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Related papers: Logical operator tradeoff for local quantum codes

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We present an improved low-overhead implementation of surface code logical H. We describe in full detail logical H applied to a single distance 7 double-defect logical qubit in an otherwise idle scalable array such qubits. Our goal is to…

Quantum Physics · Physics 2012-09-11 Austin G. Fowler

The topological color code and the toric code are two leading candidates for realizing fault-tolerant quantum computation. Here we show that the color code on a $d$-dimensional closed manifold is equivalent to multiple decoupled copies of…

Quantum Physics · Physics 2015-09-02 Aleksander Kubica , Beni Yoshida , Fernando Pastawski

We develop a multi-valued logic for quantum computing for use in multi-level quantum systems, and discuss the practical advantages of this approach for scaling up a quantum computer. Generalizing the methods of binary quantum logic, we…

Quantum Physics · Physics 2012-08-27 Ashok Muthukrishnan , C. R. Stroud,

It is commonly believed that logical states of quantum error-correcting codes have to be highly entangled such that codes capable of correcting more errors require more entanglement to encode a qubit. Here, we show that the validity of this…

Quantum Physics · Physics 2025-06-16 Sergey Bravyi , Dongjin Lee , Zhi Li , Beni Yoshida

Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are a promising candidate for fault-tolerant quantum computation due to…

Quantum Physics · Physics 2025-12-23 Friederike Butt , Lars Esser , Markus Müller

Constant-rate low-density parity-check (LDPC) codes are promising candidates for constructing efficient fault-tolerant quantum memories. However, if physical gates are subject to geometric-locality constraints, it becomes challenging to…

Quantum Physics · Physics 2025-05-07 Christopher A. Pattison , Anirudh Krishna , John Preskill

There have been significant recent advances in constructing theoretical and practical quantum error correcting codes that function well as quantum memories; however, performing fault-tolerant logical gates on these codes is less studied,…

Quantum Physics · Physics 2025-10-22 Noah Berthusen , Elijah Durso-Sabina

The non-local interactions in several quantum device architectures allow for the realization of more compact quantum encodings while retaining the same degree of protection against noise. Anticipating that short to medium-length codes will…

Quantum Physics · Physics 2025-06-05 Shubham P. Jain , Victor V. Albert

Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computation with constant overhead. Recent advancements have shown that qLDPC codes can outperform the quantum memory capability of…

Quantum Physics · Physics 2024-07-08 Jens Niklas Eberhardt , Vincent Steffan

One hurdle to performing reliable quantum computations is overcoming noise. One possibility is to reduce the number of particles needing to be protected from noise and instead use systems with more states, so called qudit quantum computers.…

Quantum Physics · Physics 2022-04-27 Lane G. Gunderman

Given a quantum error correcting code, an important task is to find encoded operations that can be implemented efficiently and fault-tolerantly. In this Letter we focus on topological stabilizer codes and encoded unitary gates that can be…

Quantum Physics · Physics 2013-10-04 Sergey Bravyi , Robert Koenig

Quantum computation must be performed in a fault-tolerant manner to be realizable in practice. Recent progress has uncovered quantum error-correcting codes with sparse connectivity requirements and constant qubit overhead. Existing schemes…

Quantum Physics · Physics 2026-04-20 Dominic J. Williamson , Theodore J. Yoder

We provide a detailed study of the general structure of two-dimensional topological stabilizer quantum error correcting codes, including subsystem codes. Under the sole assumption of translational invariance, we show that all such codes can…

Quantum Physics · Physics 2015-05-28 H. Bombin

Modern platforms for potential qubit candidates, such as trapped ions or neutral atoms, allow long range connectivity between distant physical qubits through shuttling. This opens up an avenue for transversal logical CNOT gates between…

Quantum Physics · Physics 2025-04-14 Kwok Ho Wan , Mark Webber , Austin G. Fowler , Winfried K. Hensinger

In this paper, we explore the relationship between the width of a qubit lattice constrained in one dimension and physical thresholds for scalable, fault-tolerant quantum computation. To circumvent the traditionally low thresholds of small…

Quantum Physics · Physics 2022-12-15 Alexis T. E. Shaw , Michael J. Bremner , Alexandru Paler , Daniel Herr , Simon J. Devitt

We introduce tile codes, a simple yet powerful way of constructing quantum codes that are local on a planar 2D-lattice. Tile codes generalize the usual surface code by allowing for a bit more flexibility in terms of locality and stabilizer…

Quantum computers will need effective error-correcting codes. Current quantum processors require precise control of each particle, so having fewer particles to control might be beneficial. Although traditionally quantum computers are…

Quantum Physics · Physics 2021-10-25 Arun J. Moorthy , Lane G. Gunderman

Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing. We present a no-go theorem that places very strong limitations on the potential of such schemes for…

Quantum Physics · Physics 2020-08-11 Paul Webster , Stephen D. Bartlett

Error correction has long been suggested to extend the sensitivity of quantum sensors into the Heisenberg Limit. However, operations on logical qubits are only performed through universal gate sets consisting of finite-sized gates such as…

Quantum Physics · Physics 2023-05-05 Cameron Cianci

We design and analyze a logical qubit composed of a linear array of electron spins in semiconductor quantum dots. To avoid the difficulty of fully controlling a two-dimensional array of dots, we adapt spin control and error correction to a…