[Paper Review] Randomized compiling for scalable quantum computing on a noisy superconducting quantum processor

Akel Hashim, Ravi Naik+12 more|arXiv (Cornell University)|Oct 1, 2020

Quantum Computing Algorithms and ArchitectureComputer Science46 references133 citations

TL;DR

This paper demonstrates that randomized compiling (RC) effectively suppresses coherent errors in superconducting quantum processors by converting them into stochastic Pauli noise, enabling reliable prediction of quantum algorithm performance via cycle benchmarking. Experimental results show significant performance gains—up to a 5× improvement in fidelity—for the four-qubit quantum Fourier transform and random circuits, with error rates measured via cycle benchmarking accurately predicting algorithmic outcomes under RC.

ABSTRACT

The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic miscalibrations, drift, and crosstalk in the control of qubits can lead to a coherent form of error which has no classical analog. Coherent errors severely limit the performance of quantum algorithms in an unpredictable manner, and mitigating their impact is necessary for realizing reliable quantum computations. Moreover, the average error rates measured by randomized benchmarking and related protocols are not sensitive to the full impact of coherent errors, and therefore do not reliably predict the global performance of quantum algorithms, leaving us unprepared to validate the accuracy of future large-scale quantum computations. Randomized compiling is a protocol designed to overcome these performance limitations by converting coherent errors into stochastic noise, dramatically reducing unpredictable errors in quantum algorithms and enabling accurate predictions of algorithmic performance from error rates measured via cycle benchmarking. In this work, we demonstrate significant performance gains under randomized compiling for the four-qubit quantum Fourier transform algorithm and for random circuits of variable depth on a superconducting quantum processor. Additionally, we accurately predict algorithm performance using experimentally-measured error rates. Our results demonstrate that randomized compiling can be utilized to leverage and predict the capabilities of modern-day noisy quantum processors, paving the way forward for scalable quantum computing.

Motivation & Objective

• To address the challenge of unpredictable performance degradation in NISQ-era quantum processors caused by coherent errors from control miscalibrations and crosstalk.
• To develop a scalable, hardware-agnostic method that converts coherent errors into stochastic noise without prior knowledge of the error model.
• To validate that cycle benchmarking error rates can reliably predict algorithmic performance after RC, overcoming limitations of traditional randomized benchmarking.

Proposed method

• RC inserts random single-qubit twirling gates (from Pauli group) into a circuit to create logically equivalent randomized circuits, preserving the overall unitary operation without increasing depth.
• Each randomized circuit is measured n/N times, and results are combined to form a statistical distribution equivalent to measuring the original circuit n times.
• The protocol leverages Pauli twirling to average coherent errors into stochastic Pauli channels, suppressing off-diagonal terms in the error process.
• The method is compatible with universal quantum computation as it works for any universal gate set, including the Clifford+T basis.
• RC is implemented in situ on a superconducting processor, with classical pre-processing generating N randomizations efficiently before runtime.
• Performance is evaluated using total variation distance (TVD) between experimental and ideal output distributions, with cycle benchmarking used to extract error rates for prediction.

Experimental results

Research questions

• RQ1 Can randomized compiling effectively suppress coherent errors in a real superconducting quantum processor, leading to more predictable and improved algorithmic performance?
• RQ2 To what extent can error rates measured via cycle benchmarking predict the actual performance of quantum algorithms after applying randomized compiling?
• RQ3 How does the performance gain from RC scale with the fraction of coherent errors in the total error budget?
• RQ4 Does RC maintain its effectiveness as overall error rates decrease, particularly in near-coherence-limited systems?
• RQ5 Can RC be applied efficiently in practice without increasing circuit depth or requiring detailed knowledge of the underlying error model?

Key findings

• Randomized compiling reduced the total variation distance (TVD) between experimental and ideal output distributions by up to a factor of 5 for the four-qubit quantum Fourier transform circuit.
• For single-qubit random circuits, RC achieved an average TVD improvement factor of 2.5–3.5 across all tested depths, with performance gains increasing when coherent errors contributed more to the total error rate.
• The study demonstrated that cycle benchmarking error rates accurately predicted algorithmic performance under RC, validating its use as a predictive tool.
• In multi-qubit parallel circuits, crosstalk increased coherent error contributions, yet RC still provided consistent TVD reduction, showing robustness to crosstalk.
• Simulations showed that RC performance improves as total error rates decrease, indicating that even in low-error regimes, RC provides meaningful fidelity gains.
• The results confirm that randomized compiling provides measurable performance improvements across all tested systems where coherent errors persist, regardless of the absolute error level.