Quantum error mitigation (QEM) schemes have greatly enhanced the performance of quantum computers, mostly by reducing errors caused by interactions with the environment. Nevertheless, the presence of coherence errors, typically arising from miscalibration and interqubit crosstalk, is a significant challenge to the scalability of quantum computing. Such errors are often addressed using a refined Pauli twirling scheme called randomized compiling (RC) that converts the coherent errors into incoherent errors that can then be mitigated by conventional QEM. Unfortunately for multiqubit gates, RC is restricted to Clifford gates such as cnot and cphase. However, it has been demonstrated experimentally that a direct implementation of multiqubit non-Clifford gates, i.e., without using multiqubit Clifford gates, has reduced the depth of the circuit by a factor of four and more. Recently, a framework called pseudotwirling (PST) for treating coherent error in multiqubit non-Clifford gates has been introduced and experimentally demonstrated. We show analytically that a higher-order correction to the existing PST theory yields an over-rotation coherent error generated by the PST protocol itself. This PST effect has no analog in RC. Although the small induced over-rotation can amount to a significant coherent error in deep circuits, we explain why it does not degrade the performance of the gate. Interestingly, we find that a simplified twirling scheme that was introduced and exploited experimentally by Kim et al. also displays an induced over-rotation. We study the conditions under which the two twirling schemes display the same over-rotation behavior.
Quantum error mitigation (QEM) schemes have greatly enhanced the performance of quantum computers, mostly by reducing errors caused by interactions with the environment. Nevertheless, the presence of coherence errors, typically arising from miscalibration and interqubit crosstalk, is a significant challenge to the scalability of quantum computing. Such errors are often addressed using a refined Pauli twirling scheme called randomized compiling (RC) that converts the coherent errors into incoherent errors that can then be mitigated by conventional QEM. Unfortunately for multiqubit gates, RC is restricted to Clifford gates such as cnot and cphase. However, it has been demonstrated experimentally that a direct implementation of multiqubit non-Clifford gates, i.e., without using multiqubit Clifford gates, has reduced the depth of the circuit by a factor of four and more. Recently, a framework called pseudotwirling (PST) for treating coherent error in multiqubit non-Clifford gates has been introduced and experimentally demonstrated. We show analytically that a higher-order correction to the existing PST theory yields an over-rotation coherent error generated by the PST protocol itself. This PST effect has no analog in RC. Although the small induced over-rotation can amount to a significant coherent error in deep circuits, we explain why it does not degrade the performance of the gate. Interestingly, we find that a simplified twirling scheme that was introduced and exploited experimentally by Kim et al. also displays an induced over-rotation. We study the conditions under which the two twirling schemes display the same over-rotation behavior.
The conventional circuit paradigm, utilizing a small set of gates to construct arbitrary quantum circuits, is hindered by significant noise. In the quantum Fourier transform, for instance, the standard gate paradigm employs two CNOT gates for the partial CPhase. In contrast, some quantum computers can directly implement such operations using their native interaction, resulting in less noisy gates. Unfortunately, coherent errors degrade the performance of these gates. In Clifford gates such as the CNOT, these errors can be addressed through randomized compiling (RC). However, RC does not apply to the non-Clifford multi-qubit native implementations described above. The present work introduces and experimentally demonstrates a technique called ‘Pseudo Twirling’ (PST) to address coherent errors. We demonstrate experimentally that integrating PST with the ‘Adaptive KIK’ quantum error mitigation method enables the simultaneous mitigation of noise and coherent errors in multi-qubit non-Clifford gates.
Abstract Quantum noise limits the reliability of noisy intermediate-scale quantum (NISQ) devices. Quantum error mitigation (QEM) provides a near-term path to improved accuracy, with randomized compiling (RC) serving as a key technique for transforming arbitrary gate noise into a stochastic Pauli form. However, its sampling complexity grows exponentially with circuit depth, hindering practical use. We introduce twirling scheduling (TS), which groups gate cycles into configurable units twirled collectively. By incorporating pseudo-twirling for non-Clifford gates, TS reduces the sampling-space dimension, mitigating this exponential scaling. Our theoretical analysis provides rigorous error bounds. Numerical simulations on Quantum Approximate Optimization Algorithm circuits up to 50 layers show that TS reduces estimation error by approximately 62% compared to conventional RC under a very small sampling budget and maintains superior performance when combined with established QEM protocols, including zero-noise extrapolation, Clifford data regression, and virtual distillation. TS thus offers a scalable, practical advance for error-mitigated quantum computation on NISQ hardware.
