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arXiv:2210.14753 · Physical Review A

Virtual distillation with noise dilution

Yong Siah Teo, Seongwook Shin, Hyukgun Kwon, Seok-Hyung Lee, Hyunseok Jeong

Published Feb 8, 2023• 8 citations
arXivHTMLPDF

Abstract

Virtual distillation is an error-mitigation technique that reduces quantum-computation errors without assuming the noise type. In scenarios where the user of a quantum circuit is required to additionally employ peripherals, such as delay lines, that introduce excess noise, we find that the error-mitigation performance can be improved if the peripheral, whenever possible, is split across the entire circuit, that is, when the noise channel is uniformly distributed in layers within the circuit. We show that under the multiqubit loss and Pauli noise channels, respectively, for a given overall error rate, the average mitigation performance improves monotonically as the noisy peripheral is split (diluted) into more layers, with each layer sandwiched between subcircuits that are sufficiently deep to behave as 2-designs. For both channels, analytical and numerical evidence show that second-order distillation is generally sufficient for (near-)optimal mitigation. We propose an application of these findings in designing a quantum-computing cluster that houses realistic noisy intermediate-scale quantum circuits that may be shallow in depth, where measurement detectors are limited and delay lines are necessary to queue output qubits from multiple circuits.

DOI
10.1103/physreva.107.022608

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Virtual distillation is an error-mitigation technique that reduces quantum-computation errors without assuming the noise type. In scenarios where the user of a quantum circuit is required to additionally employ peripherals, such as delay lines, that introduce excess noise, we find that the error-mitigation performance can be improved if the peripheral, whenever possible, is split across the entire circuit, that is, when the noise channel is uniformly distributed in layers within the circuit. We show that under the multiqubit loss and Pauli noise channels, respectively, for a given overall error rate, the average mitigation performance improves monotonically as the noisy peripheral is split (diluted) into more layers, with each layer sandwiched between subcircuits that are sufficiently deep to behave as 2-designs. For both channels, analytical and numerical evidence show that second-order distillation is generally sufficient for (near-)optimal mitigation. We propose an application of these findings in designing a quantum-computing cluster that houses realistic noisy intermediate-scale quantum circuits that may be shallow in depth, where measurement detectors are limited and delay lines are necessary to queue output qubits from multiple circuits.
Virtual distillation is a technique that aims to mitigate errors in noisy quantum computers. It works by preparing multiple copies of a noisy quantum state, bridging them through a circuit, and conducting measurements. As the number of copies increases, this process allows for the estimation of the expectation value with respect to a state that approaches the ideal pure state rapidly. However, virtual distillation faces a challenge in realistic scenarios: preparing multiple copies of a quantum state and bridging them through a circuit in a noisy quantum computer will significantly increase the circuit size and introduce excessive noise, which will degrade the performance of virtual distillation. To overcome this challenge, we propose an error mitigation strategy that uses circuit-cutting technology to cut the entire circuit into fragments. With this approach, the fragments responsible for generating the noisy quantum state can be executed on a noisy quantum device, while the remaining fragments are efficiently simulated on a noiseless classical simulator. By running each fragment circuit separately on quantum and classical devices and recombining their results, we can reduce the noise accumulation and enhance the effectiveness of the virtual distillation technique. Our strategy has good scalability in terms of both runtime and computational resources. We demonstrate our strategy’s effectiveness through noisy simulation and experiments on a real quantum device.
Shadow estimation is a method for deducing numerous properties of an unknown quantum state through a limited set of measurements, which suffers from noises in quantum devices. In this paper, we introduce an error-mitigated shadow estimation approach based on virtual distillation, tailored for applications in near-term quantum devices. Our methodology leverages the qubit reset technique, thereby reducing the associated qubit overhead. Crucially, our approach ensures that the required qubit resources remain independent of the desired accuracy and avoid an exponential measurement overhead, marking a substantial advancement in practical applications. Furthermore, our technique accommodates a mixed Clifford and Pauli-type shadow, which can result in a reduction in the number of required measurements across various scenarios. We also study the trade-off between circuit depth and measurement overhead quantitatively. Through numerical simulations, we substantiate the efficacy of our error mitigation method, establishing its utility in enhancing the robustness of shadow estimations on near-term quantum devices.
