Noise tailoring for scalable quantum computation via randomized compiling

By Joel J. Wallman, Joseph Emerson. 2015

620 citations recorded by the source corpus.

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 performing robust computations. 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, which can dramatically reduce error rates while introducing little or no experimental overhead. Moreover, we prove that our technique is robust to the inevitable variation in errors over the randomizing gates and numerically illustrate the dramatic reductions in worst-case error that are achievable. Given such tailored noise, gates with significantly lower fidelity---comparable to fidelities realized in current experiments---are sufficient to achieve fault-tolerant quantum computation. Furthermore, the worst-case error rate of the tailored noise can be directly and efficiently measured through randomized benchmarking protocols, enabling a rigorous certification of the performance of a quantum computer.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/375279c93ed2e4656614e81b1517cb1b4f27c5d3

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

The randomized measurement toolbox (2022, methodology): “This idea was further developed into a scheme called randomized compiling [97], which improves over naive schemes by reducing circuit depth slightly and comes with a perturbative error analysis.”
Quantum error mitigation (2022, background): “Most of these random Pauli gates can in fact be absorbed into the existing Pauli gates (Wallman and Emerson, 2016) and thus it can often be implemented with a relatively small gate cost.”
QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits (2021, background): “For example, various gate errors can be suppressed by dynamical decoupling [8], [23], [36], [60], composite pulses [10], [41], [46], randomized compiling [61], hidden inverses [66], qubit mapping [34], [48], [58], instruction scheduling [49], [64], and frequency tuning [16], [26], [59].”
Digital zero noise extrapolation for quantum error mitigation (2020, methodology): “There are many examples of error-mitigating techniques, including probabilistic error cancellation [5], [6], randomized compiling [7], Pauli-frame randomization [8], dynamical decoupling [9]–[12], quantum optimal control [13], [14], etc.”
Quantum Computing in the NISQ era and beyond (2018, background): “time. Further near-term experiments exploring quantum error correction are bound to advance our understanding of noise in quantum devices, and to suggest more eﬀective techniques for noise mitigation [47, 48] and device validation [49]. Nevertheless, solving really hard problems (like factoring numb”
Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography (2016, background): “An exciting recent development in this area is the introduction of randomized compiling [58], which has the potential to provably reduce the importance of coherent errors.”
t|ket⟩: a retargetable compiler for NISQ devices (2020, methodology): “Minimising the number of operations helps, but other techniques may be employed [22, 23, 24, 25].”
A Race-Track Trapped-Ion Quantum Processor (2023, methodology): “The irreps are the span of the identity II, the spans of weight-1 Pauli operators on each qubit {IX, IY, IZ} and {XI, Y I, ZI}, and the span of the weight-2 Pauli operators.”
Probabilistic error cancellation with sparse Pauli–Lindblad models on noisy quantum processors (2022, methodology): “However, it has been shown [23–26] that conjugation of the noise channel with randomly sampled operators from the Pauli group results in an averaged channel with a diagonal transfer matrix The averaging operation in (S1) is called a Pauli twirl.”