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:2511.22624

Recursive Clifford noise reduction

Aharon Brodutch, Gregory Baimetov, Edwin Tham, Nicolas Delfosse

quant-phSubmitted Nov 27, 2025• Announced Nov 28, 2025• 0 citations
arXivHTMLPDF

Abstract

Clifford noise reduction (CliNR) is a partial error correction scheme that reduces the logical error rate of Clifford circuits at the cost of a modest qubit and gate overhead. The CliNR implementation of an $n$-qubit Clifford circuit of size $s$ achieves a vanishing logical error rate if $snp^2\rightarrow 0$ where $p$ is the physical error rate. Here, we propose a recursive version of CliNR that can reduce errors on larger circuits with a relatively small gate overhead. When $np \rightarrow 0$, the logical error rate can be vanishingly small. This implementation requires $\left(2\left\lceil \log(sp)\right\rceil+3\right)n+1$ qubits and at most $24 s \left\lceil(sp)^4\right\rceil $ gates. Using numerical simulations, we show that the recursive method can offer an advantage in a realistic near-term parameter regime. When circuit sizes are large enough, recursive CliNR can reach a lower logical error rate than the original CliNR with the same gate overhead. The results offer promise for reducing logical errors in large Clifford circuits with relatively small overheads.

Related papers

Low-Cost Noise Reduction for Clifford Circuits

Nicolas Delfosse, Edwin Tham

We propose a Clifford noise reduction (CliNR) scheme that provides a reduction of the logical error rate of Clifford circuit with lower overhead than error correction and without the exponential sampling overhead of error mitigation. CliNR implements Clifford circuits by splitting them into subcircuits that are performed using gate teleportation. A few random stabilizer measurements are used to detect errors in the resources states consumed by the gate teleportation. This can be seen as a teleported version of the coherent parity-check scheme [1-3], with offline fault-detection making it scalable. We prove that CliNR achieves a vanishing logical error rate for families of n-qubit Clifford circuits with size s such that nsp^{2} goes to 0, where p is the physical error rate, meaning that it reaches the regime ns=o(1/p^{2}), whereas the direct implementation is limited to s=o(1/p). Moreover, CliNR uses only 3n+1 qubits, 2s+o(s) gates and has zero rejection rate. This small overhead makes it more practical than quantum error correction in the near term and our numerical simulations show that CliNR provides a reduction of the logical error rate in relevant noise regimes.

arXiv:2407.06583•Physical Review Letters•Mar 7, 2025•6 citations

Optimized Clifford Noise Reduction: Theory, Simulations and Experiments

Edwin Tham, Nicolas Delfosse

We propose several optimizations of the CliNR partial error correction scheme which implements Clifford circuits by consuming a resource state. Errors are corrected by measuring a sequence of Pauli operators that we refer to as the verification sequence. We first propose a global optimization algorithm searching for a verification sequence resulting in a low logical error rate using tabu search. Then, we introduce a proxy for the logical error rate which is easier to evaluate and we design a two-step optimization algorithm. First, a verification sequence minimizing the proxy is computed, then this sequence is refined by reintroducing the logical error rate. Finally, we identify a large group of automorphisms of the search space which preserve the proxy and we use this symmetry to reduce the size of the search space. This results in a 168 × (respectively 20,160 × ) reduction of the size of the search space for the optimization of verification sequences with three (respectively four) Pauli operators. Our numerical simulations for 20-qubit Clifford circuits with size 400 under the ion chain model show that our optimization algorithms improve the performance of CliNR by 25% and that the two-step optimization achieves the same results as the global optimization with 64% fewer evaluations of the logical error rate. Finally, we perform experiments on a 36-qubit trapped ion quantum computer, without mid-circuit measurements, showing that the CZNR variant of CliNR is at breakeven.

