Probabilistic Error Cancellation (PEC) is a standard technique for mitigating noise in quantum computations, but its unbiasedness relies on accurate knowledge of the underlying noise parameters. In practice, these parameters are inferred from experimental data and may be inaccurate. We introduce a protocol that tests PEC parameter consistency on hardware by applying Direct Fidelity Estimation (DFE) to the effective mitigated state. The resulting DFE overlap serves not only as a witness of parameter miscalibration but, under appropriate conditions, also reveals whether the PEC parameters have been overestimated or underestimated. We establish this behavior for arbitrary circuits under global depolarizing noise and for Clifford circuits under general Pauli-stochastic noise. For arbitrary circuits subject to Pauli-stochastic noise, the underestimation result holds generally, while the corresponding overestimation result is established perturbatively for sufficiently small consistent miscalibrations under an additional nondegeneracy condition. We further show that the purity of the effective mitigated operator provides a more general diagnostic, allowing the miscalibration direction to be identified for arbitrary circuits and arbitrary parameter deviations. Finally, we describe a two-copy PEC procedure for measuring this quantity and show that, together with the DFE overlap, it determines the Hilbert-Schmidt distance from the ideal state. The sampling overhead incurred by our protocol is the same as that of PEC, and we discuss strategies to improve it.
Probabilistic Error Cancellation (PEC) is a standard technique for mitigating noise in quantum computations, but its unbiasedness relies on accurate knowledge of the underlying noise parameters. In practice, these parameters are inferred from experimental data and may be inaccurate. We introduce a protocol that tests PEC parameter consistency on hardware by applying Direct Fidelity Estimation (DFE) to the effective mitigated state. The resulting DFE overlap serves not only as a witness of parameter miscalibration but, under appropriate conditions, also reveals whether the PEC parameters have been overestimated or underestimated. We establish this behavior for arbitrary circuits under global depolarizing noise and for Clifford circuits under general Pauli-stochastic noise. For arbitrary circuits subject to Pauli-stochastic noise, the underestimation result holds generally, while the corresponding overestimation result is established perturbatively for sufficiently small consistent miscalibrations under an additional nondegeneracy condition. We further show that the purity of the effective mitigated operator provides a more general diagnostic, allowing the miscalibration direction to be identified for arbitrary circuits and arbitrary parameter deviations. Finally, we describe a two-copy PEC procedure for measuring this quantity and show that, together with the DFE overlap, it determines the Hilbert-Schmidt distance from the ideal state. The sampling overhead incurred by our protocol is the same as that of PEC, and we discuss strategies to improve it.
Quantum error mitigation (QEM) is an essential tool for mitigating hardware noise without incurring space overhead. Yet, its reliability depends on modeling, calibration, and implementation, leaving end-to-end security on untrusted quantum hardware unresolved. We address this problem by introducing verifiable blind probabilistic error cancellation (VBPEC), the first secure verification protocol against a fully malicious adversary that integrates QEM. VBPEC brings probabilistic error cancellation (PEC), a widely studied QEM technique, within the scope of composable security by formalizing delegated mitigation as a cryptographic resource in the abstract cryptography framework. The protocol performs PEC with perfect blindness and an exponentially small security error. VBPEC retains the absence of quantum-space overhead from recent statistically-secure verified quantum computation protocols and from PEC. The only overhead takes the form of additional repetitions due to the QEM procedure. To achieve this, we extend trap-based verification from deterministic pass/fail checks to statistical tests that benefit from QEM and develop a new proof technique that integrates the corresponding additional deviation sources. Rather than merely tolerating honest noise below a fixed threshold, VBPEC actively cancels it, enabling correctly mitigated estimates to be accepted with high probability without compromising security. Our framework thus establishes an essential route towards secure, reliable, and practical delegated quantum computation on near-future quantum hardware: VBPEC fundamentally improves the practicality of verification.
Quantum error mitigation is regarded as a possible path to near-term quantum utility. The methods under the quantum error mitigation umbrella term, such as probabilistic error cancellation (PEC), zero-noise extrapolation (ZNE) or Clifford data regression (CDR) are able to significantly reduce the error for the estimation of expectation values, although at an exponentially scaling cost, i.e., in the sampling overhead. In this work, we present a method to reduce the sampling overhead of PEC through Pauli error propagation combined with classical preprocessing. Our findings indicate that this method significantly reduces sampling overheads for Clifford circuits, leveraging the well-defined interaction between the Clifford group and Pauli noise. Additionally, we show that the method is applicable to non-Clifford circuits, though with more limited effectiveness, primarily constrained by the number of non-Clifford gates present in the circuit. We further provide examples of Clifford sub-circuits commonly encountered in relevant calculations, such as resource state generation in measurement-based quantum computing.
