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

• URL: http://arxiv.org/abs/2407.20173v2
• Date: Tue, 07 Oct 2025 17:51:37 GMT
• Title: Purification and correction of quantum channels by commutation-derived quantum filters
• Authors: Sowmitra Das, Jinzhao Sun, Michael Hanks, Bálint Koczor, M. S. Kim,
• Abstract summary: We present an explicit construction capable of correcting arbitrary noise in an n-qubit Clifford circuit using 2n ancillary qubits.<n>Unlike QEC, it achieves deterministic error reduction without encoding the input state.<n>We also propose an ancilla-efficient Pauli filter that removes nearly all low-weight erroneous Pauli components.
• Score: 0.22835610890984162
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Approximate Quantum Error Correction with 1D Log-Depth Circuits [0.824969449883056]
  We construct quantum error-correcting codes based on one-dimensional, logarithmic-depth random Clifford encoding circuits with a two-layer circuit structure. We show that the error correction inaccuracy decays exponentially with circuit depth, resulting in negligible errors for these logarithmic-depth circuits.
  arXiv  Detail & Related papers  (2025-03-22T12:54:04Z)
• Quantum Error Mitigation via Linear-Depth Verifier Circuits [0.044998333629984864]
  We provide a method for constructing verifier circuits for any quantum circuit that is accurately represented by a low-dimensional matrix product operator (MPO) By transpiling the circuits to a 2D array of qubits, we estimate the crossover point where the verifier circuit is shallower than the circuit itself, and hence useful for quantum error mitigation (QEM) We conclude that our approach may be useful for calibrating quantum sub-circuits to counter coherent noise but cannot correct for the incoherent noise present in current devices.
  arXiv  Detail & Related papers  (2024-11-05T16:44:18Z)
• Reshaping quantum device noise via quantum error correction [0.818005422059368]
  We show that quantum error correction codes can reshape the native noise profiles of quantum devices. We analytically derive the quantum channels describing noisy two-qubit entangling gates. We then demonstrate the noise reshaping on the IonQ Aria-1 quantum hardware.
  arXiv  Detail & Related papers  (2024-11-01T17:20:04Z)
• Mitigating Errors on Superconducting Quantum Processors through Fuzzy Clustering [38.02852247910155]
  A new Quantum Error Mitigation (QEM) technique uses Fuzzy C-Means clustering to specifically identify measurement error patterns. We report a proof-of-principle validation of the technique on a 2-qubit register, obtained as a subset of a real NISQ 5-qubit superconducting quantum processor. We demonstrate that the FCM-based QEM technique allows for reasonable improvement of the expectation values of single- and two-qubit gates based quantum circuits.
  arXiv  Detail & Related papers  (2024-02-02T14:02:45Z)
• QuantumSEA: In-Time Sparse Exploration for Noise Adaptive Quantum Circuits [82.50620782471485]
  QuantumSEA is an in-time sparse exploration for noise-adaptive quantum circuits. It aims to achieve two key objectives: (1) implicit circuits capacity during training and (2) noise robustness. Our method establishes state-of-the-art results with only half the number of quantum gates and 2x time saving of circuit executions.
  arXiv  Detail & Related papers  (2024-01-10T22:33:00Z)
• Fast Flux-Activated Leakage Reduction for Superconducting Quantum Circuits [84.60542868688235]
  leakage out of the computational subspace arising from the multi-level structure of qubit implementations. We present a resource-efficient universal leakage reduction unit for superconducting qubits using parametric flux modulation. We demonstrate that using the leakage reduction unit in repeated weight-two stabilizer measurements reduces the total number of detected errors in a scalable fashion.
  arXiv  Detail & Related papers  (2023-09-13T16:21:32Z)
• A fault-tolerant variational quantum algorithm with limited T-depth [2.7648976108201815]
  We propose a variational quantum eigensolver (VQE) algorithm that uses a fault-tolerant gate-set. VQE is suitable for implementation on a future error-corrected quantum computer.
  arXiv  Detail & Related papers  (2023-03-08T10:31:12Z)
• Deep Quantum Error Correction [73.54643419792453]
  Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. In this work, we efficiently train novel emphend-to-end deep quantum error decoders. The proposed method demonstrates the power of neural decoders for QECC by achieving state-of-the-art accuracy.
  arXiv  Detail & Related papers  (2023-01-27T08:16:26Z)
• Improving the speed of variational quantum algorithms for quantum error correction [7.608765913950182]
  We consider the problem of devising a suitable Quantum Error Correction (QEC) procedures for a generic quantum noise acting on a quantum circuit. In general, there is no analytic universal procedure to obtain the encoding and correction unitary gates. We address this problem using a cost function based on the Quantum Wasserstein distance of order 1.
