Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2608.18332

Generalizing Pauli Checks for Qudit-based Quantum Error Detection and Mitigation

Noble Agyeman-Bobie, Quinn Langfitt, Salahedeen Issa, Nikos Hardavellas, Kaitlin N. Smith

quant-phSubmitted Aug 18, 2026• Announced Aug 20, 2026• Revised Sep 23, 2026 (v2)
v1 · Aug 18, 2026v2 · Sep 23, 2026
arXivHTMLPDF

Abstract

Pauli Check Sandwiching (PCS) is a quantum error detection (QED) technique that protects a quantum circuit by utilizing a pair of controlled Pauli operators, or checks, and detecting errors that anti-commute with the checks. Further, PCS can be used for quantum error mitigation (QEM) via post-selection based on the Pauli check syndrome values. Currently, PCS is leveraged in the qubit space. In this paper, we introduce a generalized approach for applying PCS-based QED and QEM to quantum information of arbitrary dimension in the Hilbert space. Each pair of these extended checks consists of a sequence of gates in the Heisenberg-Weyl operator set that extend Pauli operators into the qudit space. These qudit checks use at least one ancilla qudit to detect qudit errors that do not commute with the unitary selected for the check. We show that our proposed methods for qudit QED can detect errors of arbitrary dimensions. More specifically, we prove that an arbitrary Heisenberg-Weyl error maps deterministically to a unique ancilla readout, and further, post-selecting on the $|0 \rangle$ readout guarantees unit fidelity in the noiseless check limit. We validate these findings numerically across dimensions $d=2$ through $d=9$, achieving error-mitigated fidelities above $97.5\% $ under realistic depolarizing error rates.

Comments
11 pages, 13 figures. Accepted to the 2026 IEEE International Conference on Quantum Computing and Engineering (QCE), IEEE Quantum Week 2026

Related papers

Quantum error mitigation by Pauli check sandwiching

Alvin Gonzales, Ruslan Shaydulin, Zain H. Saleem +1 more

We describe and analyze an error mitigation technique that uses multiple pairs of parity checks to detect the presence of errors. Each pair of checks uses one ancilla qubit to detect a component of the error operator and represents one layer of the technique. We build on the results on extended flag gadgets and put it on a firm theoretical foundation. We prove that this technique can recover the noiseless state under the assumption of noise not affecting the checks. The method does not incur any encoding overhead and instead chooses the checks based on the input circuit. We provide an algorithm for obtaining such checks for an arbitrary target circuit. Since the method applies to any circuit and input state, it can be easily combined with other error mitigation techniques. We evaluate the performance of the proposed methods using extensive numerical simulations on 1850 random input circuits composed of Clifford gates and non-Clifford single-qubit rotations, a class of circuits encompassing most commonly considered variational algorithm circuits. We observe average improvements in fidelity of 34 percentage points with six layers of checks.

arXiv:2206.00215•Scientific Reports•Feb 6, 2023•26 citations

Pauli Check Sandwiching for Quantum Characterization and Error Mitigation during Runtime

Joshua Gao, Ji Liu, Alvin Gonzales +3 more

This work presents a novel quantum system characterization and error mitigation framework that applies Pauli check sandwiching (PCS). We motivate our work with prior art in software optimizations for quantum programs like noise-adaptive mapping and multi-programming, and we introduce the concept of PCS while emphasizing design considerations for its practical use. We show that by carefully embedding Pauli checks within a target application (i.e. a quantum circuit), we can learn quantum system noise profiles. Further, PCS combined with multi-programming unlocks non-trivial fidelity improvements.

