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Encoding quantum information to protect it from errors is essential for performing large-scale quantum computations. Performing a universal set of quantum gates on encoded states demands a potentially large resource overhead and minimizing…

Most quantum error correcting codes are predicated on the assumption that there exists a reservoir of qubits in the state $\ket{0}$, which can be used as ancilla qubits to prepare multi-qubit logical states. In this report, we examine the…

量子物理 · 物理学 2013-05-30 Ben Criger , Osama Moussa , Raymond Laflamme

We demonstrate an improved concatenated encoded ancilla preparation procedure. Simulations show that this procedure significantly increases the error threshold beneath which arbitrarily long quantum computations are possible.

量子物理 · 物理学 2007-05-23 Ben W. Reichardt

Generation of logical zero states encoded with a quantum error-correcting code is the first step for fault-tolerant quantum computation, but requires considerably large resource overheads in general. To reduce such overheads, we propose an…

量子物理 · 物理学 2023-11-14 Hayato Goto , Yinghao Ho , Taro Kanao

Fault-tolerant logical operations for qubits encoded by CSS codes are discussed, with emphasis on methods that apply to codes of high rate, encoding k qubits per block with k>1. It is shown that the logical qubits within a given block can…

量子物理 · 物理学 2013-05-29 Andrew M. Steane , Ben Ibinson

An important approach to the fault-tolerant quantum computation is protecting the logical information using the quantum error correction. Usually, the logical information is in the form of logical qubits, which are encoded in physical…

量子物理 · 物理学 2018-08-08 Ying Li

The goal of this paper is to review the theoretical basis for achieving a faithful quantum information transmission and processing in the presence of noise. Initially encoding and decoding, implementing gates and quantum error correction…

量子物理 · 物理学 2007-05-23 P. J. Salas

Quantum error correcting codes protect quantum information, allowing for large quantum computations provided that physical error rates are sufficiently low. We combine post-selection with surface code error correction through the use of a…

量子物理 · 物理学 2024-12-23 Samuel C. Smith , Benjamin J. Brown , Stephen D. Bartlett

Fault-tolerant quantum computing based on surface code has emerged as an attractive candidate for practical large-scale quantum computers to achieve robust noise resistance. To achieve universality, magic states preparation is a commonly…

We investigate a family of fault-tolerant quantum error correction schemes based on the concatenation of small error detection or error correction codes with the three-dimensional cluster state. We propose fault-tolerant state preparation…

量子物理 · 物理学 2023-08-23 Zhaoyi Li , Isaac Kim , Patrick Hayden

We present a comprehensive architectural analysis for a proposed fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware, we propose a system of acoustic…

Quantum Error Correction (QEC) codes store information reliably in logical qubits by encoding them in a larger number of less reliable qubits. The surface code, known for its high resilience to physical errors, is a leading candidate for…

量子物理 · 物理学 2025-06-13 Satvik Maurya , Swamit Tannu

When storing encoded qubits, if single faults can be corrected and double faults postselected against, logical errors only occur due to at least three faults. At current noise rates, having to restart when two errors are detected prevents…

量子物理 · 物理学 2024-08-15 Prithviraj Prabhu , Ben W. Reichardt

Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…

量子物理 · 物理学 2009-04-17 Daniel Gottesman

Fault-tolerant quantum computation demands extremely low logical error rates, yet superconducting qubit arrays are subject to radiation-induced correlated noise arising from cosmic-ray muon-generated quasiparticles. The quasiparticle…

In order to use quantum error-correcting codes to actually improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a general theory of fault-tolerant…

量子物理 · 物理学 2011-07-19 Daniel Gottesman

Fault-tolerant quantum computation critically depends on architectures uniting high encoding rates with physical implementability. Quantum low-density parity-check (qLDPC) codes, including bivariate bicycle (BB) codes, achieve dramatic…

量子物理 · 物理学 2025-06-24 Yingli Yang , Guo Zhang , Ying Li

Quantum error correction is an essential component for practical quantum computing on noisy quantum hardware. However, logical operations on error-corrected qubits require a significant resource overhead, especially for high-precision and…

量子物理 · 物理学 2023-03-31 Hyeongrak Choi , Frederic T. Chong , Dirk Englund , Yongshan Ding

Cat states are an important resource for fault-tolerant quantum computing, where they serve as building blocks for a variety of fault-tolerant primitives. Consequently, the ability to prepare high-quality cat states at large fault distances…

量子物理 · 物理学 2026-01-08 Tom Peham , Erik Weilandt , Robert Wille

Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have…

量子物理 · 物理学 2026-04-10 Andi Gu , J. Pablo Bonilla Ataides , Mikhail D. Lukin , Susanne F. Yelin