Noise tailoring for scalable quantum computation via randomized compiling (1512.01098v3)

Abstract: Quantum computers are poised to radically outperform their classical counterparts by manipulating coherent quantum systems. A realistic quantum computer will experience errors due to the environment and imperfect control. When these errors are even partially coherent, they present a major obstacle to achieving robust computation. Here, we propose a method for introducing independent random single-qubit gates into the logical circuit in such a way that the effective logical circuit remains unchanged. We prove that this randomization tailors the noise into stochastic Pauli errors, leading to dramatic reductions in worst-case and cumulative error rates, while introducing little or no experimental overhead. Moreover we prove that our technique is robust to variation in the errors over the gate sets and numerically illustrate the dramatic reductions in worst-case error that are achievable. Given such tailored noise, gates with significantly lower fidelity are sufficient to achieve fault-tolerant quantum computation, and, importantly, the worst case error rate of the tailored noise can be directly and efficiently measured through randomized benchmarking experiments. Remarkably, our method enables the realization of fault-tolerant quantum computation under the error rates observed in recent experiments.

• The paper introduces a technique that transforms coherent errors into stochastic Pauli errors using randomized compiling, significantly lowering error magnitude in quantum systems.
• It employs the insertion of random single-qubit gates to convert noise into measurable stochastic processes, facilitating rigorous error benchmarking.
• Findings reveal that this approach reduces worst-case error rates, making scalable and fault-tolerant quantum computing achievable with current gate fidelities.

Insights into Noise Tailoring for Quantum Computation via Randomized Compiling

The paper by WaLLMan and Emerson presents a compelling methodology for managing errors in quantum computing: noise tailoring through randomized compiling. The foundational premise of this work is the inherent challenge facing quantum computers arising from errors induced by environmental interactions and control imperfections. These errors could be partially coherent, which poses significant obstacles in achieving robust quantum computations.

Through the proposed method, the authors introduce independent random single-qubit gates into logical quantum circuits such that the effective logical circuit remains unchanged. Remarkably, this randomization transforms the noise into stochastic Pauli errors, thereby reducing error rates while maintaining low experimental overhead. The paper presents a thorough theoretical framework to establish that stochastic noise can considerably lower the bar for fault-tolerant quantum computation, making it possible even with lower fidelity gates—fidelities comparable to those currently achieved experimentally.

The numerical simulations presented in the paper significantly highlight how the noise-tailing technique can lead to a drastic reduction in worst-case error rates. This reduction is made possible because the worst-case error in stochastic noise is directly measurable and verifiable through randomized benchmarking protocols. This capability not only facilitates rigorous performance certification of quantum computers but also aligns with the requirements for fault-tolerance.

Beyond the practical applications of the technique, the theoretical implications of the research are noteworthy. The work explores a rigorous comparison between coherent and stochastic errors, offering insights into error accumulation in extended quantum computations. Randomized compiling, as elucidated, demonstrates robustness against variable errors across randomizing gates, emphasizing its adaptability across different quantum architectures and gate implementations.

Furthermore, the technique is robust under robust gate-dependent errors, which often result from natural gate calibration imperfections. The implications for quantum computing are profound: the same coherent errors and spatial correlations do not detract from the overall computation fidelity, given the assumptions and conditions outlined. Especially important is the fact that tailored noise is achievable with only limited classical overhead in terms of compilation cost, or alternatively, in real-time using swift classical control.

Future developments may see the proposed methodology applied extensively in experimental settings, capitalizing on its ability to enable efficient error management in large-scale quantum systems. Moreover, refining the technique to address non-Markovian noise presents a promising avenue of exploration, which may eventually lead to more comprehensive error correction strategies.

In summary, the insights offered by WaLLMan and Emerson's work delineate a clear path forward for advancing scalable quantum computing by effectively managing erroneous influences inherent in present-day quantum computing systems. Through seamless integration of random compiling techniques, the paper reinforces that adaptable and experimentally feasible error correction is not just ideal but imminently practical, setting the stage for the future of quantum computation.