Noise poses a fundamental challenge to quantum information processing, with amplitude-damping (AD) noise being particularly detrimental. Preserving high-fidelity quantum systems therefore relies critically on effective error correction and purification methods. In this work, we introduce a novel approach for mitigating AD noise that can be applied to both state and channel purification. Our method achieves a substantial enhancement in the fidelity of affected states or channels while maintaining a low resource overhead, requiring only one or two ancilla qubits in combination with two Clifford gates, and exhibits a relatively high success probability. This approach provides a practical and scalable framework for addressing AD noise in realistic quantum systems.
Noise poses a fundamental challenge to quantum information processing, with amplitude-damping (AD) noise being particularly detrimental. Preserving high-fidelity quantum systems therefore relies critically on effective error correction and purification methods. In this work, we introduce a novel approach for mitigating AD noise that can be applied to both state and channel purification. Our method achieves a substantial enhancement in the fidelity of affected states or channels while maintaining a low resource overhead, requiring only one or two ancilla qubits in combination with two Clifford gates, and exhibits a relatively high success probability. This approach provides a practical and scalable framework for addressing AD noise in realistic quantum systems.
Effectively managing various types of decoherence is crucial for leveraging entanglement in quantum information processing and quantum computing. In this paper, we propose purification circuits that deterministically produce a maximally entangled state from a single copy of an imperfect entangled pair affected by various noise sources. Unlike conventional methods, our approach eliminates the need for multiple copies of the entangled state, pre-purification operations, and imposes no restrictions on the initial entanglement fidelity of the imperfect pair. Our method utilizes ancilla qubits and CNOT gates to address errors from Pauli X and Z (bit flip and phase flip), as well as combinations of these errors that create general mixed entangled states and amplitude-damped entangled states. Our analysis shows that noisy CNOT gates impact fidelity minimally, with only the final two gates being critical. We validate our approach through mathematical analysis and practical implementation in Qiskit, demonstrating its effectiveness and robustness.
We propose a single auxiliary-assisted purification-based framework for quantum error correction, capable of correcting errors that drive a system from its ground-state subspace into excited-state sectors. The protocol consists of a joint time evolution of the system-auxiliary duo under a specially engineered interaction Hamiltonian, followed by a single measurement of the auxiliary in its energy eigenbasis and a subsequent post-selection of one of the measurement outcomes. We show that the resulting purified state always achieves unit fidelity, while the probability of obtaining any energy of the auxiliary other than its ground state energy yields the success rate of the protocol. We demonstrate the power of this proposed method for several low-distance quantum codes, including the three-, four-, and five-qubit codes, and for the one-dimensional isotropic Heisenberg model, subjected to bit-flip, phase-flip, and amplitude-damping noises acting on all qubits. Notably, the protocol expands the class of correctable errors for a given code, particularly in the presence of amplitude-damping noise. We further analyze the impact of replacing the auxiliary qudit with a single auxiliary qubit, and the changes in the performance of the protocol under the realistic scenario where noise remains active during the correction cycle.
All realistic quantum systems are inevitably in contact with the environment. Suppressing theimpact of environmental noise is a critical challenge in cutting-edge quantum technologies. In thiswork, we introduce and systematically analyze a scheme for the protection of quantum states againstamplitude-damping (AD) noise based on the circuit structure called the quantum filter. Filtrationcircuits employing single- and multi-control qubits are examined, and their capability to enhance stateprotection fidelity while preserving a high success probability is discussed. Moreover, for many-bodyqubit states, those with a fixed quantum Hamming weight can be perfectly protected against ADnoise, whereas states with the largest Hamming weight difference set a lower bound on the achievableprotection fidelity. Our work provides a resource-efficient route for quantum state protection withoutrequiring full quantum error correction.
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.
Quantum error correcting (QEC) plays a crucial role in protecting quantum information against decoherence and enabling scalable, reliable quantum computing. One of the most realistic and ubiquitous sources of noise affecting quantum hardware today is generalized amplitude-damping (GAD) noise. Conventional, deterministic QEC codes struggle to correct for GAD noise because of their inherent structure, leading to fidelity losses that scale linearly with the damping strength. In this work, we introduce the framework of probabilistic approximate quantum error correction (PAQEC), that combines the flexibility of approximate QEC with the potential of post-selected recovery, enabling high-fidelity, resource-efficient error correction. We construct a five-qubit permutation-invariant code that, under probabilistic recovery, achieves a fidelity loss quadratic in the damping strength, thus outperforming existing QEC codes. Formulating PAQEC as an optimization problem, we present a numerical technique based on Charnes-Cooper and semidefinite programming to identify the optimal recovery map for any PAQEC code. Our results establish PAQEC as a powerful tool for developing resource-efficient, high-fidelity quantum codes tailored to realistic noise, with promising implications for near-term quantum devices and future fault-tolerant architectures.
We construct two simple error correction schemes adapted to amplitude damping noise for Bacon-Shor codes and investigate their prospects for fault-tolerant implementation. Both consist solely of Clifford gates and require far fewer qubits, relative to the standard method, to achieve exact correction to a desired order in the damping rate. The first, employing one-bit teleportation and single-qubit measurements, needs only one-fourth as many physical qubits, while the second, using just stabilizer measurements and Pauli corrections, needs only half. The improvements stem from the fact that damping events need only be detected, not corrected, and that effective phase errors arising due to undamped qubits occur at a lower rate than damping errors. For error correction that is itself subject to damping noise, we show that existing fault-tolerance methods can be employed for the latter scheme, while the former can be made to avoid potential catastrophic errors and can easily cope with damping faults in ancilla qubits.