We develop and apply an extension of the randomized compiling (RC) protocol that includes a special treatment of neighboring qubits and dramatically reduces crosstalk effects caused by the application of faulty gates on superconducting qubits in IBMQ quantum computers ( and ). Crosstalk errors, stemming from controlled- () two-qubit gates, are a crucial source of errors on numerous quantum computing platforms. For the IBMQ machines, their effect on the performance of a given quantum computation is often overlooked. Our RC protocol turns coherent noise due to crosstalk into a depolarizing noise channel that can then be treated using established error mitigation schemes, such as noise estimation circuits. We apply our approach to the quantum simulation of the nonequilibrium dynamics of the Bardeen-Cooper-Schrieffer (BCS) Hamiltonian for superconductivity, a particularly challenging model to simulate on quantum hardware because of the long-range interaction of Cooper pairs. With 135 gates, we work in a regime where crosstalk, as opposed to either Trotterization or qubit decoherence, dominates the error. Our twirling of neighboring qubits is shown to dramatically improve the noise estimation protocol without the need to add new qubits or circuits and allows for a quantitative simulation of the BCS model. Published by the American Physical Society 2024
Quantum circuit ensembles that have the properties of unitary k-designs represent applications where there is no obvious bias toward any particular Pauli support, as is the case in simulating systems exhibiting ''quantum chaos,'' which range from quantum dynamics near black holes to gapless spin fluid analysis. However, noisy hardware makes quantum circuits prone to a myriad of error sources, of which depolarizing and coherent error can be particularly destructive. To combat depolarizing error, popular techniques typically involve circuit or gate folding, which can be time-intensive procedures due to increased circuit depth and shot overhead. Other tensor-network-based mitigation techniques suffer from intractability in high-entanglement regimes. In this work, we leverage the structure of unitary k-design Pauli support distributions by introducing a technique we name ''circuit balancing,'' along with gate benchmarking data, in order to estimate circuit-wide depolarization. We describe how to invert the diagnosed circuit depolarization even in the presence of coherent error, via Pauli twirling. We provide asymptotics to estimate the number of twirls needed to maintain a desired output fidelity. We test our method numerically in a variety of simulation settings and find that it can significantly reduce average random circuit infidelity. Further, we employ our methods to find significant infidelity reductions when running a random circuit ensemble on a contemporary superconducting quantum computer, IBM Fez. Overall, we show that the method effectively reduces gate-based error for unitary k-designs without incurring any two-qubit gate overhead.
Group twirling is crucial in quantum information processing, particularly in randomized benchmarking and randomized compiling. While protocols based on Pauli twirling have been effectively crafted to transform arbitrary noise channels into Pauli channels for Clifford gates—thereby facilitating efficient benchmarking and mitigating worst-case errors—the lack of practical twirling groups for multiqubit non-Clifford gates remains a challenge. To address this gap, we study the issue of finding twirling groups for generic quantum gates, focusing on a widely used circuit structure in randomized benchmarking or randomized compiling. Specifically, for multiqubit controlled phase gates, which are essential in quantum algorithms and directly implementable in practice, we determine optimal twirling groups within the realm of classically replaceable unitary operations. Contrasting with the local Pauli twirling group for Clifford gates, the optimal groups for such gates contain nonlocal operations, highlighting the overhead of tailoring noise in global non-Clifford contexts. We design new benchmarking procedures for multiqubit controlled phase gates based on the optimal twirling groups. Our simulation results show that our scheme can improve the precision and accuracy of benchmarking in small-scale systems. Published by the American Physical Society 2024
Current hardware for quantum computing suffers from high levels of noise, and so to achieve practical fault-tolerant quantum computing will require powerful and efficient methods to correct for errors in quantum circuits. Here, we explore the role and effectiveness of using noise tailoring techniques to improve the performance of error correcting codes. Noise tailoring methods such as randomized compiling (RC) convert complex coherent noise processes to effective stochastic noise. While it is known that this can be leveraged to design efficient diagnostic tools, we explore its impact on the performance of error correcting codes. Of particular interest is the important class of coherent errors, arising from control errors, where RC has the maximum effect---converting these into purely stochastic errors. For these errors, we show here that RC delivers an improvement in performance of the concatenated Steane code by several orders of magnitude. We also show that below a threshold rotation angle, the gains in logical fidelity can be arbitrarily magnified by increasing the size of the codes. These results suggest that using randomized compiling can lead to a significant reduction in the resource overhead required to achieve fault tolerance.