arXiv:2607.25704

Verifiable blind probabilistic error cancellation

Bo Yang, Elham Kashefi, Harold Ollivier

quant-phcs.CRSubmitted Jul 28, 2026• Announced Jul 29, 2026• 0 citations

Abstract

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.

Comments: 29 pages, 7 figures

Related papers

Verifiable blind observable estimation

Bo Yang, Elham Kashefi, Harold Ollivier

Abstract Cryptographic verification is essential for establishing trust in quantum-computing-as-a-service. However, a fundamental gap exists in the current verification landscape: existing efficient protocols are largely restricted to decision problems where correctness is boosted by classical majority voting. This excludes observable estimation, the statistical task underpinning nearly all near-term quantum advantage applications. For such tasks, current verification techniques face a prohibitive trade-off: either weak security guarantees or massive space overhead that exceeds the capacity of near-term hardware. To resolve this, we introduce the Secure Delegated Observable Estimation (SDOE) ideal resource, the first formal cryptographic framework for trustworthy expectation-value estimation within Abstract Cryptography. We then present the Verifiable Blind Observable Estimation (VBOE) protocol, which efficiently constructs this resource. VBOE circumvents the limitations inherent in prior methodologies by enabling the sequential collection of samples with negligible security error, requiring zero extra qubit overhead. By directly averaging computation rounds in classical post-processing, our protocol provides the only known path to rigorous, composable verification for the most common class of near-term quantum-classical hybrid algorithms. This work bridges foundational cryptographic theory with practical quantum tasks, enabling the certification of quantum utility on current and near-future devices.

arXiv:2510.08548Mar 5, 20260 citations

Optimizing Resource Costs: A Practical Guide to Achieving Target Security in Verifiable Blind Quantum Computing

Janice van Dam, Michał van Hooft, Stephanie D. C. Wehner

Verifiable blind quantum computing (VBQC) enables a resource-limited client to securely delegate computations to an untrusted quantum server while maintaining privacy and detecting deviations from the prescribed computation. The noise-robust VBQC protocol of Leichtle et al. achieves this through a round-based structure: the client delegates multiple computation rounds and test rounds, using the test outcomes to detect cheating while tolerating honest hardware noise. The protocol's security proof involves numerous interdependent parameters, making it non-trivial to find a valid parameter set for a given hardware noise level and security target. We formalize this as a constrained optimization problem and develop a practical framework to solve it. The framework yields the protocol parameters that minimize the number of rounds for any given setup. We derive a heuristic formula for the minimal number of rounds to help understand the scaling with noise and security targets and to provide rapid resource estimation. Since the number of rounds depends on noise while the time per round depends on hardware rate, the framework also enables optimization of rate-fidelity trade-offs to minimize end-to-end runtime. We demonstrate both applications through a case study of a trapped-ion server with a measurement-only client, showing how the client's polarization control hardware specifications translate into protocol parameters and runtime estimates, providing concrete guidance for near-term implementations.

quant-pharXiv:2606.28139Jun 29, 20260 citations

Quantum Error Correction on Error-mitigated Physical Qubits

Minjun Jeon, Zhenyu Cai

We present a general framework for applying linear quantum error mitigation (QEM) techniques directly to physical qubits within a logical qubit to suppress logical errors. By exploiting the linearity of quantum error correction (QEC), we demonstrate that any linear QEM method$\unicode{x2014}$including probabilistic error cancellation (PEC), zero-noise extrapolation (ZNE), and symmetry verification$\unicode{x2014}$can be integrated into the physical layer without requiring modifications to the subsequent QEC decoder. Applying this framework to memory experiments using PEC, we analytically prove and numerically verify that the leading-order contribution to the logical error can be removed, increasing the effective code distance by 2. Our simulations on repetition and rotated surface codes show that a distance-3 code with physical-level PEC achieves logical error rates lower than or similar to a distance-5 unmitigated code while using 40% and 64% fewer qubits, respectively. These results establish physical-level QEM as a widely compatible and resource-efficient strategy for enhancing logical performance in early fault-tolerant architectures.

