Abstract In many platforms, errors from state-preparation and measurement (SPAM) dominate over single-qubit gate errors. To inform further hardware improvements and the development of more effective SPAM mitigation strategies, it is necessary to separately characterize the error contributions from SP and measurement (M). Here, we show how to construct a protocol that can efficiently and separately characterize the SP and M error parameters by using only high-fidelity single-qubit gates and repeated single-qubit measurements without reset. The measurements are assumed to be non-destructive and M errors are taken to be (spatially and temporally) uncorrelated and classical. Notably, the circuit depth of the protocol is independent of system size, and the target parameters may be characterized to a precision that is only limited by the number of experimental repetitions. We employ our protocol for the parallel characterization of SPAM errors on multiple qubits in the IBM quantum platform devices, where we find SP infidelities up to 6.57% and readout assignment errors up to 19.1%. Using numerical simulations, we also demonstrate how measurement-error mitigation that does not properly account for SP errors generally leads to a biased estimate of measured observable expectation values.
Abstract In many platforms, errors from state-preparation and measurement (SPAM) dominate over single-qubit gate errors. To inform further hardware improvements and the development of more effective SPAM mitigation strategies, it is necessary to separately characterize the error contributions from SP and measurement (M). Here, we show how to construct a protocol that can efficiently and separately characterize the SP and M error parameters by using only high-fidelity single-qubit gates and repeated single-qubit measurements without reset. The measurements are assumed to be non-destructive and M errors are taken to be (spatially and temporally) uncorrelated and classical. Notably, the circuit depth of the protocol is independent of system size, and the target parameters may be characterized to a precision that is only limited by the number of experimental repetitions. We employ our protocol for the parallel characterization of SPAM errors on multiple qubits in the IBM quantum platform devices, where we find SP infidelities up to 6.57% and readout assignment errors up to 19.1%. Using numerical simulations, we also demonstrate how measurement-error mitigation that does not properly account for SP errors generally leads to a biased estimate of measured observable expectation values.
Correctly characterizing state preparation and measurement (SPAM) processes is a necessary step towards building reliable quantum processing units (QPUs). In this work, we discuss the subtleties behind separately measuring SPAM errors. We propose a protocol that can separately estimate SPAM errors, in the case where quantum gates are ideal. In the case where the quantum gates are imperfect, we derive bounds on the estimated SPAM error rates, based on gate error measures, which can be estimated independently of SPAM processes. Our method shows that the gauge ambiguity in characterizing SPAM operations can be resolved by assuming that there exists one qubit whose initial state is uncorrelated with other qubits in a QPU. We test the protocol on a publicly available five-qubit QPU and demonstrate its validity by comparing our results with simulations.
Quantum error correction of a grid-state qubit with state preparation and measurement errors below 10−3
Grid state qubits offer a hardware-efficient approach to large-scale fault-tolerant quantum computing. They access the information redundancy required for quantum error correction by exploiting the large Hilbert space naturally available in harmonic oscillators. Superconducting architectures are particularly suitable to implement grid state qubits due to their fast and high-fidelity operations. Grid states in superconducting circuits enable quantum error correction (QEC) with performance beyond break-even. However, the state preparation and measurements (SPAM) errors of grid states has been a significant limitation to computational performances. In this work, we leverage high-performance QEC to enable repeat-until-success state preparation of both cardinal and magic states of the single-mode grid-state qubit. We combine this with an improved measurement protocol that corrects for both finite-energy envelope and auxiliary qubit readout errors, and increases robustness to photon loss. Our experiments, using both techniques, achieve a combined state-preparation and measurement error below 10−3. This represents two orders-of-magnitude improvement over the state of the art, bringing this platform on par with standard SPAM error levels measured in transmon qubits.