IEEE International Conference on Quantum Computing and Engineering (QCE)•Sep 15, 2024•0 citations

Pauli Check Extrapolation for Quantum Error Mitigation

Quinn Langfitt, Ji Liu, Benchen Huang +4 more

Pauli Check Sandwiching (PCS) is an error mitigation scheme that uses pairs of parity checks to detect errors in the payload circuit. While increasing the number of check pairs improves error detection, it also introduces additional noise to the circuit and exponentially increases the required sampling size. To address these limitations, we propose a novel error mitigation scheme, Pauli Check Extrapolation (PCE), which integrates PCS with an extrapolation technique similar to Zero-Noise Extrapolation (ZNE). However, instead of extrapolating to the ‘zero-noise’ limit, as is done in ZNE, PCE extrapolates to the ‘maximum check’ limit-the number of check pairs theoretically required to achieve unit fidelity. In this study, we focus on applying a linear model for extrapolation and also derive a more general exponential ansatz based on the Markovian error model. We demonstrate the effectiveness of PCE by using it to mitigate errors in the shadow estimation protocol, particularly for states prepared by the variational quantum eigensolver (VQE). Our results show that this method can achieve higher fidelities than the state-of-the-art Robust Shadow (RS) estimation scheme, while significantly reducing the number of required samples by eliminating the need for a calibration procedure. We validate these findings on both fully-connected topologies and simulated IBM hardware backends.

IEEE International Conference on Quantum Computing and Engineering (QCE)•Sep 15, 2024•1 citation

Detecting errors in a quantum network with Pauli checks

Alvin Gonzales, Daniel Dilley, Bikun Li +2 more

We apply the quantum error detection scheme Pauli check sandwiching (PCS) to quantum networks by turning it into a distributed multiparty protocol. PCS provides protection on the targeted qubits and generally requires less resource overhead than standard quantum error correction and detection codes. We provide analytical equations for the final fidelity and postselection rate for different PCS checks. We also introduce a recursive version of PCS that generates a family of distance 2 quantum codes that are locally equivalent to Calderbank--Shor--Steane (CSS) codes. Our analytical results are benchmarked against the Bennet-Brassard--Popescu--Schumacher--Smolin--Wooters (BBPSSW) protocol in comparable scenarios. We also perform simulations with noisy gates for entanglement swapping and attain fidelity improvements. Lastly, we discuss various setups and graph state properties of PCS.

arXiv:2405.15236•Physical Review A•May 30, 2025•3 citations

Extrapolating Pauli Checks for Expectation Value Estimation on Noisy Quantum Devices

Quinn Langfitt, Ji Liu, Benchen Huang +4 more

Pauli Check Sandwiching (PCS) is an error detection scheme that protects quantum circuits by inserting pairs of parity checks and discarding runs that signal errors. However, each additional check introduces noise and exponentially increases sampling costs. To address these limitations, we propose Pauli Check Extrapolation (PCE), an error mitigation technique that obtains measured expectation values from circuits with different numbers of checks and, analogous to ZNE, extrapolates to the “maximum check” limit - the theoretical number of checks required for unit fidelity. We test linear and exponential ansatzes, deriving the exponential form from the Markovian error model. Benchmarking PCE against ZNE on random Clifford circuits with simulated depolarizing noise shows PCE outperforming ZNE for larger circuits. On real IBM hardware, PCE achieves an accuracy of up to 99.2% (56.2% improvement over baseline), compared to ZNE's 82% accuracy (29.1% improvement over baseline), for 4-qubit circuits. To demonstrate a practical use case, we then apply PCE towards mitigating errors in classical shadow measurements. Our results show that PCE can achieve fidelities greater than the state-of-the-art Robust Shadow estimation, while significantly reducing the number of required samples by eliminating the need for a calibration procedure. We validate these findings on both fully connected topologies and simulated IBM hardware backends.

arXiv:2406.14759•IEEE Transactions on Quantum Engineering•Jan 1, 2026•0 citations