arXiv:2504.13356•Quantum•Aug 27, 2025•0 citations

Mid-Circuit Measurements for Clifford Noise Reduction in Hamiltonian Simulations

James Brown, Jason Iaconis, Yuri Alexeev +6 more

Quantum simulation of fermionic Hamiltonians is a leading application of quantum computing, but accurate execution on present-day hardware is limited by error accumulation in deep Trotter circuits. We present a device-matched noise-reduction framework for encoded Hamiltonian simulation that combines symplectic-transvection-based Trotter synthesis in the Generalized Superfast Encoding (GSE) with Clifford Noise Reduction (CliNR) and Shor-style stabilizer verification enabled by mid-circuit measurement. We implement this approach for a six-qubit encoded Clifford Trotter step on a Barium development system similar to the forthcoming IonQ Tempo line and benchmark it against direct execution using both hardware experiments and a calibrated device-level noise model. The encoded CliNR execution achieves up to 54% lower logical error rate. Crucially, this advantage disappears when stabilizer readout is deferred to the end of the circuit, showing that timely mid-circuit fault detection, rather than verification overhead alone, drives the improvement. As a proof of concept, we further show that machine-learning-guided stabilizer selection can identify verification operators that outperform random choices. These results demonstrate that encoding-native verification combined with dynamic-circuit primitives can materially improve application-motivated quantum simulation without the full overhead of quantum error correction.

quant-pharXiv:2605.06792•May 11, 2026•0 citations

Low-overhead error detection with spacetime codes

Simon Martiel, Ali Javadi-Abhari

We introduce a low-overhead approach for detecting errors in arbitrary Clifford circuits on arbitrary qubit connectivities. Our method is based on the framework of spacetime codes, and is particularly suited to near-term hardware since it has a much milder overhead in qubits and gates compared to error correction, while achieving a better sampling overhead than existing error mitigation methods. We present efficient algorithms for finding valid checks that are simultaneously low weight, satisfy connectivity constraints, and cover large detecting regions within the circuit. Using this approach, we experimentally demonstrate error detection on circuits of up to 50 logical qubits containing 2450 CZ gates, and show physical to logical fidelity gains of up to $236\times$. Furthermore, we show our algorithm can efficiently find checks in universal circuits, but the space of valid checks diminishes exponentially with the non-Cliffordness of the circuit. These theoretical and experimental results suggest that Clifford-dominated circuits are promising candidates for near-term quantum advantage.

arXiv:2504.15725•Apr 22, 2025•3 citations

Single-Shot Error Correction at Optimal Spacetime Cost

Kishor Bharti, Tobias Haug, Derek Khu +1 more

Recent work established that, for independent erasures, storing $K$ logical qubits for $S$ time steps with error at most $\varepsilon$ requires a spacetime cost of $Ω(S(K+\log(S/\varepsilon)))$. A matching construction was also given, but assumes ideal error correction. Here we show that the same scaling can be achieved with an explicit noisy error-correction circuit and efficient decoding, counting all state-preparation, gate, measurement, and wait locations, provided that the hardware supports long-range qubit connectivity and fast, reliable classical processing. Thus, reliability adds only a logarithmic overhead shared by all stored qubits. The construction works for sufficiently weak but otherwise general circuit noise, including faults during syndrome extraction and correlated faults, and for independent erasures it matches the best known lower bound up to constant factors. We attain this scaling using quantum Tanner codes, with each memory step consisting of one round of syndrome extraction followed by a fixed number of parallel classical decoder steps that reduce the residual error enough to keep later faults correctable, regardless of memory size, storage time, or target accuracy. Together, this gives exponentially small failure probability per step while keeping the cost of each memory step linear in the code size. The same analysis also extends to certain constant-depth logical Clifford operations.

quant-pharXiv:2610.03684•Oct 5, 2026•0 citations

Purification and correction of quantum channels by commutation-derived quantum filters

Sowmitra Das, Jinzhao Sun, Michael Hanks +2 more

Reducing errors is essential for reliable quantum computation. Quantum error mitigation (QEM) and quantum error correction (QEC) are two leading approaches for this task, each with challenges: QEM suffers from high sampling costs and cannot recover states, while QEC incurs large qubit and gate overheads. We combine ideas from both and introduce an information-theoretic device called a quantum filter that can purify or correct quantum channels. We present an explicit construction capable of correcting arbitrary noise in an n-qubit Clifford circuit using 2n ancillary qubits through a commutation-derived error-detection circuit. This scheme can also partially purify noise in non-Clifford gates such as T and CCZ. Unlike QEC, it achieves deterministic error reduction without encoding the input state. Under the assumption of clean ancillas, it overcomes the exponential sampling overhead in QEM using a single query to the channel. We also propose an ancilla-efficient Pauli filter that removes nearly all low-weight erroneous Pauli components in noisy Clifford circuits using only two ancillas. For local depolarizing noise, it achieves a quadratic reduction in average infidelity. Beyond existing QEM methods, our approach enables systematic error correction as the infidelity can be exponentially reduced with each added ancilla. Through numerical simulations under ancilla noise, we identify regimes where quantum filters outperform other techniques, demonstrating their effectiveness as a scalable error-reduction tool for quantum information processing.