quant-pharXiv:2601.18384Jan 27, 20260 citations

A Novel Approach for Mitigating Gate- Level Noise in IBM Quantum Hardware via Zero Noise Extrapolation (ZNE) and Probabilistic Error Cancellation (PEC) Techniques

Mohammed Suhaib, V. Karthick, D. Maria Monica

Abstract The practical application of Noisy Intermediate-Scale Quantum (NISQ) hardware is fundamentally limited by gate-level noise, which corrupts computational results. This research addresses this challenge through the development and validation of a modular software framework for Quantum Error Mitigation (QEM). We implement and compare two leading QEM strategies: Zero-Noise Extrapolation (ZNE) and Probabilistic Error Cancellation (PEC). The framework is built using the Qiskit library and is validated using a realistic, hardware-calibrated noisy simulator that mimics the error characteristics of a real IBM Quantum device. Our methodology focuses on a robust implementation of ZNE via unitary folding and a proof-of-concept demonstration of the PEC algorithm. The framework's effectiveness is demonstrated on a simulated noisy backend where, for a 3-qubit Greenberger-Horne-Zeilinger (GHZ) state, the baseline state fidelity was increased from 93.5% to 97.3% via ZNE, corresponding to a 59% reduction in the state's infidelity. This work provides a practical demonstration of how software-based error mitigation can enhance the reliability of quantum computations on current noisy hardware.

Dec 8, 20251 citation

Verifying BQP Computations on Noisy Devices with Minimal Overhead

Dominik Leichtle, Luka Music, Elham Kashefi +1 more

With the development of delegated quantum computation, clients will want to ensure confidentiality of their data and algorithms and the integrity of their computations.While protocols for blind and verifiable quantum computation exist, they suffer from high overheads and from oversensitivity: when running on noisy devices, imperfections trigger the same detection mechanisms as malicious attacks, resulting in perpetually aborted computations.We introduce the first blind and verifiable protocol for delegating bounded-error quantum polynomial (BQP) computations to a powerful server, with repetition as the only overhead.It is composable and statistically secure with exponentially low bounds and can tolerate a constant amount of global noise.

arXiv:2109.04042PRX QuantumOct 4, 202142 citations

Error Mitigation of Fault-Tolerant Quantum Circuits with Soft Information

Zeyuan Zhou, Shaun Pexton, Aleksander Kubica +1 more

Quantum error mitigation (QEM) is typically viewed as a suite of practical techniques for today's noisy intermediate-scale quantum devices, with limited relevance once fault-tolerant quantum computers become available. In this work, we challenge this conventional wisdom by showing that QEM can continue to provide substantial benefits in the era of quantum error correction (QEC), and in an even more efficient manner than it does on current devices. We introduce a framework for logical-level QEM that leverages soft information naturally produced by QEC decoders, requiring no additional data, hardware modifications, or runtime overhead beyond what QEC protocols already provide. Within this framework, we develop and analyze three logical-level QEM techniques: post-selection and runtime abort policies, probabilistic error cancellation, and zero-noise extrapolation. Our techniques reduce logical error rates by more than 100x while discarding fewer than 0.1% of shots; they also provide in situ characterization of logical channels for QEM protocols. As a proof of principle, we benchmark our approach using a surface-code architecture and two state-of-the-art decoders based on tensor-network contraction and minimum-weight perfect matching. We evaluate logical-level QEM on random Clifford circuits and molecular simulation algorithms and find that, compared to previous approaches relying on QEC only or QEC combined with QEM, we can achieve up to 87.4% spacetime overhead savings. Our results demonstrate that logical-level QEM with QEC decoder soft information can reliably improve logical performance, underscoring the efficiency and usefulness of QEM techniques for fault-tolerant quantum computers.

quant-pharXiv:2512.09863Dec 11, 20250 citations