Single-shot error mitigation by coherent Pauli checks

E. van den Berg, Sergey B. Bravyi, Jay Gambetta +3 more

Generating samples from the output distribution of a quantum circuit is a ubiquitous task used as a building block of many quantum algorithms. Here we show how to accomplish this task on a noisy quantum processor lacking full-blown error correction for a special class of quantum circuits dominated by Clifford gates. Our approach is based on Coherent Pauli Checks (CPCs) that detect errors in a Clifford circuit by verifying commutation rules between random Pauli-type check operators and the considered circuit. Our main contributions are as follows. First, we derive a simple formula for the probability that a Clifford circuit protected by CPCs contains a logical error. In the limit of a large number of checks, the logical error probability is shown to approach the value ${\approx}7εn/5$, where $n$ is the number of qubits and $ε$ is the depolarizing error rate. Our formula agrees nearly perfectly with the numerical simulation results. Second, we show that CPCs are well-suited for quantum processors with a limited qubit connectivity. For example, the difference between all-to-all and linear qubit connectivity is only a 3X increase in the number of CNOT gates required to implement CPCs. Third, we describe simplified one-sided CPCs which are well-suited for mitigating measurement errors in the single-shot settings. Finally, we report an experimental demonstration of CPCs with up to 10 logical qubits and more than 100 logical CNOT gates. Our experimental results show that CPCs provide a marked improvement in the logical error probability for the considered task of sampling the output distribution of quantum circuits.