arXiv:2407.20173•Jul 29, 2024•1 citation
Clifford noise reduction (CliNR) is a partial error correction scheme that reduces the logical error rate of Clifford circuits at the cost of a modest qubit and gate overhead. The CliNR implementation of an nnn-qubit Clifford circuit of size sss achieves a vanishing logical error rate if snp2→0snp^2\rightarrow 0snp2→0 where ppp is the physical error rate. Here, we propose a recursive version of CliNR that can reduce errors on larger circuits with a relatively small gate overhead. When np→0np \rightarrow 0np→0, the logical error rate can be vanishingly small. This implementation requires (2⌈log⁡(sp)⌉+3)n+1\left(2\left\lceil \log(sp)\right\rceil+3\right)n+1(2⌈log(sp)⌉+3)n+1 qubits and at most 24s⌈(sp)4⌉24 s \left\lceil(sp)^4\right\rceil 24s⌈(sp)4⌉ gates. Using numerical simulations, we show that the recursive method can offer an advantage in a realistic near-term parameter regime. When circuit sizes are large enough, recursive CliNR can reach a lower logical error rate than the original CliNR with the same gate overhead. The results offer promise for reducing logical errors in large Clifford circuits with relatively small overheads.
We propose a Clifford noise reduction (CliNR) scheme that provides a reduction of the logical error rate of Clifford circuit with lower overhead than error correction and without the exponential sampling overhead of error mitigation. CliNR implements Clifford circuits by splitting them into subcircuits that are performed using gate teleportation. A few random stabilizer measurements are used to detect errors in the resources states consumed by the gate teleportation. This can be seen as a teleported version of the coherent parity-check scheme [1-3], with offline fault-detection making it scalable. We prove that CliNR achieves a vanishing logical error rate for families of n-qubit Clifford circuits with size s such that nsp^{2} goes to 0, where p is the physical error rate, meaning that it reaches the regime ns=o(1/p^{2}), whereas the direct implementation is limited to s=o(1/p). Moreover, CliNR uses only 3n+1 qubits, 2s+o(s) gates and has zero rejection rate. This small overhead makes it more practical than quantum error correction in the near term and our numerical simulations show that CliNR provides a reduction of the logical error rate in relevant noise regimes.
We propose several optimizations of the CliNR partial error correction scheme which implements Clifford circuits by consuming a resource state. Errors are corrected by measuring a sequence of Pauli operators that we refer to as the verification sequence. We first propose a global optimization algorithm searching for a verification sequence resulting in a low logical error rate using tabu search. Then, we introduce a proxy for the logical error rate which is easier to evaluate and we design a two-step optimization algorithm. First, a verification sequence minimizing the proxy is computed, then this sequence is refined by reintroducing the logical error rate. Finally, we identify a large group of automorphisms of the search space which preserve the proxy and we use this symmetry to reduce the size of the search space. This results in a 168 × (respectively 20,160 × ) reduction of the size of the search space for the optimization of verification sequences with three (respectively four) Pauli operators. Our numerical simulations for 20-qubit Clifford circuits with size 400 under the ion chain model show that our optimization algorithms improve the performance of CliNR by 25% and that the two-step optimization achieves the same results as the global optimization with 64% fewer evaluations of the logical error rate. Finally, we perform experiments on a 36-qubit trapped ion quantum computer, without mid-circuit measurements, showing that the CZNR variant of CliNR is at breakeven.
Quantum simulation of fermionic Hamiltonians is a leading application of quantum computing, but accurate execution on present-day hardware is limited by error accumulation in deep Trotter circuits. We present a device-matched noise-reduction framework for encoded Hamiltonian simulation that combines symplectic-transvection-based Trotter synthesis in the Generalized Superfast Encoding (GSE) with Clifford Noise Reduction (CliNR) and Shor-style stabilizer verification enabled by mid-circuit measurement. We implement this approach for a six-qubit encoded Clifford Trotter step on a Barium development system similar to the forthcoming IonQ Tempo line and benchmark it against direct execution using both hardware experiments and a calibrated device-level noise model. The encoded CliNR execution achieves up to 54% lower logical error rate. Crucially, this advantage disappears when stabilizer readout is deferred to the end of the circuit, showing that timely mid-circuit fault detection, rather than verification overhead alone, drives the improvement. As a proof of concept, we further show that machine-learning-guided stabilizer selection can identify verification operators that outperform random choices. These results demonstrate that encoding-native verification combined with dynamic-circuit primitives can materially improve application-motivated quantum simulation without the full overhead of quantum error correction.
