Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session G40: Noisy Intermediate Scale Quantum Computers V
11:30 AM–2:30 PM,
Tuesday, March 15, 2022
Room: McCormick Place W-196B
Sponsoring
Units:
DQI DCOMP
Chair: Peter Johnson, Zapata Computing
Abstract: G40.00001 : NISQ Algorithm for Semidefinite Programming
11:30 AM–11:42 AM
Presenter:
Kishor Bharti
(Joint Center for Quantum Information and Computer Science)
Authors:
Kishor Bharti
(Joint Center for Quantum Information and Computer Science)
Tobias Haug
(Imperial College London)
Vlatko Vedral
(Centre for Quantum Technologies)
Leong-Chuan Kwek
(Centre for Quantum Technologies)
Here, we present a NISQ algorithm for solving SDPs. The classical optimization program of our NISQ solver is another SDP over a lower dimensional ansatz space. Using the SDP formulation of the Hamiltonian ground state problem, we design a NISQ eigensolver. Unlike variational quantum eigensolvers, the classical optimization program of our eigensolver is convex, can be solved in polynomial time and every local minimum is a global minimum.
Further, we demonstrate the potential of our NISQ SDP solver by finding the largest eigenvalue of $2^{1000}$ dimensional matrices and solving graph problems related to quantum contextuality. We also discuss NISQ algorithms for rank-constrained SDPs. Our work extends the application of NISQ computers onto one of the most successful algorithmic frameworks of the past few decades.
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