[논문 리뷰] Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors

E. van den Berg, Zlatko Minev외 2명|arXiv (Cornell University)|2022. 01. 24.

Quantum Computing Algorithms and Architecture참고 문헌 52인용 수 51

한 줄 요약

이 연구는 대규모 양자 장치용 희소 Pauli-Lindblad 노이즈 모델을 학습하는 실용적인 프로토콜을 제시하고, Crosstalk가 있는 초전도 프로세서에서 PEC를 적용하여 노이즈를 완화하여 더 큰 회로 규모에서도 바이어스 없는 관측치를 가능하게 한다.

ABSTRACT

Noise in pre-fault-tolerant quantum computers can result in biased estimates of physical observables. Accurate bias-free estimates can be obtained using probabilistic error cancellation (PEC), which is an error-mitigation technique that effectively inverts well-characterized noise channels. Learning correlated noise channels in large quantum circuits, however, has been a major challenge and has severely hampered experimental realizations. Our work presents a practical protocol for learning and inverting a sparse noise model that is able to capture correlated noise and scales to large quantum devices. These advances allow us to demonstrate PEC on a superconducting quantum processor with crosstalk errors, thereby providing an important milestone in opening the way to quantum computing with noise-free observables at larger circuit volumes.

연구 동기 및 목표

• Motivate error mitigation in near-term quantum devices by removing bias from observable estimates.
• Develop a scalable, learnable noise model that captures correlated cross-talk across many qubits.
• Demonstrate probabilistic error cancellation (PEC) using the learned model on superconducting processors.
• Show scalability and practical overheads of PEC for larger two-qubit gate layers.

제안 방법

• Model a layer of noisy two-qubit gates as a sparse Pauli-Lindblad channel with coefficients bbi and Pauli terms Pk.
• Represent the layer noise via a Pauli-Lindblad generator L(\u00131\rho)=\u00131k\u00027e1\u000261k(Pk\u00131\rhoPk^†- \u00131\rho).
• Compute the resulting Λ(ρ)=exp[L](ρ)=∏k (wk+(1-wk)Pk·Pk^†)ρ with wk=1/2(1+e^{-2λk}).
• Fit model coefficients λk \u0001e0 \u0010≥0 from measured fidelities f_b of Pauli channels using a nonnegative least-squares scheme in log(f).
• Obtain an invertible inverse map Λ^{-1} by negating L, yielding a quasi-probability distribution for PEC sampling with overhead γ=exp(∑k 2λk).
• Sample the inverse map efficiently by selecting identities with probability wk or applying Pk and combining results to produce unbiased mitigated observables.]

실험 결과

연구 질문

• RQ1 Can a sparse Pauli-Lindblad noise model capture cross-talk and correlations across large qubit layers?
• RQ2 Is it practical to learn such a model accurately with scalable data and bounded sample complexity?
• RQ3 Does PEC using the learned sparse model yield unbiased observable estimates with manageable sampling overhead on larger devices?
• RQ4 How does PEC perform in real-time Ising-model simulations and high-weight observables on superconducting processors?
• RQ5 What are the limitations and resource trade-offs (sampling overhead) as system size and circuit depth grow?

주요 결과

• A sparse Pauli-Lindblad noise model with weight-one and weight-two Paulis can capture correlated noise across layers and scale linearly with the number of qubits.
• The learned model produces fidelities that closely match measured fidelities, validating the noise representation.
• PEC mitigates noise in Ising-model time evolution with high accuracy across small (4-qubit) and larger (20-qubit) layers, including high-weight observables.
• The sampling overhead γ grows with the number of layers and qubits, but remains manageable and can be characterized by a qubit- and depth-normalized metric \u0012bar{γ}, guiding hardware improvements.
• The approach enables unbiased estimates of observables in circuits with crosstalk, representing a practical path toward noise-free observables on noisy processors.]