We introduce a low-overhead approach for detecting errors in arbitrary Clifford circuits on arbitrary qubit connectivities. Our method is based on the framework of spacetime codes, and is particularly suited to near-term hardware since it has a much milder overhead in qubits and gates compared to error correction, while achieving a better sampling overhead than existing error mitigation methods. We present efficient algorithms for finding valid checks that are simultaneously low weight, satisfy connectivity constraints, and cover large detecting regions within the circuit. Using this approach, we experimentally demonstrate error detection on circuits of up to 50 logical qubits containing 2450 CZ gates, and show physical to logical fidelity gains of up to 236×236\times236×. Furthermore, we show our algorithm can efficiently find checks in universal circuits, but the space of valid checks diminishes exponentially with the non-Cliffordness of the circuit. These theoretical and experimental results suggest that Clifford-dominated circuits are promising candidates for near-term quantum advantage.
Recent work established that, for independent erasures, storing KKK logical qubits for SSS time steps with error at most ε\varepsilonε requires a spacetime cost of Ω(S(K+log⁡(S/ε)))Ω(S(K+\log(S/\varepsilon)))Ω(S(K+log(S/ε))). A matching construction was also given, but assumes ideal error correction. Here we show that the same scaling can be achieved with an explicit noisy error-correction circuit and efficient decoding, counting all state-preparation, gate, measurement, and wait locations, provided that the hardware supports long-range qubit connectivity and fast, reliable classical processing. Thus, reliability adds only a logarithmic overhead shared by all stored qubits. The construction works for sufficiently weak but otherwise general circuit noise, including faults during syndrome extraction and correlated faults, and for independent erasures it matches the best known lower bound up to constant factors. We attain this scaling using quantum Tanner codes, with each memory step consisting of one round of syndrome extraction followed by a fixed number of parallel classical decoder steps that reduce the residual error enough to keep later faults correctable, regardless of memory size, storage time, or target accuracy. Together, this gives exponentially small failure probability per step while keeping the cost of each memory step linear in the code size. The same analysis also extends to certain constant-depth logical Clifford operations.
Reducing errors is essential for reliable quantum computation. Quantum error mitigation (QEM) and quantum error correction (QEC) are two leading approaches for this task, each with challenges: QEM suffers from high sampling costs and cannot recover states, while QEC incurs large qubit and gate overheads. We combine ideas from both and introduce an information-theoretic device called a quantum filter that can purify or correct quantum channels. We present an explicit construction capable of correcting arbitrary noise in an n-qubit Clifford circuit using 2n ancillary qubits through a commutation-derived error-detection circuit. This scheme can also partially purify noise in non-Clifford gates such as T and CCZ. Unlike QEC, it achieves deterministic error reduction without encoding the input state. Under the assumption of clean ancillas, it overcomes the exponential sampling overhead in QEM using a single query to the channel. We also propose an ancilla-efficient Pauli filter that removes nearly all low-weight erroneous Pauli components in noisy Clifford circuits using only two ancillas. For local depolarizing noise, it achieves a quadratic reduction in average infidelity. Beyond existing QEM methods, our approach enables systematic error correction as the infidelity can be exponentially reduced with each added ancilla. Through numerical simulations under ancilla noise, we identify regimes where quantum filters outperform other techniques, demonstrating their effectiveness as a scalable error-reduction tool for quantum information processing.