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IEEE VLSI Test Symposium (VTS)

Diagnosis of Quantum Circuits in the NISQ Era

Yumin Li, Cheng-Yun Hsieh, Yen-Wei Li, James Chien-Mo Li

Published Apr 24, 2023• 4 citations
Publisher

Abstract

Currently, noisy intermediate-scale quantum (NISQ) circuits may not always generate correct outputs due to noise and faults. In this work, we propose a diagnosis technique for NISQ circuits. The proposed technique contains static diagnosis and dynamic diagnosis. Static diagnosis uses a fault dictionary that contains output probability distribution for each fault. Dynamic diagnosis uses binary search to find the accurate fault locations of faulty quantum circuits. We demonstrate our technique using the Qiskit simulator with realistic noise models. We evaluate 15 benchmarks with unitary and non-unitary faults injected. Simulation results show that the average accuracy and resolution are 97.70% and 1.81. Experiments on the IBM Q devices have also been performed, and results show that our technique is feasible on real quantum circuit devices.

DOI
10.1109/vts56346.2023.10140030

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Currently, noisy intermediate-scale quantum (NISQ) circuits may not always generate correct outputs due to noise and faults. In this work, we propose a diagnosis technique for NISQ circuits. The proposed technique contains static diagnosis and dynamic diagnosis. Static diagnosis uses a fault dictionary that contains output probability distribution for each fault. Dynamic diagnosis uses binary search to find the accurate fault locations of faulty quantum circuits. We demonstrate our technique using the Qiskit simulator with realistic noise models. We evaluate 15 benchmarks with unitary and non-unitary faults injected. Simulation results show that the average accuracy and resolution are 97.70% and 1.81. Experiments on the IBM Q devices have also been performed, and results show that our technique is feasible on real quantum circuit devices.
Errors caused by faults would strongly affect the correctness of noisy intermediate-scale quantum (NISQ) circuits. In this work, we propose a technique for diagnosing coherent and incoherent faults for NISQ circuits. The proposed technique contains three phases: rough diagnosis, fine diagnosis, and depolarizing diagnosis. Rough diagnosis grid searches the Bloch sphere to locate an approximate range of a coherent fault. Fine diagnosis then precisely locates the coherent fault size based on the narrowed-down search space. At last, depolarizing diagnosis measures the depolarizing fault size. We demonstrate our technique using the Qiskit simulator with noise-free and noisy backends. The diagnosis accuracy between the diagnosed faulty gates and the injected faulty gates is over 99.95%, which is better than traditional quantum process tomography under the same conditions. Our results show that the diagnosis error of coherent faults does not affect the diagnosis accuracy of depolarizing faults. Experiments on the IBM Q devices have also been performed, and results of over 99.83% diagnosis accuracy show that our technique still preserves good resolution on real quantum circuit devices.
A new approach to detecting and diagnosing faults in quantum circuits is introduced. In order to account for the probabilistic nature of quantum circuits, collections of test experiments, called binary tomographic tests (BTTs), are generated. A BTT can identify a fault with respect to some user-defined confidence threshold τ. We present an algorithm to generate BTTs that either detect, or ensure the absence of, all modeled faults in a given circuit. We also present an adaptive diagnostic method to locate quantum faults. While classical circuits, even probabilistic ones, only handle ordinary probabilities, quantum circuits deal with quantum states, which have phase as an extra probabilistic parameter. The tomographic testing methods introduced previously for probabilistic circuits are unable to detect differences in phase, and therefore leave many quantum faults undetected. In contrast, we develop a design-for-test method which is specifically intended to detect faults that only affect the phase of a quantum state. We give experimental results for benchmark and random circuits which show high coverage of quantum faults by BTTs, and good resolution in the case of the adaptive diagnosis method.
