Based on numerically-optimized real-device gates and parameters we study the performance of the phase-flip (repetition) code on a linear array of Gallium Arsenide (GaAs) quantum dots hosting singlet-triplet qubits. We first examine the expected performance of the code using simple error models of circuit-level and phenomenological noise, reporting, for example, a circuit-level depolarizing noise threshold of approximately 3%. We then perform density-matrix simulations using a maximum-likelihood and minimum-weight matching decoder to study the effect of real-device dephasing, read-out error, quasi-static as well as fast gate noise. Considering the trade-off between qubit read-out error and dephasing time (T2) over measurement time, we identify a sub-threshold region for the phase-flip code which lies within experimental reach.
Single-qubit operations on singlet-triplet qubits in GaAs double quantum dots have not yet reached the fidelities required for fault-tolerant quantum information processing. Considering experimentally important constraints and using measured noise spectra, we numerically minimize the effect of decoherence (including high-frequency 1/f-like noise) and show theoretically that quantum gates with fidelities higher than 99.9% are achievable. We also present a self-consistent tuning protocol which should allow the elimination of individual systematic gate errors directly in an experiment.
We report a single-shot-based projective readout of a semiconductor hybrid qubit formed by three electrons in a GaAs double quantum dot. Voltage-controlled adiabatic transitions between the qubit operations and readout conditions allow high-fidelity mapping of quantum states. We show that a large ratio both in relaxation time vs. tunneling time (~ 50) and singlet-triplet splitting vs. thermal energy (~ 20) allow energy-selective tunneling-based spin-to-charge conversion with readout visibility ~ 92.6%. Combined with ac driving, we demonstrate high visibility coherent Rabi and Ramsey oscillatio…
The current work investigates the performance of dual-gate GaAs-nanowire FET as a charge-qubit device operating at room temperature. In compatibility with the state-of-the-art classical bit technology, it is shown that the single gate of a nanowire FET can be replaced by two localized gates to achieve such charge-qubit operation. On application of relevant biases to the localized gates, two voltage tunable quantum dots are created within the nanowire channel with electrostatically controlled single-state-occupancy and inter-dot coupling leading to charge-qubit operation at room temperature. Th…
We demonstrate negative polarization created by light-hole exciton excitation in g-factor engineered GaAs quantum wells measured by time-resolved Kerr rotation and polarization-resolved photoluminescence. This negative polarization is a result of polarization transfer from a photon to an electron spin mediated by a light hole. This demonstration is an important step towards achieving quantum media conversion from a photonic qubit to an electron spin qubit required for building a quantum repeater.
Semiconductor spin qubits have recently seen major advances in coherence time and control fidelities, leading to a single-qubit performance that is on par with other leading qubit platforms. Most of this progress is based on microwave control of single spins in devices made of isotopically purified silicon. For controlling spins, the exchange interaction is an additional key ingredient which poses new challenges for high-fidelity control. Here, we demonstrate exchange-based single-qubit gates of two-electron spin qubits in GaAs double quantum dots. Using careful pulse optimization and closed-l…
Inspired by the scenario by Bennett et al., a teleportation protocol of qubits formed in a two-dimensional electron gas formed at the interface of a GaAs heterostructure is presented. The teleportation is carried out using three GaAs quantum dots (say $\mathcal{P}\mathcal{P}'$, $\mathcal{Q}\mathcal{Q}'$, $\mathcal{R}\mathcal{R}'$) and three electrons. The electron spin on GaAs quantum dots $\mathcal{P}\mathcal{P}'$ is used to encode the unknown qubit. The GaAs quantum dot $\mathcal{Q}\mathcal{Q}'$ and $\mathcal{R}\mathcal{R}'$ combine to form {an} entangled state. Alice (the sender) performs a…
