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Link: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.105.012423
Authors: H Patil, Y Wang, PS Krstić
Variational quantum algorithms have found success in the noisy intermediate-scale quantum era owing to their hybrid quantum-classical approach which mitigate the problems of noise in quantum computers. In our paper, we introduce the dynamic ansatz in the variational quantum linear solver for a system of linear algebraic equations. In this improved algorithm, the number of layers in the hardware efficient ansatz circuit is evolved, starting from a small and gradually increasing until convergence of the solution is reached. We demonstrate the algorithm advantage in comparison to the standard static ansatz by utilizing fewer quantum resources and with a smaller quantum depth on average in the presence and absence of quantum noise and in cases when the number of qubits or condition number of the system matrices are increased. The numbers of iterations and layers can be altered by a switching parameter. The performance of the algorithm in using quantum resources is quantified by a newly defined metric.
Link: https://ieeexplore.ieee.org/abstract/document/10313621
Authors: H. Patil, P. Li, J. Liu, and H. Zhou
Quantum computers in the NISQ era are prone to noise. A range of quantum error mitigation techniques has been proposed to address this issue. Zero-noise extrapolation (ZNE) stands out as a promising one. ZNE involves increasing the noise levels in a circuit and then using extrapolation to infer the zero noise case from the noisy results obtained. This paper presents a novel ZNE approach that does not require circuit folding or noise scaling to mitigate depolarizing and/or decoherence noise. To mitigate depolarizing noise, we propose leveraging the extreme/infinite noisy case, which allows us to avoid circuit folding. Specifically, the circuit output with extreme noise becomes the maximally mixed state. We show that using circuit reliability metrics, simple linear extrapolation can effectively mitigate depolarizing noise. With decoherence noise, different states decay into the all-zero state at a rate that depends on the number of excited states and time. Therefore, we propose a state and latency-aware exponential extrapolation that does not involve folding or scaling. When dealing with a quantum system affected by both decoherence and depolarizing noise, we propose to use our two mitigation techniques in sequence: first applying decoherence error mitigation, followed by depolarizing error mitigation. A common limitation of ZNE schemes is that if the circuit of interest suffers from high noise, scaling-up noise levels could not provide useful data for extrapolation. We propose using circuit-cut techniques to break a large quantum circuit into smaller sub-circuits to overcome this limitation. This way, the noise levels of the sub-circuits are lower than the original circuit, and ZNE can become more effective in mitigating their noises.
Maximum Likelihood Quantum Error Mitigation for Algorithms with a Single Correct Output
Maximum Likelihood Quantum Error Mitigation for Algorithms with a Single Correct Output
Link: QCE 2024
Authors: D. Baron, H. Patil, and H. Zhou
Quantum error mitigation is an important technique to reduce the impact of noise in quantum computers. With more and more qubits being supported on quantum computers, there are two emerging fundamental challenges. First, the number of shots required for quantum algorithms with large numbers of qubits needs to increase in order to obtain a meaningful distribution or expected value of an observable. Second, although steady progress has been made in improving the fidelity of each qubit, circuits with a large number of qubits are likely to produce erroneous results. This low-shot, high-noise regime calls for highly scalable error mitigation techniques. In this paper, we propose a simple and effective mitigation scheme, qubit-wise majority vote, for quantum algorithms with a single correct output. We show that our scheme produces the maximum likelihood (ML) estimate under certain assumptions, and bound the number of shots required. Our experimental results on real quantum devices confirm that our proposed approach requires fewer shots than existing ones, and can sometimes recover the correct answers even when they are not observed from the measurement results.
Accepted at QCE 2025
Authors: H. Patil, D. Baron, and H. Zhou
Quantum error mitigation (QEM) is critical in reducing the impact of noise in the pre-fault-tolerant era, and is expected to complement error correction in fault-tolerant quantum computing (FTQC). In this paper, we propose a novel QEM approach, Q-Cluster, that uses unsupervised learning (clustering) to reshape the measured bit-string distribution. Our approach starts with a simplified bit-flip noise model. It first performs clustering on noisy measurement results, i.e., bit-strings, based on the Hamming distance. The centroid of each cluster is calculated using a qubit-wise majority vote. Next, the noisy distribution is adjusted with the clustering outcomes and the bit-flip error rates using Bayesian inference. Our simulation results show that Q-Cluster can mitigate high noise rates (up to 40% per qubit) with the simple bit-flip noise model. However, real quantum computers do not fit such a simple noise model. To address the problem, we (a) apply Pauli twirling to tailor the complex noise channels to Pauli errors, and (b) employ a machine learning model, ExtraTrees regressor, to estimate an effective bit-flip error rate using a feature vector consisting of machine calibration data (gate & measurement error rates), circuit features (number of qubits, numbers of different types of gates, etc.) and the shape of the noisy distribution (entropy). Our experimental results show that our proposed Q-Cluster scheme improves the fidelity by a factor of 1.46x, on average, compared to the unmitigated output distribution, for a set of low-entropy benchmarks on five different IBM quantum machines. Our approach outperforms the state-of-art QEM approaches RZNE, M3, Hammer, and QBEEP by 1.26x, 1.29x, 1.47x, and 2.65x, respectively.
Accepted at QCE 25
Authors: S. Mohapatra, H. Patil, J. Liu, and H. Zhou,
Quantum computers are susceptible to noise or errors, and it is critical to quantify the impact of noise acting on a quantum circuit. The density matrix-based fidelity, referred to as DM Fidelity, aka Uhlmann fidelity, provides a measure that quantifies the closeness between a noise-free density matrix and its noisy density matrix. However, DM Fidelity is computationally expensive, since density matrices require full-state tomography, and also necessitates noise-free results. Consequently, different metrics have been proposed to estimate the noise impact of a quantum circuit. In this paper, we study the commonly used metrics, including Hellinger Fidelity, Total Variational Distance (TVD), Estimated Success Probability (ESP), Probability of Successful Trials (PST), Clifford-based Fidelity Estimation, purity measure using either CSWAP or Classical Shadows, and Shadow Overlap, and show how well these metrics correlate to DM Fidelity. We also identify certain regions and conditions where one metric correlates with DM Fidelity better than others. The metrics are computed with a noise simulator using noise models derived from IBMQ quantum computers on the SupermarQ benchmarks. Among the aforementioned metrics, our results show that ESP and PST have the highest correlation with DM Fidelity: ESP has a Spearman correlation of 0.88, signifying a positive nonlinear correlation, while PST has a Pearson correlation of 0.92, signifying a positive linear correlation. Accurate fidelity estimation has many applications. In our paper, we present an application in quantum error mitigation. We show that using fidelity metrics that correlate well with DM Fidelity is more effective than using other metrics. In particular, our results on real IBM Quantum hardware show that Reliability Based Zero Noise Extrapolation (RZNE), using ESP/PST achieves a fidelity (Hellinger) improvement of 7.44x/7.83x over the baseline without error-mitigation. Using other metrics like Clifford fidelity which has a Spearman Correlation of 0.73 to DM Fidelity, would be less effective: RZNE with Clifford fidelity shows a fidelity improvement gain of 4.31x.
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