Fusing the single-excitation subspace with $${\mathbb C}^{2^n}$$ C 2 n

Fusing the single-excitation subspace with $${\mathbb C}^{2^n}$$ C 2 n

Abstract There is a tremendous interest in developing practical applications for noisy intermediate-scale quantum processors without the overhead required by full error correction. Near-term quantum information processing is especially challenging within the standard gate model, as algorithms quickl...

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Autor principal: Michael R. Geller
Formato: article
Lenguaje:EN
Publicado: Nature Portfolio 2021
Materias:
Medicine
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Science
Q
Acceso en línea:https://doaj.org/article/1d674b9200234feeb6886411ce46e9f2
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spelling oai:doaj.org-article:1d674b9200234feeb6886411ce46e9f22021-12-02T14:12:41ZFusing the single-excitation subspace with $${\mathbb C}^{2^n}$$ C 2 n10.1038/s41598-020-79853-32045-2322https://doaj.org/article/1d674b9200234feeb6886411ce46e9f22021-01-01T00:00:00Zhttps://doi.org/10.1038/s41598-020-79853-3https://doaj.org/toc/2045-2322Abstract There is a tremendous interest in developing practical applications for noisy intermediate-scale quantum processors without the overhead required by full error correction. Near-term quantum information processing is especially challenging within the standard gate model, as algorithms quickly lose fidelity as the problem size and circuit depth grow. This has lead to a number of non-gate-model approaches such as analog quantum simulation and quantum annealing. These come with specific hardware requirements that are different than that of a universal gate-based quantum computer. We have previously proposed an approach called the single-excitation subspace (SES) method, which uses a complete graph of superconducting qubits with tunable coupling. Without error correction the SES method is not scalable, but it offers several algorithmic components with constant depth, which is highly desirable for near-term use. The challenge of the SES method is that it requires a physical qubit for every basis state in the computer’s Hilbert space. This imposes exponentially large resource costs for algorithms using registers of ancillary qubits, as each ancilla would double the required graph size. Here we show how to circumvent this doubling by leaving the SES and fusing it with a multi-ancilla Hilbert space. Specifically, we implement the tensor product of an SES register holding “data” with one or more ancilla qubits, which are able to independently control arbitrary $$n\!\times \!n$$ n × n unitary operations on the data in a constant number of steps. This enables a hybrid form of quantum computation where fast SES operations are performed on the data, traditional logic gates and measurements are performed on the ancillas, and controlled-unitaries act between. As example applications, we give ancilla-assisted SES implementations of quantum phase estimation and the quantum linear system solver of Harrow, Hassidim, and Lloyd.Michael R. GellerNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-10 (2021)
institution DOAJ
collection DOAJ
language EN
topic Medicine
R
Science
Q
spellingShingle Medicine
R
Science
Q
Michael R. Geller
Fusing the single-excitation subspace with $${\mathbb C}^{2^n}$$ C 2 n
description Abstract There is a tremendous interest in developing practical applications for noisy intermediate-scale quantum processors without the overhead required by full error correction. Near-term quantum information processing is especially challenging within the standard gate model, as algorithms quickly lose fidelity as the problem size and circuit depth grow. This has lead to a number of non-gate-model approaches such as analog quantum simulation and quantum annealing. These come with specific hardware requirements that are different than that of a universal gate-based quantum computer. We have previously proposed an approach called the single-excitation subspace (SES) method, which uses a complete graph of superconducting qubits with tunable coupling. Without error correction the SES method is not scalable, but it offers several algorithmic components with constant depth, which is highly desirable for near-term use. The challenge of the SES method is that it requires a physical qubit for every basis state in the computer’s Hilbert space. This imposes exponentially large resource costs for algorithms using registers of ancillary qubits, as each ancilla would double the required graph size. Here we show how to circumvent this doubling by leaving the SES and fusing it with a multi-ancilla Hilbert space. Specifically, we implement the tensor product of an SES register holding “data” with one or more ancilla qubits, which are able to independently control arbitrary $$n\!\times \!n$$ n × n unitary operations on the data in a constant number of steps. This enables a hybrid form of quantum computation where fast SES operations are performed on the data, traditional logic gates and measurements are performed on the ancillas, and controlled-unitaries act between. As example applications, we give ancilla-assisted SES implementations of quantum phase estimation and the quantum linear system solver of Harrow, Hassidim, and Lloyd.
format article
author Michael R. Geller
author_facet Michael R. Geller
author_sort Michael R. Geller
title Fusing the single-excitation subspace with $${\mathbb C}^{2^n}$$ C 2 n
title_short Fusing the single-excitation subspace with $${\mathbb C}^{2^n}$$ C 2 n
title_full Fusing the single-excitation subspace with $${\mathbb C}^{2^n}$$ C 2 n
title_fullStr Fusing the single-excitation subspace with $${\mathbb C}^{2^n}$$ C 2 n
title_full_unstemmed Fusing the single-excitation subspace with $${\mathbb C}^{2^n}$$ C 2 n
title_sort fusing the single-excitation subspace with $${\mathbb c}^{2^n}$$ c 2 n
publisher Nature Portfolio
publishDate 2021
url https://doaj.org/article/1d674b9200234feeb6886411ce46e9f2
work_keys_str_mv AT michaelrgeller fusingthesingleexcitationsubspacewithmathbbc2nc2n
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