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For a noisy quantum channel, a quantum error correcting code exists if and only if the joint higher rank numerical ranges associated with the error operators of the channel is non-empty. In this paper, geometric properties of the joint…

Functional Analysis · Mathematics 2008-12-31 Chi-Kwong Li , Yiu-Tung Poon

An interesting concept in quantum computation is that of global control (GC), where there is no need to manipulate qubits individually. One can implement a universal set of quantum gates on a one-dimensional array purely via signals that…

Quantum Physics · Physics 2007-05-23 Adel Bririd , Simon C. Benjamin , Alastair Kay

Quantum error-correcting codes aim to protect information in quantum systems to enable fault-tolerant quantum computations. The most prevalent method, stabilizer codes, has been well developed for many varieties of systems, however, largely…

Quantum Physics · Physics 2025-01-10 Lane G. Gunderman

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…

Quantum Physics · Physics 2009-04-17 Daniel Gottesman

Quantum deletions, which are harder to correct than erasure errors, occur in many realistic settings. It is therefore pertinent to develop quantum coding schemes for quantum deletion channels. To date, not much is known about which explicit…

Quantum Physics · Physics 2021-10-19 Yingkai Ouyang

The quantum channel decomposition techniques, which contain the so-called probabilistic error cancellation and gate/wire cutting, are powerful approach for simulating a hard-to-implement (or an ideal) unitary operation by concurrently…

Quantum Physics · Physics 2023-08-30 Ryo Nagai , Shu Kanno , Yuki Sato , Naoki Yamamoto

The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the well-known satisfiability problem from classical to quantum computation. This problem is shown to be…

Quantum Physics · Physics 2009-09-24 Bill Rosgen

We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing…

Quantum Physics · Physics 2007-05-23 Raymond Laflamme , Cesar Miquel , Juan Pablo Paz , Wojciech Hubert Zurek

Quantum error correction codes are usually designed to correct errors regardless of their physical origins. In large-scale devices, this is an essential feature. In smaller-scale devices, however, the main error sources are often…

Quantum Physics · Physics 2020-06-05 David Layden , Louisa Ruixue Huang , Paola Cappellaro

Communication over a random-parameter quantum channel when the decoder is required to reconstruct the parameter sequence is considered. We study scenarios that include either strictly-causal, causal, or non-causal channel side information…

Information Theory · Computer Science 2021-09-28 Uzi Pereg

Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and…

Quantum Physics · Physics 2007-06-26 Andrew S. Fletcher

A central challenge for the scaling of quantum computing systems is the need to control all qubits in the system without a large overhead. A solution for this problem in classical computing comes in the form of so called crossbar…

Quantum Physics · Physics 2018-03-28 Jonas Helsen , Mark Steudtner , Menno Veldhorst , Stephanie Wehner

In this paper, we propose an iterative algorithm using polar decomposition to approximate a channel characterized by a single unitary matrix based on input-output quantum state pairs. In limited data, we state and prove that the optimal…

Numerical Analysis · Mathematics 2025-06-27 Matthew M. Lin , Hao-Wei Huang , Bing-Ze Lu

We show that a subset of the basis for the irreducible representations of a tensor-product SU(2) rotation forms a covariant approximate quantum error-correcting code with transversal U(1) logical gates. Generalizing previous work on…

Quantum Physics · Physics 2025-09-25 Cheng-Ju Lin , Zi-Wen Liu , Victor V. Albert , Alexey V. Gorshkov

Quantum convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of quantum convolutional code, I report a way to decode certain quantum convolutional codes based on the…

Quantum Physics · Physics 2009-10-31 H. F. Chau

We present a quantum error correcting code with dynamically generated logical qubits. When viewed as a subsystem code, the code has no logical qubits. Nevertheless, our measurement patterns generate logical qubits, allowing the code to act…

Quantum Physics · Physics 2021-10-20 Matthew B. Hastings , Jeongwan Haah

We demonstrate that continuous-variable quantum error correction based on Gaussian ancilla states and Gaussian operations (for encoding, syndrome extraction, and recovery) can be very useful to suppress the effect of non-Gaussian error…

Quantum Physics · Physics 2008-11-24 Peter van Loock

High-rate quantum error correcting codes mitigate the imposing scale of fault-tolerant quantum computers but require efficient generation of non-local, many-body entanglement. We provide a linear-optical architecture with these properties,…

This paper presents conditions for constructing permutation-invariant quantum codes for deletion errors and provides a method for constructing them. Our codes give the first example of quantum codes that can correct two or more deletion…

Quantum Physics · Physics 2021-12-17 Taro Shibayama , Manabu Hagiwara

We study the robustness of quantum error correction in a one-parameter ensemble of codes generated by the Brownian SYK model, where the parameter quantifies the encoding complexity. The robustness of error correction by a quantum code is…

High Energy Physics - Theory · Physics 2023-08-16 Vijay Balasubramanian , Arjun Kar , Cathy Li , Onkar Parrikar , Harshit Rajgadia