arXiv:2212.03937•Dec 7, 2022•2 citations
Pauli Check Sandwiching (PCS) is a quantum error detection (QED) technique that protects a quantum circuit by utilizing a pair of controlled Pauli operators, or checks, and detecting errors that anti-commute with the checks. Further, PCS can be used for quantum error mitigation (QEM) via post-selection based on the Pauli check syndrome values. Currently, PCS is leveraged in the qubit space. In this paper, we introduce a generalized approach for applying PCS-based QED and QEM to quantum information of arbitrary dimension in the Hilbert space. Each pair of these extended checks consists of a sequence of gates in the Heisenberg-Weyl operator set that extend Pauli operators into the qudit space. These qudit checks use at least one ancilla qudit to detect qudit errors that do not commute with the unitary selected for the check. We show that our proposed methods for qudit QED can detect errors of arbitrary dimensions. More specifically, we prove that an arbitrary Heisenberg-Weyl error maps deterministically to a unique ancilla readout, and further, post-selecting on the ∣0⟩|0 \rangle∣0⟩ readout guarantees unit fidelity in the noiseless check limit. We validate these findings numerically across dimensions d=2d=2d=2 through d=9d=9d=9, achieving error-mitigated fidelities above 97.5%97.5\% 97.5% under realistic depolarizing error rates.
We describe and analyze an error mitigation technique that uses multiple pairs of parity checks to detect the presence of errors. Each pair of checks uses one ancilla qubit to detect a component of the error operator and represents one layer of the technique. We build on the results on extended flag gadgets and put it on a firm theoretical foundation. We prove that this technique can recover the noiseless state under the assumption of noise not affecting the checks. The method does not incur any encoding overhead and instead chooses the checks based on the input circuit. We provide an algorithm for obtaining such checks for an arbitrary target circuit. Since the method applies to any circuit and input state, it can be easily combined with other error mitigation techniques. We evaluate the performance of the proposed methods using extensive numerical simulations on 1850 random input circuits composed of Clifford gates and non-Clifford single-qubit rotations, a class of circuits encompassing most commonly considered variational algorithm circuits. We observe average improvements in fidelity of 34 percentage points with six layers of checks.
This work presents a novel quantum system characterization and error mitigation framework that applies Pauli check sandwiching (PCS). We motivate our work with prior art in software optimizations for quantum programs like noise-adaptive mapping and multi-programming, and we introduce the concept of PCS while emphasizing design considerations for its practical use. We show that by carefully embedding Pauli checks within a target application (i.e. a quantum circuit), we can learn quantum system noise profiles. Further, PCS combined with multi-programming unlocks non-trivial fidelity improvements.
Pauli Check Sandwiching (PCS) is an error mitigation scheme that uses pairs of parity checks to detect errors in the payload circuit. While increasing the number of check pairs improves error detection, it also introduces additional noise to the circuit and exponentially increases the required sampling size. To address these limitations, we propose a novel error mitigation scheme, Pauli Check Extrapolation (PCE), which integrates PCS with an extrapolation technique similar to Zero-Noise Extrapolation (ZNE). However, instead of extrapolating to the ‘zero-noise’ limit, as is done in ZNE, PCE extrapolates to the ‘maximum check’ limit-the number of check pairs theoretically required to achieve unit fidelity. In this study, we focus on applying a linear model for extrapolation and also derive a more general exponential ansatz based on the Markovian error model. We demonstrate the effectiveness of PCE by using it to mitigate errors in the shadow estimation protocol, particularly for states prepared by the variational quantum eigensolver (VQE). Our results show that this method can achieve higher fidelities than the state-of-the-art Robust Shadow (RS) estimation scheme, while significantly reducing the number of required samples by eliminating the need for a calibration procedure. We validate these findings on both fully-connected topologies and simulated IBM hardware backends.
We apply the quantum error detection scheme Pauli check sandwiching (PCS) to quantum networks by turning it into a distributed multiparty protocol. PCS provides protection on the targeted qubits and generally requires less resource overhead than standard quantum error correction and detection codes. We provide analytical equations for the final fidelity and postselection rate for different PCS checks. We also introduce a recursive version of PCS that generates a family of distance 2 quantum codes that are locally equivalent to Calderbank--Shor--Steane (CSS) codes. Our analytical results are benchmarked against the Bennet-Brassard--Popescu--Schumacher--Smolin--Wooters (BBPSSW) protocol in comparable scenarios. We also perform simulations with noisy gates for entanglement swapping and attain fidelity improvements. Lastly, we discuss various setups and graph state properties of PCS.
Pauli Check Sandwiching (PCS) is an error detection scheme that protects quantum circuits by inserting pairs of parity checks and discarding runs that signal errors. However, each additional check introduces noise and exponentially increases sampling costs. To address these limitations, we propose Pauli Check Extrapolation (PCE), an error mitigation technique that obtains measured expectation values from circuits with different numbers of checks and, analogous to ZNE, extrapolates to the “maximum check” limit - the theoretical number of checks required for unit fidelity. We test linear and exponential ansatzes, deriving the exponential form from the Markovian error model. Benchmarking PCE against ZNE on random Clifford circuits with simulated depolarizing noise shows PCE outperforming ZNE for larger circuits. On real IBM hardware, PCE achieves an accuracy of up to 99.2% (56.2% improvement over baseline), compared to ZNE's 82% accuracy (29.1% improvement over baseline), for 4-qubit circuits. To demonstrate a practical use case, we then apply PCE towards mitigating errors in classical shadow measurements. Our results show that PCE can achieve fidelities greater than the state-of-the-art Robust Shadow estimation, while significantly reducing the number of required samples by eliminating the need for a calibration procedure. We validate these findings on both fully connected topologies and simulated IBM hardware backends.
Generating samples from the output distribution of a quantum circuit is a ubiquitous task used as a building block of many quantum algorithms. Here we show how to accomplish this task on a noisy quantum processor lacking full-blown error correction for a special class of quantum circuits dominated by Clifford gates. Our approach is based on Coherent Pauli Checks (CPCs) that detect errors in a Clifford circuit by verifying commutation rules between random Pauli-type check operators and the considered circuit. Our main contributions are as follows. First, we derive a simple formula for the probability that a Clifford circuit protected by CPCs contains a logical error. In the limit of a large number of checks, the logical error probability is shown to approach the value ≈7εn/5{\approx}7εn/5≈7εn/5, where nnn is the number of qubits and εεε is the depolarizing error rate. Our formula agrees nearly perfectly with the numerical simulation results. Second, we show that CPCs are well-suited for quantum processors with a limited qubit connectivity. For example, the difference between all-to-all and linear qubit connectivity is only a 3X increase in the number of CNOT gates required to implement CPCs. Third, we describe simplified one-sided CPCs which are well-suited for mitigating measurement errors in the single-shot settings. Finally, we report an experimental demonstration of CPCs with up to 10 logical qubits and more than 100 logical CNOT gates. Our experimental results show that CPCs provide a marked improvement in the logical error probability for the considered task of sampling the output distribution of quantum circuits.