Related papers: Quantum Error Correction from Complexity in Browni…
Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high…
Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed…
Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…
Coherent control errors, for which ideal Hamiltonians are perturbed by unknown multiplicative noise terms, are a major obstacle for reliable quantum computing. In this paper, we present a framework for analyzing the robustness of quantum…
Extracting useful information from noisy near-term quantum simulations requires error mitigation strategies. A broad class of these strategies rely on precise characterization of the noise source. We study the robustness of probabilistic…
For a simple model of mutually interacting qubits it is shown how the errors induced by mutual interactions can be eliminated using concatenated coding. The model is solved exactly for arbitrary interaction strength, for two well-known…
To perform reliable quantum computation, quantum error correction is indispensable. In certain cases, continuous covariance symmetry of the physical system can make exact error correction impossible. In this work we study the approximate…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
We study entanglement fluctuations and quantum error correction in the weakly monitored volume-law phase of quantum automaton circuits subject to repeated local measurements. We numerically observe that the entanglement entropy exhibits…
We study how well topological quantum codes can tolerate coherent noise caused by systematic unitary errors such as unwanted $Z$-rotations. Our main result is an efficient algorithm for simulating quantum error correction protocols based on…
We establish rigorous connections between quantum circuit complexity and approximate quantum error correction (AQEC) capability, two properties of fundamental importance to the physics and practical use of quantum many-body systems,…
Quantum error correction will likely be essential for building a large-scale quantum computer, but it comes with significant requirements at the level of classical control software. In particular, a quantum error-correcting code must be…
Random measurements have been shown to induce a phase transition in an extended quantum system evolving under chaotic unitary dynamics, when the strength of measurements exceeds a threshold value. Below this threshold, a steady state with a…
The discovery of quantum error correction has greatly improved the long-term prospects for quantum computing technology. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the…
Quantum computation requires qubits that satisfy often-conflicting criteria, including scalable control and long-lasting coherence. One approach to creating a suitable qubit is to operate in an encoded subspace of several physical qubits.…
In many physical systems it is expected that environmental decoherence will exhibit an asymmetry between dephasing and relaxation that may result in qubits experiencing discrete phase errors more frequently than discrete bit errors. In the…
The first generation of multi-qubit quantum technologies will consist of noisy, intermediate-scale devices for which active error correction remains out of reach. To exploit such devices, it is thus imperative to use passive error…
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…
The surface code is designed to suppress errors in quantum computing hardware and currently offers the most believable pathway to large-scale quantum computation. The surface code requires a 2-D array of nearest-neighbor coupled qubits that…