End-to-end resource analysis for quantum interior point methods and portfolio optimization
Abstract
We study quantum interior point methods (QIPMs) for second-order cone programming (SOCP), guided by the example use case of portfolio optimization (PO). We provide a complete quantum circuit-level description of the algorithm from problem input to problem output, making several improvements to the implementation of the QIPM. We report the number of logical qubits and the quantity/depth of non-Clifford T-gates needed to run the algorithm, including constant factors. The resource counts we find depend on instance-specific parameters, such as the condition number of certain linear systems within the problem. To determine the size of these parameters, we perform numerical simulations of small PO instances, which lead to concrete resource estimates for the PO use case. Our numerical results do not probe large enough instance sizes to make conclusive statements about the asymptotic scaling of the algorithm. However, already at small instance sizes, our analysis suggests that, due primarily to large constant pre-factors, poorly conditioned linear systems, and a fundamental reliance on costly quantum state tomography, fundamental improvements to the QIPM are required for it to lead to practical quantum advantage.
Authors 11
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California Institute of Technology
Affiliation as printed
AWS Center for Quantum Computing , Pasadena , CA , USA
California Institute of Technology , Pasadena , CA , USA
AWS Center for Quantum Computing, Pasadena, CA, USA
California Institute of Technology, Pasadena, CA, USA
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Affiliation as printed
Goldman Sachs , New York , NY , USA
Goldman Sachs, New York, NY, USA
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California Institute of Technology · Amazon (United States)
Affiliation as printed
AWS Center for Quantum Computing, Pasadena, CA, USA
Amazon Quantum Solutions Lab, Seattle, WA, USA
California Institute of Technology, Pasadena, CA, USA
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California Institute of Technology · Imperial College London · RWTH Aachen University
Affiliation as printed
AWS Center for Quantum Computing, Pasadena, CA, USA
California Institute of Technology, Pasadena, CA, USA
Department of Computing, Imperial College London, London, UK
Institute for Quantum Information, RWTH Aachen University, Aachen, Germany
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Amazon (United States) · Applied Quantum Technologies (United States) · Quantum Technologies (Sweden)
Affiliation as printed
AWS Quantum Technologies , Seattle , WA , USA
AWS Quantum Technologies, Seattle, WA, USA
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New Jersey Institute of Technology · Goldman Sachs (United States)
Affiliation as printed
Goldman Sachs , New York , NY , USA
New Jersey Institute of Technology , Newark , NJ , USA
Goldman Sachs, New York, NY, USA
New Jersey Institute of Technology, Newark, NJ, USA
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Affiliation as printed
Goldman Sachs , New York , NY , USA
Goldman Sachs, New York, NY, USA
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Affiliation as printed
AWS Center for Quantum Computing , Pasadena , CA , USA
Amazon Quantum Solutions Lab , Seattle , WA , USA
AWS Center for Quantum Computing, Pasadena, CA, USA
Amazon Quantum Solutions Lab, Seattle, WA, USA
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California Institute of Technology
Affiliation as printed
AWS Center for Quantum Computing , Pasadena , CA , USA
California Institute of Technology , Pasadena , CA , USA
AWS Center for Quantum Computing, Pasadena, CA, USA
California Institute of Technology, Pasadena, CA, USA
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Amazon (United States) · University of Washington
Affiliation as printed
AWS Center for Quantum Computing, Pasadena, CA, USA
Amazon Quantum Solutions Lab, Seattle, WA, USA
University of Washington, Seattle, WA, USA
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Affiliation as printed
Goldman Sachs , New York , NY , USA
Goldman Sachs, New York, NY, USA
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