We present a realization of two-qubit controlled-phase gate, based on the linear and nonlinear properties of the probe and signal optical pulses in an asymmetric GaAs/AlGaAs double quantum wells. It is shown that, in the presence of cross-phase modulation, a giant cross-Kerr nonlinearity and mutually matched group velocities of the probe and signal optical pulses can be achieved while realizing the suppression of linear and self-Kerr optical absorption synchronously. These characteristics serve to exhibit an all-optical two-qubit controlled-phase gate within efficiently controllable photon-pho…
There has been significant progress in the implementation and manipulation of singlet-triplet qubits in GaAs quantum dots. Given the considerably longer spin coherence times measured in Si, considerable interest has been generated recently in Si quantum dots. The physics of these systems is considerably more complex than the physics of GaAs quantum dots owing to the presence of the valley degree of freedom, which constitutes the focus of this work. In this paper we investigate the physics of Si quantum dots and focus on the feasibility of quantum coherent singlet-triplet qubit experiments anal…
Decoherence of a quantum system arising from its interaction with an environment is a key concept for understanding the transition between the quantum and classical world as well as performance limitations in quantum technology applications. The effects of large, weakly coupled environments are often described as a classical, fluctuating field whose dynamics is unaffected by the qubit, whereas a fully quantum description still implies some back-action from the qubit on the environment. Here we show direct experimental evidence for such a back-action for an electron-spin-qubit in a GaAs quantum…
Gate-defined quantum dots in gallium arsenide (GaAs) have been used extensively for pioneering spin qubit devices due to the relative simplicity of fabrication and favourable electronic properties such as a single conduction band valley, a small effective mass, and stable dopants. GaAs spin qubits are readily produced in many labs and are currently studied for various applications, including entanglement, quantum non-demolition measurements, automatic tuning, multi-dot arrays, coherent exchange coupling, and teleportation. Even while much attention is shifting to other materials, GaAs devices …
Understanding the decoherence of electron spins in semiconductors due to their interaction with nuclear spins is of fundamental interest as they realize the central spin model and of practical importance for using electron spins as qubits. Interesting effects arise from the quadrupolar interaction of nuclear spins with electric field gradients, which have been shown to suppress diffusive nuclear spin dynamics. One might thus expect them to enhance electron spin coherence. Here we show experimentally that for gate-defined GaAs quantum dots, quadrupolar broadening of the nuclear Larmor precessio…
Quantum information processing offers dramatic speedups, yet is famously susceptible to decoherence, the process whereby quantum superpositions decay into mutually exclusive classical alternatives, thus robbing quantum computers of their power. This has made the development of quantum error correction an essential and inescapable aspect of both theoretical and experimental quantum computing. So far little is known about protection against decoherence in the context of quantum annealing, a computational paradigm which aims to exploit ground state quantum dynamics to solve optimization problems …
The corrected capacity of a quantum channel is defined as the best one-shot capacity that can be obtained by measuring the environment and using the result to correct the output of the channel. It is shown that (i) all qubit channels have corrected capacity log 2, (ii) a product of N qubit channels has corrected capacity N log 2, and (iii) all channels have corrected capacity at least log 2. The question is posed of finding the channel with smallest corrected capacity in any dimension d.