Detection and isolation of faults is a crucial step in the physical realization of quantum circuits. Even though quantum gates and circuits compute reversible functions, the standard techniques of automatic test pattern generation (ATPG) for classical reversible circuits are not directly applicable to quantum circuits. For faulty quantum circuits under the widely accepted single fault assumption, we show that their behavior can be fully characterized by the (single) faulty gate and the corresponding fault model. This allows us to efficiently determine test input states as well as measurement strategy for fault detection and diagnosis. Building on top of these, we design randomized algorithms which are able to detect every nontrivial single-gate fault with minimal probability of error. We also describe similar algorithms for fault diagnosis. We evaluate our algorithms by the number of output samples that needs to be collected and the probability of error. Both of these can be related to the eigenvalues of the operators corresponding to the circuit gates. We experimentally compare all our strategies with the state-of-the-art ATPG techniques for quantum circuits under the “single missing faulty gate” model and demonstrate that significant improvement is possible if we can exploit the quantum nature of circuits.
In quantum computing, noisy intermediate-scale quantum (NISQ) devices offer unprecedented computational capabilities but are vulnerable to errors, notably measurement inaccuracies that impact computation accuracy. This study explores the efficacy of error mitigation techniques in improving quantum circuit performance on NISQ devices. Techniques such as dynamic decoupling (DD), twirled readout error extraction (T-REx) and zero-noise extrapolation (ZNE) are examined through extensive experimentation on an ideal simulator, IBM Kyoto, and IBM Osaka quantum computers. Results reveal significant performance discrepancies across scenarios, with error mitigation techniques notably enhancing both estimator result and variance values, aligning more closely with ideal simulator outcomes. The comparison results with ideal simulator (having expected result value 0.8284) shows that T-Rex has improved results on IBM Kyoto and enhanced average expected result value from 0.09 to 0.35. Similarly, DD has improved average expected result values from 0.2492 to 0.3788 on IBM Osaka. These findings underscore the critical role of error mitigation in bolstering quantum computation reliability. The results suggest that selection of mitigation technique depends upon quantum circuit and its depth, type of hardware and operations to be performed.
In the noisy intermediate-scale quantum (NISQ) era, quantum error mitigation (QEM) is essential for producing reliable outputs from quantum circuits. We present a statistical signal processing approach to QEM that estimates the most likely noiseless outputs from noisy quantum measurements. Our model assumes that circuit depth is sufficient for depolarizing noise, producing corrupted observations that resemble a uniform distribution alongside classical bit-flip errors from readout. Our method consists of two steps: a filtering stage that discards uninformative depolarizing noise and an expectation-maximization (EM) algorithm that computes a maximum likelihood (ML) estimate over the remaining data. We demonstrate the effectiveness of this approach on small-qubit systems using circuit simulations in Qiskit and IBM quantum processing unit (QPU) data, and compare its performance to contemporary statistical QEM techniques. We also show that our method scales to larger qubit counts using synthetically generated data consistent with our noise model. These results suggest that principled statistical methods can offer scalable and interpretable solutions for quantum error mitigation in realistic NISQ settings.
Abstract One of the main important features of the noisy intermediate-scale quantum(NISQ) era is the correct evaluation and consideration of errors. In this paper, we analyze the main sources of errors in current (IBM) quantum computers and we present a useful tool (TED-qc) designed to facilitate the total error probability expected for any quantum circuit. We propose this total error probability as the best way to estimate a lower bound for the fidelity in the NISQ era, avoiding the necessity of comparing the quantum calculations with any classical one. In order to contrast the robustness of our tool we compute the total error probability that may occur in three different quantum models: 1) the Ising model, 2) the Quantum-Phase Estimation (QPE), and 3) the Grover’s algorithm. For each model, the main quantities of interest are computed and benchmarked against the reference simulator’s results as a function of the error probability for a representative and statistically significant sample size. The analysis is satisfactory in more than the 99% of the cases. In addition, we study how error mitigation techniques are able to eliminate the noise induced during the measurement. These results have been calculated for the IBM quantum computers, but both the tool and the analysis can be easily extended to any other quantum computer.