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Related papers: Finding good quantum codes using the Cartan form

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Current universal quantum computers have a limited number of noisy qubits. Because of this, it is difficult to use them to solve large-scale complex optimization problems. In this paper we tackle this issue by proposing a quantum…

Quantum Physics · Physics 2023-06-30 Pablo Bermejo , Roman Orus

When a logical qubit is protected using a quantum error-correcting code, the net effect of coding, decoherence (a physical channel acting on qubits in the codeword) and recovery can be represented exactly by an effective channel acting…

Quantum Physics · Physics 2009-11-07 Benjamin Rahn , Andrew C. Doherty , Hideo Mabuchi

Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…

Quantum Physics · Physics 2013-05-29 Gregory M. Crosswhite , Dave Bacon

We investigate the problem of quantum searching on a noisy quantum computer. Taking a 'fault-ignorant' approach, we analyze quantum algorithms that solve the task for various different noise strengths, which are possibly unknown beforehand.…

Quantum Physics · Physics 2014-07-28 Peter Vrana , David Reeb , Daniel Reitzner , Michael M. Wolf

Simulating quantum dynamics on classical computers is challenging for large systems due to the significant memory requirements. Simulation on quantum computers is a promising alternative, but fully optimizing quantum circuits to minimize…

Protection of quantum information from noise is a massive challenge. One avenue people have begun to explore is reducing the number of particles needing to be protected from noise and instead use systems with more states, so called qudit…

Quantum Physics · Physics 2020-06-24 Lane G. Gunderman

Self-correcting quantum memories demonstrate robust properties that can be exploited to improve active quantum error-correction protocols. Here we propose a cellular automaton decoder for a variation of the color code where the bases of the…

Quantum Physics · Physics 2023-03-15 Jonathan F. San Miguel , Dominic J. Williamson , Benjamin J. Brown

Quantum computation promises to advance a wide range of computational tasks. However, current quantum hardware suffers from noise and is too small for error correction. Thus, accurately utilizing noisy quantum computers strongly relies on…

Optimization and Control · Mathematics 2024-12-16 Friedrich Wagner , Daniel J. Egger , Frauke Liers

We investigate a scheme of fault-tolerant quantum computation based on the cluster model. Logical qubits are encoded by a suitable code such as the Steane's 7-qubit code. Cluster states of logical qubits are prepared by post-selection…

Quantum Physics · Physics 2007-05-23 Keisuke Fujii , Katsuji Yamamoto

We address the characterization of two-qubit gates, focusing on bounds to precision in the joint estimation of the three parameters that define their Cartan decomposition. We derive the optimal probe states that jointly maximize precision,…

Quantum Physics · Physics 2025-02-13 Gabriele Fazio , Jiayu He , Matteo G. A. Paris

Repetition code forms a fundamental basis for quantum error correction experiments. To date, it stands as the sole code that has achieved large distances and extremely low error rates. Its applications span the spectrum of evaluating…

Quantum error correction is vital for implementing universal quantum computing. A key component is the encoding circuit that maps a product state of physical qubits into the encoded multipartite entangled logical state. Known methods are…

Quantum Physics · Physics 2021-04-07 Xiaosi Xu , Simon C. Benjamin , Xiao Yuan

We study quantum communication in the presence of adversarial noise. In this setting, communicating with perfect fidelity requires using a quantum code of bounded minimum distance, for which the best known rates are given by the quantum…

Quantum Physics · Physics 2008-01-28 Debbie Leung , Graeme Smith

We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably…

Quantum Physics · Physics 2007-05-23 Andrei N. Soklakov , Ruediger Schack

Qutrits, three-level quantum systems, have the advantage of potentially requiring fewer components than the typically used two-level qubits to construct equivalent quantum circuits. This work investigates the potential of qutrit parametric…

Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…

Quantum Physics · Physics 2008-02-03 Dorit Aharonov , Michael Ben-Or

We derive necessary and sufficient conditions for the approximate correctability of a quantum code, generalizing the Knill-Laflamme conditions for exact error correction. Our measure of success of the recovery operation is the worst-case…

Quantum Physics · Physics 2010-03-25 Cédric Bény , Ognyan Oreshkov

The most common error models for quantum computers assume the independence of errors on different qubits. However, most noise mechanisms have some correlations in space. We show how to improve quantum information processing for few-qubit…

Quantum Physics · Physics 2018-12-19 Vickram N. Premakumar , Robert Joynt

To improve the efficiency of the encoding and the decoding is the important problem in the quantum error correction. In a preceding work, a general algorithm for decoding the stabilizer code is shown. This paper will show an decoding which…

Quantum Physics · Physics 2007-05-23 Kenichiro Furuta

Information obtained from noise characterization of a quantum device can be used in classical decoding algorithms to improve the performance of quantum error-correcting codes. Focusing on the surface code under local (i.e. single-qubit)…

Quantum Physics · Physics 2024-03-14 Andrew S. Darmawan