Precise control of an open quantum system is critical to quantum information processing, but is challenging due to inevitable interactions between the quantum system and the environment. We demonstrated experimentally at room temperature a type of dynamically corrected gates on the nitrogen-vacancy centers in diamond. The infidelity of quantum gates caused by environment nuclear spin bath is reduced from being the second-order to the sixth-order of the noise to control field ratio, which offers greater efficiency in reducing the infidelity by reducing the noise level. The decay time of the coh…
We address the problem of constructing dynamically corrected gates for non-Markovian open quantum systems in settings where limitations on the available control inputs and/or the presence of control noise make existing analytical approaches unfeasible. By focusing on the important case of singlet-triplet electron spin qubits, we show how ideas from optimal control theory may be used to automate the synthesis of dynamically corrected gates that simultaneously minimize the system's sensitivity against both decoherence and control errors. Explicit sequences for effecting robust single-qubit rotat…
We provide analytical composite pulse sequences that perform dynamical decoupling concurrently with arbitrary rotations for a qubit coded in the spin state of a triple quantum dot. The sequences are designed to respect realistic experimental constraints such as strictly nonnegative couplings. Logical errors and leakage errors are simultaneously corrected. A short pulse sequence is presented to compensate nuclear noise and a longer sequence is presented to simultaneously compensate nuclear and charge noise. The capability developed in this work provides a clear prescription for combatting the r…
We study theoretically the responses of the dynamically corrected gates to time-dependent noises in the exchange-only spin qubit system. We consider $1/f$ noises having spectra proportional to $1/ω^α$, where the exponent $α$ indicates the strength of correlation within the noise. The quantum gate errors due to noises are extracted from a numerical simulation of Randomized Benchmarking, and are compared between the application of uncorrected operations and that of dynamically corrected gates robust against the hyperfine noise. We have found that for $α\gtrsim1.5$, the dynamically corrected gate…
We consider charge qubits based on shallow donor electron states in silicon and coupled quantum dots in GaAs. Specifically, we study the feasibility of P$_2^+$ charge qubits in Si, focusing on single qubit properties in terms of tunnel coupling between the two phosphorus donors and qubit decoherence caused by electron-phonon interaction. By taking into consideration the multi-valley structure of the Si conduction band, we show that inter-valley quantum interference has important consequences for single-qubit operations of P$_2^+$ charge qubits. In particular, the valley interference leads to a…
We theoretically demonstrate that nuclear spins can be harnessed to coherently control two-electron spin states in a double quantum dot. Hyperfine interactions lead to an avoided crossing between the spin singlet state and the ms = +1 triplet state, T_+ . We show that a coherent superposition of singlet and triplet states can be achieved using finite-time Landau-Zener-Stückelberg interferometry. In this system the coherent rotation rate is set by the Zeeman energy, resulting in ~1 nanosecond single spin rotations. We analyze the coherence of this spin qubit by considering the coupling to the n…
Physical systems representing qubits typically have one or more accessible quantum states in addition to the two states that encode the qubit. We demonstrate that active involvement of such auxiliary states can be beneficial in constructing entangling two-qubit operations. We investigate the general case of two multi-state quantum systems coupled via a quantum resonator. The approach is illustrated with the examples of three systems: self-assembled InAs/GaAs quantum dots, NV-centers in diamond, and superconducting transmon qubits. Fidelities of the gate operations are calculated based on numer…
To solve classically hard problems, quantum computers need to be resilient to the influence of noise and decoherence. In such a fault-tolerant quantum computer, noise-induced errors must be detected and corrected in real-time to prevent them from propagating between components. This requirement is especially pertinent while applying quantum gates, when the interaction between components can cause errors to quickly spread throughout the system. However, the large overhead involved in most fault-tolerant architectures makes implementing these systems a daunting task, which motivates the search f…
The ability to perform gates in multiqubit systems that are robust to noise is of crucial importance for the advancement of quantum information technologies. However, finding control pulses that cancel noise while performing a gate is made difficult by the intractability of the time-dependent Schrodinger equation, especially in multiqubit systems. Here, we show that this issue can be sidestepped by using a formalism in which the cumulative error during a gate is represented geometrically as a curve in a multi-dimensional Euclidean space. Cancellation of noise errors to leading order correspond…
We describe how a universal set of dynamically-corrected quantum gates can be implemented using sequences of shaped decoupling pulses on any qubit network forming a sparse bipartite graph with always-on Ising interactions. These interactions are constantly decoupled except when they are needed for two-qubit gates. We analytically study the error operators associated with the constructed gates up to third order in the Magnus expansion, analyze these errors numerically in the unitary time evolution of small qubit clusters, and give a bound on high-order errors for qubits on a large square lattic…
Error correction, in the standard meaning of the term, implies the ability to correct all small analog errors and some large errors. Examining assumptions at the basis of the recently proposed quantum error-correcting codes, it is pointed out that these codes can correct only a subset of errors, and are unable to correct small phase errors which can have disastrous consequences for a quantum computation. This shortcoming will restrict their usefulness in real applications.
