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Efficient Application of the Factorized form of the Unitary Coupled-Cluster Ansatz for the Variational Quantum Eigensolver Algorithm by Using Linear Combination of Unitaries

Journal Article · · Symmetry
DOI:https://doi.org/10.3390/sym15071429· OSTI ID:2424442
 [1];  [1]
  1. Georgetown University, Washington, DC (United States)
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The variational quantum eigensolver is one of the most promising algorithms for near-term quantum computers. It has the potential to solve quantum chemistry problems involving strongly correlated electrons with relatively low-depth circuits, which are otherwise difficult to solve on classical computers. The variational eigenstate is constructed from a number of factorized unitary coupled-cluster terms applied onto an initial (single-reference) state. Current algorithms for applying one of these operators to a quantum state require a number of operations that scale exponentially with the rank of the operator. We exploit a hidden SU(2) symmetry to allow us to employ the linear combination of unitaries approach, Our Prepare subroutine uses n+2 ancilla qubits for a rank-n operator. Our Select (U) scheme uses O(n) Cnot gates. This results in a full algorithm that scales like the cube of the rank of the operator n3, a significant reduction in complexity for rank five or higher operators. This approach, when combined with other algorithms for lower-rank operators (when compared to the standard implementation), will make the factorized form of the unitary coupled-cluster approach much more efficient to implement on all types of quantum computers.
Research Organization:
Georgetown University, Washington, DC (United States)
Sponsoring Organization:
USDOE
OSTI ID:
2424442
Journal Information:
Symmetry, Journal Name: Symmetry Journal Issue: 7 Vol. 15; ISSN 2073-8994
Publisher:
MDPICopyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

97 MATHEMATICS AND COMPUTING
Science & Technology - Other Topics
factorized unitary coupled-cluster ansatz
linear combination of unitaries
quantum chemistry