Probabilistic error cancellation (PEC) is unbiased but suffers exponential sampling overhead set by noise-weighted circuit volume, whereas quantum error-detecting codes (QEDCs) remove many physical faults by stabilizer post-selection but leave an undetectable logical residue. We exploit this complementarity by using post-selection to map physical noise to a weaker accepted logical channel, and then applying PEC only to the residual channel. The resulting feedback-free QED+PEC scheme interleaves Clifford logical blocks, stabilizer measurements, post-selection, and probabilistic cancellation on accepted trajectories, without real-time decoding or active recovery. A key complication is that post-selection correlates accepted fault branches through stabilizer-commutation constraints, so the sparse Pauli-Lindblad factorization underlying bare PEC no longer applies directly. We therefore construct the inverse channel perturbatively: for fixed order K, only accepted fault branches up to order K are retained, reducing preprocessing from 2m branches to O(mK) per block. The order-K protocol cancels the normalized post-selected channel through degree K, leaving a per-block error O(WK+1) that accumulates at most linearly. For logical GHZ-state preparation with the [[n,n−2,2]] Iceberg code under circuit-level depolarizing noise and ideal stabilizer measurements, first-order QED+PEC reaches n=200 physical qubits and lowers sampling overhead by three to four orders of magnitude relative to standard PEC while maintaining F≃0.956. Syndrome-noise tests show that readout-only flips mainly increase post-selection cost, whereas noisy GHZ-assisted global stabilizer extraction can remove the advantage. This identifies a discrete-Zeno trade-off: cheap detection reshapes the effective channel PEC must invert, rather than simply adding overhead.
Probabilistic error cancellation (PEC) is a leading quantum error mitigation method that provides an unbiased estimate, although it is known to have a large sampling overhead. In this work, we propose a new method to perform PEC, which results in a lower sampling cost than the standard way. It works by decomposing the inverse channel of each gate or each circuit layer into the identity part and the non-identity part and reorganizing the full circuit as different powers of the inverse generator. The ideal circuit becomes a linear combination of noisy circuits with different weights where shots are deterministically allocated to each circuit based on its weight. This naturally sets the achievable bias given a finite amount of shots. As the number of shots is increased, smaller bias terms can be gradually resolved and become bias-free in the limit of sufficient shots. We show the saving both analytically and numerically over the standard PEC and identify situations where it can outperform heuristic approach, such as zero-noise extrapolation, due to the well-controlled bias. We also demonstrated this method experimentally and found excellent agreement between the mitigated and the ideal values.
Probabilistic error cancellation (PEC) is a technique that generates error-mitigated estimates of expectation values from ensembles of quantum circuits. In this work we extend the application of PEC from unitary-only circuits to dynamic circuits with midcircuit measurements and classically controlled (feedforward) Clifford operations. Our approach extends the sparse Pauli-Lindblad noise model from characterizing gates to characterizing target channels containing midcircuit measurements and feedforward while accounting for nonlocal measurement crosstalk in superconducting processors. Our mitigation and monitoring experiments provide a holistic view for the performance of the protocols developed in this work. These capabilities will be a crucial tool in the exploration of near-term dynamic circuit applications.
Fidelity estimation is a fundamental tool for assessing quantum resource states across quantum information science. For small infidelity ε, tomography and direct fidelity estimation (DFE) have worst-case sample complexity O(1/ε2) at fixed relative accuracy and confidence. Direct target projections achieve O(1/ε) but generally require non-Clifford operations whose reliability depends on the resource states that are typically the target of benchmarking. Here, we introduce the Bell--coherence fidelity estimation (BCFE) with optimal sample complexity Θ(1/ε) using only Clifford gates and Pauli measurements. We prove that BCFE is applicable to arbitrary pure targets, possibly multi-qubit, with the statistical error of the single-copy coherence part explicitly controlled. To evaluate BCFE in a practical setting, we apply BCFE to analog rotation resource states in the candidate early-FTQC architecture called the Space-Time Efficient Analog Rotations (STAR) architecture. In the simulations using surface codes, BCFE is estimated to require up to approximately 27 times fewer resource states than DFE for the same standard error in the infidelity estimate, while its estimates remain close to reference values despite circuit-level noise in the additional Bell measurement operations. These results support efficient resource benchmarking within fault-tolerant quantum computing.