  arXiv  Detail & Related papers  (2023-01-12T19:44:53Z)
• Averaging gate approximation error and performance of Unitary Coupled Cluster ansatz in Pre-FTQC Era [0.0]
  Fault-tolerant quantum computation (FTQC) is essential to implement quantum algorithms in a noise-resilient way. In FTQC, a quantum circuit is decomposed into universal gates that can be fault-tolerantly implemented. In this paper, we propose that the Clifford+$T$ decomposition error for a given quantum circuit can be modeled as the depolarizing noise.
  arXiv  Detail & Related papers  (2023-01-10T19:00:01Z)
• Overcoming leakage in scalable quantum error correction [128.39402546769284]
  Leakage of quantum information out of computational states into higher energy states represents a major challenge in the pursuit of quantum error correction (QEC) Here, we demonstrate the execution of a distance-3 surface code and distance-21 bit-flip code on a Sycamore quantum processor where leakage is removed from all qubits in each cycle. We report a ten-fold reduction in steady-state leakage population on the data qubits encoding the logical state and an average leakage population of less than $1 times 10-3$ throughout the entire device.
  arXiv  Detail & Related papers  (2022-11-09T07:54:35Z)
• Suppressing Amplitude Damping in Trapped Ions: Discrete Weak Measurements for a Non-unitary Probabilistic Noise Filter [62.997667081978825]
  We introduce a low-overhead protocol to reverse this degradation. We present two trapped-ion schemes for the implementation of a non-unitary probabilistic filter against amplitude damping noise. This filter can be understood as a protocol for single-copy quasi-distillation.
  arXiv  Detail & Related papers  (2022-09-06T18:18:41Z)
• Quantum error mitigation via matrix product operators [27.426057220671336]
  Quantum error mitigation (QEM) can suppress errors in measurement results via repeated experiments and post decomposition of data. MPO representation increases the accuracy of modeling noise without consuming more experimental resources. Our method is hopeful of being applied to circuits in higher dimensions with more qubits and deeper depth.
  arXiv  Detail & Related papers  (2022-01-03T16:57:43Z)
• Quantum Error Mitigation Relying on Permutation Filtering [84.66087478797475]
  We propose a general framework termed as permutation filters, which includes the existing permutation-based methods as special cases. We show that the proposed filter design algorithm always converges to the global optimum, and that the optimal filters can provide substantial improvements over the existing permutation-based methods.
  arXiv  Detail & Related papers  (2021-07-03T16:07:30Z)
• Sampling Overhead Analysis of Quantum Error Mitigation: Uncoded vs. Coded Systems [69.33243249411113]
  We show that Pauli errors incur the lowest sampling overhead among a large class of realistic quantum channels. We conceive a scheme amalgamating QEM with quantum channel coding, and analyse its sampling overhead reduction compared to pure QEM.
  arXiv  Detail & Related papers  (2020-12-15T15:51:27Z)
• Quantum circuit architecture search for variational quantum algorithms [88.71725630554758]
  We propose a resource and runtime efficient scheme termed quantum architecture search (QAS) QAS automatically seeks a near-optimal ansatz to balance benefits and side-effects brought by adding more noisy quantum gates. We implement QAS on both the numerical simulator and real quantum hardware, via the IBM cloud, to accomplish data classification and quantum chemistry tasks.
  arXiv  Detail & Related papers  (2020-10-20T12:06:27Z)
• Efficient and robust certification of genuine multipartite entanglement in noisy quantum error correction circuits [58.720142291102135]
  We introduce a conditional witnessing technique to certify genuine multipartite entanglement (GME) We prove that the detection of entanglement in a linear number of bipartitions by a number of measurements scales linearly, suffices to certify GME. We apply our method to the noisy readout of stabilizer operators of the distance-three topological color code and its flag-based fault-tolerant version.
  arXiv  Detail & Related papers  (2020-10-06T18:00:07Z)
• Fault-tolerant Coding for Quantum Communication [71.206200318454]
  encode and decode circuits to reliably send messages over many uses of a noisy channel. For every quantum channel $T$ and every $eps>0$ there exists a threshold $p(epsilon,T)$ for the gate error probability below which rates larger than $C-epsilon$ are fault-tolerantly achievable. Our results are relevant in communication over large distances, and also on-chip, where distant parts of a quantum computer might need to communicate under higher levels of noise.
  arXiv  Detail & Related papers  (2020-09-15T15:10:50Z)
• Minimizing estimation runtime on noisy quantum computers [0.0]
  "engineered likelihood function" (ELF) is used for carrying out Bayesian inference. We show how the ELF formalism enhances the rate of information gain in sampling as the physical hardware transitions from the regime of noisy quantum computers. This technique speeds up a central component of many quantum algorithms, with applications including chemistry, materials, finance, and beyond.
  arXiv  Detail & Related papers  (2020-06-16T17:46:18Z)
• Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem [77.34726150561087]
  We present a proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code with its ability to achieve a universal set of logical gates. Our derivation employs powerful bounds on the quantum Fisher information in generic quantum metrological protocols.
  arXiv  Detail & Related papers  (2020-04-24T17:58:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.