Quantum Interior Point Methods for Semidefinite Optimization

Journal Article · Mon Sep 11 00:00:00 EDT 2023 · Quantum

DOI:https://doi.org/10.22331/q-2023-09-11-1110· OSTI ID:1999443

Augustino, Brandon ^[1]; Nannicini, Giacomo ^[2]; Terlaky, Tamás ^[1]; Zuluaga, Luis F. ^[1]

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1. Department of Industrial and Systems Engineering, Quantum Computing and Optimization Lab, Lehigh University
2. Department of Industrial and Systems Engineering, University of Southern California

We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact search direction and is not guaranteed to explore only feasible points; the second scheme uses a nullspace representation of the Newton linear system to ensure feasibility even with inexact search directions. The second is a novel scheme that might seem impractical in the classical world, but it is well-suited for a hybrid quantum-classical setting. We show that both schemes converge to an optimal solution of the semidefinite optimization problem under standard assumptions. By comparing the theoretical performance of classical and quantum interior point methods with respect to various input parameters, we show that our second scheme obtains a speedup over classical algorithms in terms of the dimension of the problem $n$ , but has worse dependence on other numerical parameters.

• Sponsoring Organization: USDOE
• Grant/Contract Number: N000142312585
• OSTI ID: 1999443
• Journal Information: Quantum, Journal Name: Quantum Vol. 7; ISSN 2521-327X
• Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
• Country of Publication: Austria
• Language: English