence for MBSs under intensive searching.