Mitigating errors is a significant challenge for near-term quantum computers. One of the most important sources of errors is related to the readout of the quantum state into a classical bit stream. A variety of techniques have been proposed to mitigate these errors with post-hoc corrections. We propose a complementary scheme to actively reduce readout errors on a shot-by-shot basis by encoding single qubits, immediately prior to readout, into multiqubit states. The computational resources of our technique are independent of the circuit depth and are compatible with the error rates and connectivity of many current devices. We analyze the potential of our approach using two types of error-correcting codes, and, as a proof of principle, we demonstrate an 80% improvement in readout error on the IBMQ Mumbai quantum computer.
Mitigating errors is a significant challenge for near-term quantum computers. One of the most important sources of errors is related to the readout of the quantum state into a classical bit stream. A variety of techniques have been proposed to mitigate these errors with post-hoc corrections. We propose a complementary scheme to actively reduce readout errors on a shot-by-shot basis by encoding single qubits, immediately prior to readout, into multiqubit states. The computational resources of our technique are independent of the circuit depth and are compatible with the error rates and connectivity of many current devices. We analyze the potential of our approach using two types of error-correcting codes, and, as a proof of principle, we demonstrate an 80% improvement in readout error on the IBMQ Mumbai quantum computer.
Readout errors on near-term quantum computers can introduce significant error to the empirical probability distribution sampled from the output of a quantum circuit. These errors can be mitigated by classical postprocessing given the access of an experimental response matrix that describes the error associated with the measurement of each computational basis state. However, the resources required to characterize a complete response matrix and to compute the corrected probability distribution scale exponentially with the number of qubits, n. In this work, we modify standard matrix inversion techniques using perturbative approximations with significantly reduced complexity and bounded error when the likelihood of high-order bit-flip events is strongly suppressed. Given a characteristic error rate q, we discuss a method to recover the probability of the all-zeros bit string p0 by sampling only a small subspace of the response matrix before inverting readout error, resulting in a relative speedup of poly[2n/(nw)], which we motivate using a simplified error model for which the approximation incurs only O(qw) error for some integer w. We then provide a generalized technique to efficiently recover full output distributions with O(qw) error in the perturbative limit. These approximate techniques for readout-error correction may greatly accelerate near-term quantum computing applications.
Readout errors are one of the dominant sources of noise in current quantum processors, limiting both expectation-value estimation and sampling-based applications. Since they affect only the classical measurement outcomes, they can be addressed using classical coding techniques: immediately before measurement, each data qubit is redundantly encoded with ancilla qubits, and the resulting bit string is decoded either by post-selection or by majority voting. Unlike conventional readout error mitigation, which corrects only aggregate quantities such as expectation values, this approach operates on individual measurement shots and can therefore produce approximately corrected samples. We present a systematic cross-platform and cross-generation experimental evaluation of repetition-code readout error detection and correction. We benchmark the same protocol on IBM Heron r1-r3 superconducting processors and Quantinuum H1 and H2 trapped-ion processors while independently varying the code distance, hardware generation, and encoding layout. We find that both error detection and correction improve readout fidelity on every device and generation tested, even as the unencoded baseline improves substantially across successive hardware releases. At the same time, the value of additional redundancy depends strongly on the underlying hardware. On superconducting processors, the extra gate errors introduced by the encoding rapidly offset its benefits, whereas on trapped-ion processors the much lower gate error rates allow larger code distances to remain advantageous.
Readout errors are a significant source of noise for near-term intermediate-scale quantum computers. Mismeasuring a qubit as $|1\ensuremath{\rangle}$ when it should be $|0\ensuremath{\rangle}$ occurs much less often than mismeasuring a qubit as $|0\ensuremath{\rangle}$ when it should have been $|1\ensuremath{\rangle}$. We make the simple observation that one can improve the readout fidelity of quantum computers by applying targeted X gates prior to performing a measurement. These X gates are placed so that the expected number of qubits in the $|1\ensuremath{\rangle}$ state is minimized. Classical postprocessing can undo the effect of the X gates so that the expectation value of any observable is unchanged. This protocol is designed to have no effect when readout errors are symmetric. We show that the statistical uncertainty following readout error corrections is smaller when using readout rebalancing. The statistical advantage is circuit and computer dependent and is demonstrated for the W state, a Grover search, and for a Gaussian state. The benefit in statistical precision is most pronounced (and nearly a factor of 2 in some cases) when states with many qubits in the excited state have high probability.
Quantum computing is entering a transitional regime between noisy intermediate-scale quantum (NISQ) processing and early fault-tolerant quantum computation (FTQC), in which increasingly capable hardware is beginning to support repeated syndrome measurements, partial error correction, and logical-qubit operations, while residual physical and logical errors remain non-negligible. In this regime, error suppression, error mitigation, and quantum error correction are increasingly better viewed as complementary layers of a unified error-reduction strategy rather than as separate approaches, with each acting at a different stage of the quantum computation to improve simulation reliability. Thus, in this review, we provide a practical and forward-looking overview of the principal hardware error sources and the corresponding error suppression and mitigation methods for reducing their impact across the current NISQ-FTQC transition. We discuss hardware-aware circuit design, coherent-error suppression, readout mitigation, noise extrapolation, classical inference, and software-supported workflows, with particular emphasis on their implementation on actual quantum processors. We further examine how error mitigation techniques can be adapted to encoded and logical-qubit settings so that they can operate alongside quantum error correction to suppress residual logical errors and improve the accuracy of computation in the early fault-tolerant regime.
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.