Contemporary quantum computers have relatively high levels of noise, making it difficult to use them to perform useful calculations, even with a large number of qubits.Quantum error correction is expected to eventually enable fault-tolerant quantum computation at large scales, but until then, it will be necessary to use alternative strategies to mitigate the impact of errors.We propose a near-term friendly strategy to mitigate errors by entangling and measuring M copies of a noisy state ρ.This enables us to estimate expectation values with respect to a state with dramatically reduced error ρ M =Trðρ M Þ without explicitly preparing it, hence the name "virtual distillation."As M increases, this state approaches the closest pure state to ρ exponentially quickly.We analyze the effectiveness of virtual distillation and find that it is governed in many regimes by the behavior of this pure state (corresponding to the dominant eigenvector of ρ).We numerically demonstrate that virtual distillation is capable of suppressing errors by multiple orders of magnitude and explain how this effect is enhanced as the system size grows.Finally, we show that this technique can improve the convergence of randomized quantum algorithms, even in the absence of device noise.
Virtual distillation is a promising error-mitigation technique that exploits multiple copies of a noisy quantum state to estimate observables as if measured on a purified state. Although originally introduced in the context of bosonic many-body systems under the name of virtual cooling, its development and applications have largely focused on qubit-based quantum computation. Here, we establish a framework for virtual distillation in bosonic quantum information processing and continuous-variable quantum computing. Building on a diagonalization of cyclic shift operators implemented with passive linear-optical interferometers, we derive experimentally accessible protocols for estimating virtually distilled expectation values of observables relevant to bosonic architectures. In particular, we show how to recover noise-mitigated expectation values of number operators, phase-shift operators, and arbitrary quadratures from multi-copy measurements. For number operators, we further demonstrate the estimation of virtually distilled correlators of arbitrary order through the characteristic function of the photon-number distribution. We apply the framework to states affected by photon loss and dephasing, two of the dominant noise mechanisms in bosonic quantum computation, and quantify the resulting suppression of noise contributions. Our results extend virtual distillation beyond its original setting and provide a practical route toward error-mitigated measurements in bosonic quantum processors using experimentally available linear-optical resources.
Abstract Quantum error mitigation (QEM) is crucial for near-term quantum devices, as noise inherently exists in physical quantum systems and undermines the accuracy of quantum algorithms. A typical QEM method, called Virtual Distillation (VD), aims to mitigate errors for expectation values of observables and achieve effective exponential suppression using multiple copies of the noisy state. However, imperfect VD circuit implementation may yield negative mitigation outcomes, potentially more severe than those achieved without QEM. To address this, we introduce Circuit-Noise-Resilient Virtual Distillation (CNR-VD). This method, featuring a calibration procedure that utilizes easily-prepared input states, refines the outcomes of VD when its circuit is contaminated by noise, seeking to recover the results of an ideally conducted VD circuit. Simulation results demonstrate that the CNR-VD estimator effectively reduces deviations induced by noise in the VD circuit, showcasing improvements in accuracy by an order of magnitude at most compared to the original VD. Meanwhile, CNR-VD enables positive mitigation effects, even in the presence of higher noise levels where the original VD performs worse than the unmitigated estimation. The proposed CNR-VD significantly enhances the noise-resilience of VD, and thus is anticipated to elevate the performance of quantum algorithm implementations on near-term quantum devices.
Abstract As quantum computing hardware steadily increases in qubit count and quality, one important question is how to allocate these resources to mitigate the effects of hardware noise. In a transitional era between noisy small-scale and fully fault-tolerant systems, we envisage a scenario in which we are only able to error-correct a fraction of the qubits required to perform an interesting computation. In this work, we develop concrete constructions of logical operations on a joint system of a collection of noisy and a collection of error-corrected logical qubits. Within this setting and under Pauli noise assumptions, we provide analytic evidence that brick-layered circuits display on average slower concentration to the “useless” uniform distribution with increasing circuit depth compared to fully noisy circuits. We corroborate these findings by numerical demonstration of slower decoherence with an increasing fraction of error-corrected qubits under depolarizing noise acting at the circuit level. We find that this advantage only manifests when the number of error-corrected qubits passes a specified threshold which depends on the number of couplings between error-corrected and noisy registers.