Measurement error mitigation (MEM) techniques are postprocessing strategies to counteract systematic read-out errors on quantum computers (QC). Currently used MEM strategies face a tradeoff: methods that scale well with the number of qubits return negative probabilities, while those that guarantee a valid probability distribution are not scalable. Here, we present a scheme that addresses both of these issues. In particular, we present a scalable implementation of iterative Bayesian unfolding, a standard mitigation technique used in high-energy physics experiments. We demonstrate our method by mitigating QC data from experimental preparation of Greenberger-Horne-Zeilinger (GHZ) states up to 127 qubits and implementation of the Bernstein-Vazirani algorithm on up to 26 qubits.
Measurement error mitigation (MEM) techniques are postprocessing strategies to counteract systematic read-out errors on quantum computers (QC). Currently used MEM strategies face a tradeoff: methods that scale well with the number of qubits return negative probabilities, while those that guarantee a valid probability distribution are not scalable. Here, we present a scheme that addresses both of these issues. In particular, we present a scalable implementation of iterative Bayesian unfolding, a standard mitigation technique used in high-energy physics experiments. We demonstrate our method by mitigating QC data from experimental preparation of Greenberger-Horne-Zeilinger (GHZ) states up to 127 qubits and implementation of the Bernstein-Vazirani algorithm on up to 26 qubits.
Measurement errors are a significant obstacle to achieving scalable quantum computation. To counteract systematic readout errors, researchers have developed postprocessing techniques known as measurement error mitigation methods. However, these methods face a tradeoff between scalability and returning nonnegative probabilities. In this paper, we present a solution to overcome this challenge. Our approach focuses on iterative Bayesian unfolding, a standard mitigation technique used in high-energy physics experiments, and implements it in a scalable way. We demonstrate our method on experimental Greenberger-Horne-Zeilinger state preparation on up to 127 qubits and on the Bernstein-Vazirani algorithm on up to 26 qubits. Compared to state-of-the-art methods (such as M3), our implementation guarantees valid probability distributions, returns comparable or better-mitigated results, and does so without a noticeable time and memory overhead. Published by the American Physical Society 2024
In Phys. Rev. A 108, L060402 (2023), we introduced a Bayesian measurement error mitigation algorithm, which leveraged complete information from the readout signal, and validated the protocol on a quantum device with five superconducting qubits. Here, we present an improved algorithm's implementation, tailored for multiqubit experiments on near-term superconducting qubit quantum devices. In particular, we provide a detailed algorithm workflow, from calibrating the detector response functions to the postprocessing of measurement outcomes, offering a computationally efficient solution for the output size typical of current quantum computing devices. We show how the numerical representation of the noise function affects the performance of the error mitigation algorithm and test the convergence criteria. We benchmark our protocol on actual quantum computers with superconducting qubits, where the readout signal encodes the measurement information as unprocessed analog data before qubit state assignment. Finally, we compare the performance of our algorithm against other measurement error mitigation methods, such as iterative Bayesian unfolding and the Mthree method, and show how our method can be integrated on top of other readout error mitigation protocols.
We show that the method of iterative Bayesian unfolding for mitigating readout errors in quantum computers can be derived from an information theoretic analysis. This inspires more flexible applications of this error-mitigation scheme. In particular, we distinguish between structural mitigation and unstructural mitigation. Structural mitigation addresses nearly deterministic quantum computation, where the computer is expected to output a single- or few-outcome bit strings. It is shown that the readout errors alone can be corrected by few repetitions of the computation. In contrast, unstructural mitigation is designed for quantum simulation, where the computer outputs bit strings broadly distributed. In this case, one is interested in mitigating certain observables of interest. As most observables of interest are dependent on few bits and not the whole bit string, it is sufficient to mitigate the marginal distributions over these dependent bits. As long as the cross talk of readout errors can be ignored, it is shown that the iterative Bayesian unfolding applied locally for these marginal distributions gives similar results as mitigation using least squared errors. We illustrate our analysis using the data of the preparation of the Greenberger-Horne-Zeilinger state in a 127-qubit quantum computer.
Abstract In the current era of noisy intermediate-scale quantum computers, noisy qubits can result in biased results for early quantum algorithm applications. This is a significant challenge for interpreting results from quantum computer simulations for quantum chemistry, nuclear physics, high energy physics (HEP), and other emerging scientific applications. An important class of qubit errors are readout errors. The most basic method to correct readout errors is matrix inversion, using a response matrix built from simple operations to probe the rate of transitions from known initial quantum states to readout outcomes. One challenge with inverting matrices with large off-diagonal components is that the results are sensitive to statistical fluctuations. This challenge is familiar to HEP, where prior-independent regularized matrix inversion techniques (“unfolding”) have been developed for years to correct for acceptance and detector effects, when performing differential cross section measurements. We study one such method, known as iterative Bayesian unfolding, as a potential tool for correcting readout errors from universal gate-based quantum computers. This method is shown to avoid pathologies from commonly used matrix inversion and least squares methods.
Reducing measurement errors in multiqubit quantum devices is critical for performing any quantum algorithm. Here we show how to mitigate measurement errors by a classical postprocessing of the measured outcomes. Our techniques apply to any experiment where measurement outcomes are used for computing expected values of observables. Two error-mitigation schemes are presented based on tensor product and correlated Markovian noise models. Error rates parametrizing these noise models can be extracted from the measurement calibration data using a simple formula. Error mitigation is achieved by applying the inverse noise matrix to a probability vector that represents the outcomes of a noisy measurement. The error-mitigation overhead, including the number of measurements and the cost of the classical postprocessing, is exponential in $\ensuremath{\epsilon}n$, where $\ensuremath{\epsilon}$ is the maximum error rate and n is the number of qubits. We report experimental demonstration of our error-mitigation methods on IBM Quantum devices using stabilizer measurements for graph states with $n\ensuremath{\le}12$ qubits and entangled 20-qubit states generated by low-depth random Clifford circuits.
Measurement error mitigation (MEM) is essential for realizing reliable quantum computation. Model-free measurement error mitigation (MF-MEM) is an important class of MEM methods that employs Pauli twirling—typically with a random twirling set—to convert measurement noise into a state-independent scaling factor, thereby enabling error mitigation through simple calibration. However, such methods face prohibitive sampling overhead, limiting their scalability. To address this, we introduce subsystem-balanced Pauli twirling (SB-PT), a twirling method designed for MF-MEM that enforces Pauli operator balance on measuring subsystems to selectively suppress dominant measurement noise. Theoretically, for a weight- τ Pauli observable, SB-PT removes all independent error components using only O ( 4 τ ) random circuits, substantially reducing the sampling overhead over conventional Pauli twirling. This efficiency gain is most significant for sparse observables. To extend such resource-efficient mitigation to arbitrary observables, we generalize and integrate a hardware-efficient measurement transformation framework that converts high-weight Pauli operators into low-weight effective ones via linear-depth circuits. The circuit noise introduced during this transformation is jointly mitigated with native measurement noise using a unified twirling protocol, ensuring robust performance. Extensive numerical simulations demonstrate a greater than 16-fold improvement in sampling efficiency over conventional random twirling, with consistent performance gains across varying system sizes and error regimes. This work provides a resource-frugal and experimentally viable path toward high-fidelity measurement in near-term quantum devices.