We construct a universal set of high fidelity quantum gates to be used on a sparse bipartite lattice with always-on Ising couplings. The gates are based on dynamical decoupling sequences using shaped pulses, they protect against low-frequency phase noise, and can be run in parallel on non-neighboring qubits. This makes them suitable for implementing quantum error correction with low-density parity check codes like the surface codes and their finite-rate generalizations. We illustrate the construction by simulating quantum Zeno effect with the $[[4,2,2]]$ toric code on a spin chain.
The spin states of electrons and holes confined in InAs quantum dot molecules have recently come to fore as a promising system for the storage or manipulation of quantum information. We describe here a feasible scheme for complete quantum optical control of two electron spin qubits in two vertically-stacked singly-charged InAs quantum dots coupled by coherent electron tunneling. With an applied magnetic field transverse to the growth direction, we construct a universal set of gates that corresponds to the possible Raman transitions between the spin states. We detail the procedure to decompose …
Error-Corrected Memory and Logic on a Heavy-Hex Superconducting-Qubit Processor
The University of Sydney（悉尼大学）；Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Sungkyunkwan University（成均馆大学）；IBM Quantum, T. J. Watson Research Center（IBM量子T.J.沃森研究中心）；IBM Denmark（IBM丹麦）
Most of the research done on quantum error correction studies an error model in which each qubit is affected by noise, independently of the other qubits. In this paper we study a different noise model -- one in which the noise may be correlated with the qubits it acts upon. We show both positive and negative results. On the one hand, we show controlled-X errors cannot be perfectly corrected, yet can be approximately corrected with sub-constant approximation error. On the other hand, we show that no non-trivial quantum error correcting code can approximately correct controlled phase error with …
One of the most promising routes towards scalable quantum computing is a modular approach. We show that distinct surface code patches can be connected in a fault-tolerant manner even in the presence of substantial noise along their connecting interface. We quantify analytically and numerically the combined effect of errors across the interface and bulk. We show that the system can tolerate 14 times higher noise at the interface compared to the bulk, with only a small effect on the code's threshold and sub-threshold behavior, reaching threshold with $\sim 1 \%$ bulk errors and $\sim 10 \%$ inte…
In addition to magnetic field and electric charge noise adversely affecting spin qubit operations, performing single-qubit gates on one of multiple coupled singlet-triplet qubits presents a new challenge---crosstalk, which is inevitable (and must be minimized) in any multiqubit quantum computing architecture. We develop a set of dynamically-corrected pulse sequences that are designed to cancel the effects of both types of noise (i.e., field and charge) as well as crosstalk to leading order, and provide parameters for these corrected sequences for all 24 of the single-qubit Clifford gates. We t…
We present composite pulse sequences that perform fault-tolerant two-qubit gate operations on exchange-only quantum dot spin qubits in various experimentally relevant geometries. We show how to perform dynamically corrected two-qubit gates in exchange-only systems with the leading hyperfine error term cancelled. These pulse sequences are constructed to conform to the realistic experimental constraint of strictly non-negative couplings. We establish that our proposed pulse sequences lead to several orders of magnitude improvement in the gate fidelity compared with their uncorrected counterparts…
Implementing high-fidelity quantum control and reducing the effect of the coupling between a quantum system and its environment is a major challenge in developing quantum information technologies. Here, we show that there exists a geometrical structure hidden within the time-dependent Schrödinger equation that provides a simple way to view the entire solution space of pulses that suppress noise errors in a system's evolution. In this framework, any single-qubit gate that is robust against quasistatic noise to first order corresponds to a closed three-dimensional space curve, where the driving …
We investigate decoherence due to pure dephasing of a localized spin qubit interacting with a nuclear spin bath. Although in the limit of a very large magnetic field the only decoherence mechanism is spectral diffusion due to dipolar flip-flops of nuclear spins, with decreasing field the hyperfine-mediated interactions between the nuclear spins become important. We take advantage of their long-range nature, and resum the leading terms in an 1/N expansion of the decoherence time-evolution function (N, being the number of nuclear spins interacting appreciably with the electron spin, is large). F…
