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Error Correction in Quantum Computing

Jesús Yaljá Montiel-Pérez, Jordi Fabián González-Contreras, Erik Zamora +1 more

Studies in computational intelligenceJan 1, 20250 citations

Introduction to Autonomous Quantum Error Correction

Hyukjoon KWON

Autonomous Quantum Error Correction (AutoQEC) has recently been emerged as a promising technique for suppressing errors in quantum computing devices. The main idea of the protocol is to overcome quantum noise through a passive approach using continuous-time open quantum dynamics. This article explains the basic mechanisms of AutoQEC and discusses the protocols’ usefulness, limitations, and prospects.

Physics and High TechnologyOct 31, 20240 citations

Effects of dynamical phases in Shor’s factoring algorithm with operational delays

L. F. Wei, Xiao Li, Xuedong Hu +1 more

Ideal quantum algorithms usually assume that quantum computing is performed continuously by a sequence of unitary transformations. However, there always exist idle finite time intervals between consecutive operations in a realistic quantum computing process. During these delays, coherent errors will accumulate from the dynamical phases of the superposed wave functions. Here we explore the sensitivity of Shor's quantum factoring algorithm to such errors. Our results clearly show a severe sensitivity of Shor's factorization algorithm to the presence of delay times between successive unitary transformations. Specifically, in the presence of these coherent errors, the probability of obtaining the correct answer decreases exponentially with the number of qubits of the work register. A particularly simple phase-matching approach is proposed in this paper to avoid or suppress these coherent errors when using Shor's algorithm to factorize integers. The robustness of this phase-matching condition is evaluated analytically and numerically for the factorization of several integers: 4, 15, 21, and 33.Ideal quantum algorithms usually assume that quantum computing is performed continuously by a sequence of unitary transformations. However, there always exist idle finite time intervals between consecutive operations in a realistic quantum computing process. During these delays, coherent errors will accumulate from the dynamical phases of the superposed wave functions. Here we explore the sensitivity of Shor's quantum factoring algorithm to such errors. Our results clearly show a severe sensitivity of Shor's factorization algorithm to the presence of delay times between successive unitary transformations. Specifically, in the presence of these coherent errors, the probability of obtaining the correct answer decreases exponentially with the number of qubits of the work register. A particularly simple phase-matching approach is proposed in this paper to avoid or suppress these coherent errors when using Shor's algorithm to factorize integers. The robustness of this phase-matching condition is evaluated analytically and numerically for the factorization of several integers: 4, 15, 21, and 33.

arXiv:quant-ph/0305039Physical Review AFeb 22, 200511 citations

Error suppression for Hamiltonian-based quantum computation

Milad Marvian

Bulletin of the American Physical SocietyMar 9, 20180 citations

Experimental demonstration of continuous quantum error correction

William P. Livingston, Machiel Blok, Emmanuel Flurin +3 more

The storage and processing of quantum information are susceptible to external noise, resulting in computational errors. A powerful method to suppress these effects is quantum error correction. Typically, quantum error correction is executed in discrete rounds, using entangling gates and projective measurement on ancillary qubits to complete each round of error correction. Here we use direct parity measurements to implement a continuous quantum bit-flip correction code in a resource-efficient manner, eliminating entangling gates, ancillary qubits, and their associated errors. An FPGA controller actively corrects errors as they are detected, achieving an average bit-flip detection efficiency of up to 91%. Furthermore, the protocol increases the relaxation time of the protected logical qubit by a factor of 2.7 over the relaxation times of the bare comprising qubits. Our results showcase resource-efficient stabilizer measurements in a multi-qubit architecture and demonstrate how continuous error correction codes can address challenges in realizing a fault-tolerant system.The storage and processing of quantum information are susceptible to external noise, resulting in computational errors. A powerful method to suppress these effects is quantum error correction. Typically, quantum error correction is executed in discrete rounds, using entangling gates and projective measurement on ancillary qubits to complete each round of error correction. Here we use direct parity measurements to implement a continuous quantum bit-flip correction code in a resource-efficient manner, eliminating entangling gates, ancillary qubits, and their associated errors. An FPGA controller actively corrects errors as they are detected, achieving an average bit-flip detection efficiency of up to 91%. Furthermore, the protocol increases the relaxation time of the protected logical qubit by a factor of 2.7 over the relaxation times of the bare comprising qubits. Our results showcase resource-efficient stabilizer measurements in a multi-qubit architecture and demonstrate how continuous error correction codes can address challenges in realizing a fault-tolerant system.

arXiv:2107.11398Nature CommunicationsApr 28, 202273 citations

Mitigating errors in noisy quantum computers

Samuele Ferracin, nate stemen, Joel J. Wallman

Bulletin of the American Physical SocietyMar 16, 20210 citations

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