State preparation and measurement (SPAM) errors limit the performance of many gate-based quantum computing architecures, but are partly correctable after a calibration step that requires, for an exact implementation on a register of n qubits, 2n additional characterization experiments, as well as classical post-processing. Here we introduce an approximate but efficient method for SPAM error characterization requiring the {\it classical} processing of 2n×2n real matrices, but only O(n2) measurements. The technique assumes that multi-qubit measurement errors are dominated by pair correlations, which are estimated with n(n−1)k/2 two-qubit experiments, where k is a parameter related to the accuracy. We demonstrate the technique on the IBM and Rigetti online superconducting quantum computers, allowing comparison of their SPAM errors in both magnitude and degree of correlation. We also study the correlations as a function of the register's geometric layout. We find that the pair-correlation model is fairly accurate on linear arrays of superconducting qubits. However qubits arranged in more closely spaced two-dimensional geometries exhibit significant higher-order (such as 3-qubit) SPAM error correlations.
Several techniques have been recently introduced to mitigate errors in near-term quantum computers without the overhead required by quantum error correcting codes. While most of the focus has been on gate errors, measurement errors are significantly larger than gate errors on some platforms. A widely used transition matrix error mitigation (TMEM) technique uses measured transition probabilities between initial and final classical states to correct subsequently measured data. However from a rigorous perspective, the noisy measurement should be calibrated with perfectly prepared initial states, and the presence of any state-preparation error corrupts the resulting mitigation. Here we develop a measurement error mitigation technique, a conditionally rigorous TMEM, that is not sensitive to state-preparation errors and thus avoids this limitation. We demonstrate the importance of the technique for high-precision measurement and for quantum foundations experiments by measuring Mermin polynomials on IBM Q superconducting qubits. An extension of the technique allows one to correct for both state-preparation and measurement (SPAM) errors in expectation values as well; we illustrate this by giving a protocol for fully SPAM-corrected quantum process tomography.
Current noisy quantum computers have multiple types of errors, which can occur in the state preparation, measurement/readout, and gate operation, as well as intrinsic decoherence and relaxation. Partly motivated by the booming of intermediate-scale quantum processors, measurement and gate errors have been recently extensively studied, and several methods of mitigating them have been proposed and formulated in software packages (e.g., in IBM Qiskit). Despite this, the state preparation error and the procedure to quantify it have not yet been standardized, as state preparation and measurement errors are usually considered not directly separable. Inspired by a recent work of Laflamme, Lin, and Mor \cite{laflamme2022algorithmic}, we propose a simple and resource-efficient approach to quantify separately the state preparation and readout error rates. With these two errors separately quantified, we also propose methods to mitigate them separately, especially mitigating state preparation errors with linear (with the number of qubits) complexity. As a result of the separate mitigation, we show that the fidelity of the outcome can be improved by an order of magnitude compared to the standard measurement error mitigation scheme. We also show that the quantification and mitigation scheme is resilient against gate noise and can be immediately applied to current noisy quantum computers. To demonstrate this, we present results from cloud experiments on IBM's superconducting quantum computers. The results indicate that the state preparation error rate is also an important metric for qubit metrology that can be efficiently obtained.
We experimentally study error mitigation and finite-shot sampling on superconducting quantum hardware under a constrained execution budget. The study combines calibration-aware qubit selection, circuit-depth scaling, zero-noise extrapolation, dynamical decoupling, readout-error mitigation, and repeated-shot estimation on an IBM Quantum processor. Experiments are organized across ideal simulation, noise-model simulation, and physical-device execution to separate sampling uncertainty from device-induced error. We investigate how mitigation performance changes with circuit depth, effective noise scale, qubit connectivity, and measurement budget, and quantify accuracy using expectation-value error, mean-squared error, statistical uncertainty, and mitigation gain. A fixed hardware-execution budget is used to evaluate shot allocation strategies and repeated measurements without relying on unlimited sampling. The resulting analysis provides a hardware-aware characterization of when mitigation improves expectation-value estimation and when finite-shot fluctuations offset the benefit of additional mitigation overhead. The implementation uses contemporary Qiskit and IBM Quantum Runtime workflows and is designed to provide reproducible experimental evidence for error-mitigation studies on current quantum processors.