We show that combining quantum error detection (QED) with probabilistic error cancellation (PEC) gives more accurate and lower-variance estimates than PEC alone, provided that the symmetry measurements required for QED are carefully chosen. Because noisy symmetry measurements can negate the benefits of the PEC+QED approach, we cast the selection of measurement configurations as a classical optimization problem that systematically suppresses the impact of noise. Applying optimized PEC+QED to GHZ-state output distributions and to simulating the time-dynamics of a generalized superfast encoded Fermi-Hubbard model, we find consistent improvements over PEC. For GHZ states, the optimization over symmetry measurement configurations is essential for achieving an advantage. For the Fermi-Hubbard model, PEC+QED improves observable estimation on a $2 \times 2$ lattice and for larger systems the mitigation overheads can be reduced by measuring only subsets of stabilizers. Our results demonstrate the importance of circuit-specific tailoring of QEM techniques and that fault-tolerant design principles may already provide value for near-term devices.
We show that combining quantum error detection (QED) with probabilistic error cancellation (PEC) gives more accurate and lower-variance estimates than PEC alone, provided that the symmetry measurements required for QED are carefully chosen. Because noisy symmetry measurements can negate the benefits of the PEC+QED approach, we cast the selection of measurement configurations as a classical optimization problem that systematically suppresses the impact of noise. Applying optimized PEC+QED to GHZ-state output distributions and to simulating the time-dynamics of a generalized superfast encoded Fermi-Hubbard model, we find consistent improvements over PEC. For GHZ states, the optimization over symmetry measurement configurations is essential for achieving an advantage. For the Fermi-Hubbard model, PEC+QED improves observable estimation on a 2×2 lattice and for larger systems the mitigation overheads can be reduced by measuring only subsets of stabilizers. Our results demonstrate the importance of circuit-specific tailoring of QEM techniques and that fault-tolerant design principles may already provide value for near-term devices.
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.
Quantum error mitigation (QEM) has emerged as a powerful tool for the extraction of useful quantum information from quantum devices. Here, we introduce the Subspace Noise Tailoring (SNT) algorithm, which efficiently combines the cheap cost of Symmetry Verification (SV) and low bias of Probabilistic Error Cancellation (PEC) QEM techniques. We study the performance of our method by simulating the Trotterized time evolution of the spin-1/2 Fermi-Hubbard model (FHM) using a variety of local fermion-to-qubit encodings, which define a computational subspace through a set of stabilizers, the measurement of which can be used to post-select noisy quantum data. We study different combinations of QEM and encodings and uncover a rich state diagram of optimal combinations, depending on the hardware performance, system size and available shot budget. We then demonstrate how SNT extends the reach of current noisy quantum computers in terms of the number of fermionic lattice sites and the number of Trotter steps, and quantify the required hardware performance beyond which a noisy device may compete with current state-of-the-art classical computational methods.
Near-term quantum workloads demand error management, yet the two lightest-weight techniques, Quantum Error Detection (QED) and Probabilistic Error Cancellation (PEC), have complementary cost profiles whose joint architectural design space remains unexplored. QED encodes logical qubits and discards error-flagged runs, filtering noise with low qubit overhead but leaving residual errors; PEC can correct these in software, but at exponential cost in noise strength. If QED efficiently reduces per-gate noise, PEC's cost savings can outweigh QED's discard overhead; realizing this, however, requires solving two system-level design challenges.
First, the \textit{QED interval} -- how often detection cycles are inserted -- is a tunable architectural parameter governing the cost-accuracy tradeoff. We derive an efficiency condition and show that the canonical one-cycle-per-gate frequency does not achieve break-even in any code we evaluate, while optimized intervals on high-rate Iceberg codes do. Second, we discover that naive PEC+QED integration \textit{degrades} accuracy below the QED-only baseline. The root cause is a transient error profile in the first detection cycle that corrupts PEC's noise model. We develop \textit{steady-state extraction}, a co-designed characterization protocol that isolates steady-state error behavior, reducing estimation bias by up to 10.2×. On a [[6,4,2]] Iceberg code running QAOA (p=4--8) with a fixed shot budget, PEC+QED achieves 2--11× lower absolute error and up to 31× lower MSE versus PEC on physical qubits, with per-interval savings compounding over interval depth.
Assessing whether a noisy quantum device can potentially exhibit quantum advantage is essential for selecting practical quantum utility tasks that are not efficiently verifiable by classical means. For optimization, a prominent candidate for quantum advantage, entropy benchmarking provides insights based concomitantly on the specifics of the application and its implementation, as well as hardware noise. However, such an approach still does not account for finite-shot effects or for quantum error mitigation (QEM), a key near-term error suppression strategy that reduces estimation bias at the cost of increased sampling overhead. We address this limitation by developing a benchmarking framework that explicitly incorporates finite-shot statistics and the resource overhead induced by QEM. Our framework quantifies quantum advantage through the confidence that an estimated energy lies within an interval defined by the best-known classical upper and lower bounds. Using a proof-of-principle numerical study of the two-dimensional Fermi-Hubbard model at size 8×8, we demonstrate that the framework effectively identifies noise and shot-budget regimes in which the probabilistic error cancellation (PEC), a representative QEM method, is operationally advantageous, and potential quantum advantage is not hindered by finite-shot effects. Overall, our approach equips end-users with a framework based on lightweight numerics for assessing potential practical quantum advantage in optimization on near-future quantum hardware, in light of the allocated shot budget.
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 (QEM) bridges the gap between today's noisy NISQ hardware and fault-tolerant quantum computing by reducing the effect of hardware errors on expectation value estimates without the qubit overhead of full quantum error correction. This paper proposes the Quantum Error Mitigation Design (QEMD) framework, a systematic evaluation of six QEM techniques across four circuit families on IBM Quantum Eagle and IonQ Forte: Zero-Noise Extrapolation (ZNE), Probabilistic Error Cancellation (PEC), Clifford Data Regression (CDR), Symmetry Verification (SV), Dynamical Decoupling (DD), and a novel Adaptive Ensemble Mitigation (AEM) combining ZNE and CDR with context-aware technique selection. QEMD finds: ZNE 3-point Richardson provides the best cost-performance trade-off for QAOA and VQE circuits (4.8x overhead, 28.4pp error reduction); PEC provides the highest accuracy but at 48x shot overhead -- practical only for n <= 12; DD reduces coherence-limited errors by 18.4% on IonQ Forte at zero shot overhead; AEM outperforms all individual techniques by 6.4pp at 8.4x overhead. QEMD provides a decision guide mapping circuit type, qubit count, and shot budget to optimal QEM technique selection.