Title: Quantum state preparation and nonunitary evolution with diagonal operators

Abstract

Realizing nonunitary transformations on unitary-gate-based quantum devices is critically important for simulating a variety of physical problems, including open quantum systems and subnormalized quantum states. Here, we present a dilation-based algorithm to simulate nonunitary operations using probabilistic quantum computing with only one ancilla qubit. We utilize the singular-value decomposition (SVD) to decompose any general quantum operator into a product of two unitary operators and a diagonal nonunitary operator, which we show can be implemented by a diagonal unitary operator in a one-qubit dilated space. While dilation techniques increase the number of qubits in the calculation, and thus the gate complexity, our algorithm limits the operations required in the dilated space to a diagonal unitary operator, which has known circuit decompositions. We use this algorithm to prepare random subnormalized two-level states on a quantum device with high fidelity. Furthermore, we present the accurate nonunitary dynamics of two-level open quantum systems in a dephasing channel and an amplitude-damping channel computed on a quantum device. The algorithm presented will be most useful for implementing general nonunitary operations when the SVD can be readily computed, which is the case for most operators in the noisy intermediate-scale quantum computing era.

Authors:

Schlimgen, Anthony W.  ^[1];

• Search DOE PAGES for author "Schlimgen, Anthony W."
• Search DOE PAGES for ORCID "0000-0001-8435-6431"

Head-Marsden, Kade  ^[2];

• Search DOE PAGES for author "Head-Marsden, Kade"
• Search DOE PAGES for ORCID "0000-0002-4122-4081"

Sager-Smith, LeeAnn M.  ^[1];

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• Search DOE PAGES for ORCID "0000-0001-6760-9134"

Narang, Prineha  ^[2];

• Search DOE PAGES for author "Narang, Prineha"
• Search DOE PAGES for ORCID "0000-0003-3956-4594"

Mazziotti, David A.  ^[1]

• Search DOE PAGES for author "Mazziotti, David A."
• Search DOE PAGES for ORCID "0000-0002-9938-3886"

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+ Show Author Affiliations

1. Univ. of Chicago, IL (United States)
2. Harvard Univ., Cambridge, MA (United States)

Publication Date:

Tue Aug 16 00:00:00 EDT 2022

Research Org.:

Purdue Univ., West Lafayette, IN (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)

OSTI Identifier:

1979625

Grant/Contract Number:  

SC0019215; DMR-2037783

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review A

Additional Journal Information:

Journal Volume: 106; Journal Issue: 2; Journal ID: ISSN 2469-9926

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Optics; Physics; Open quantum systems; Quantum algorithms