We develop a theoretical model to describe the dissipative dynamics of singlet-triplet qubits in GaAs quantum dots. Using the concurrence experimentally obtained [M. D. Shulman et al., Science 336, 202 (2012)] as a guide, we found that each logical qubit fluctuates under the action of a random telegraph noise (RTN) that simulates the $1/f^α$ noise. We also study the dynamics of concurrence as a function of the amplitude of the RTN, the correlation time of the RTN, the preparation time of states, and the two-qubit coupling. Furthermore, we show that the two-qubit coupling together with the prep…
We develop a systematic method of performing corrected gate operations on an array of exchange-coupled singlet-triplet qubits in the presence of both fluctuating nuclear Overhauser field gradients and charge noise. The single-qubit control sequences we present have a simple form, are relatively short, and form the building blocks of a corrected CNOT gate when also implemented on the inter-qubit exchange link. This is a key step towards enabling large-scale quantum computation in a semiconductor-based architecture by facilitating error reduction below the quantum error correction threshold for …
The unavoidable effect of the environmental noise due to nuclear spins and charge traps is included in the study of the hybrid qubit dynamics. Hybrid qubit dues its name to the advantageous combination of manipulation speed of a charge qubit with the longevity of a spin qubit. It consists of three electrons confined through external gate voltages in a double quantum dot and deserves special interest in quantum computation applications due to its advantages in terms of fabrication, control and only electrical manipulation. Hybrid qubit is protected against global magnetic fluctuations since it …
A quantum system interacts with its environment, if ever so slightly, no matter how much care is put into isolating it. As a consequence, quantum bits (qubits) undergo errors, putting dauntingly difficult constraints on the hardware suitable for quantum computation. New strategies are emerging to circumvent this problem by encoding a qubit non-locally across the phase space of a physical system. Since most sources of decoherence are due to local fluctuations, the foundational promise is to exponentially suppress errors by increasing a measure of this non-locality. Prominent examples are topolo…
We theoretically consider a cross-resonance (CR) gate implemented by pulse sequences proposed by Calderon-Vargas & Kestner, Phys. Rev. Lett. 118, 150502 (2017). These sequences mitigate systematic error to first order, but their effectiveness is limited by one-qubit gate imperfections. Using additional microwave control pulses, it is possible to tune the effective CR Hamiltonian into a regime where these sequences operate optimally. This improves the overall feasibility of these sequences by reducing the one-qubit operations required for error correction. We illustrate this by simulating rando…
Fault-tolerant, error-corrected quantum computation is commonly acknowledged to be crucial to the realisation of large-scale quantum algorithms that could lead to extremely impactful scientific or commercial results. Achieving a universal set of quantum gate operations in a fault-tolerant error-corrected framework suffers from a `conservation of unpleasantness'. In general, no matter what error correction technique is employed, there is always one element of a universal gate set that carries a significant resource overhead - either in physical qubits, computational time, or both. Specifically,…
Open quantum system dynamics of random unitary type may in principle be fully undone. Closely following the scheme of environment-assisted error correction proposed by Gregoratti and Werner [M. Gregoratti and R. F. Werner, J. Mod. Opt. 50(6), 915-933 (2003)], we explicitly carry out all steps needed to invert a phase-damping error on a single qubit. Furthermore, we extend the scheme to a mixed-state environment. Surprisingly, we find cases for which the uncorrected state is closer to the desired state than any of the corrected ones.
Assisted with linear optical manipulation, single photon, entangled photon pairs, photon measurement, and classical communication, a scheme for two-spin qubits phase gate and teleportation of a CNOT gate between two electron spins from acting on local qubits to acting on remote qubits using quantum dots in optical microcavities is proposed. The scheme is based on spin selective photon reflection from the cavity and is achieved in a deterministic way by the sequential detection of photons and the single-qubit rotations of a single electron spin in a self-assembled GaAs/InAs quantum dot. The fea…
