Intel Corporation, Santa Clara, CA (United States)
Intel Corporation, Hillsboro, OR (United States)
NASA Ames Research Center (ARC), Moffett Field, Mountain View, CA (United States); USRA Research Institute for Advanced Computer Science, Mountain View, CA (United States)
Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing this field of research, this manuscript has three distinct purposes. First, we present an intuitive method for synthesizing and analyzing discrete (i.e., integer-based) optimization problems, wherein the problem and corresponding algorithmic primitives are expressed using a discrete quantum intermediate representation (DQIR) that is encoding-independent. This compact representation often allows for more efficient problem compilation, automated analyses of different encoding choices, easier interpretability, more complex runtime procedures, and richer programmability, as compared to previous approaches, which we demonstrate with a number of examples. Second, we perform numerical studies comparing several qubit encodings; the results exhibit a number of preliminary trends that help guide the choice of encoding for a particular set of hardware and a particular problem and algorithm. Our study includes problems related to graph coloring, the traveling salesperson problem, factory/machine scheduling, financial portfolio rebalancing, and integer linear programming. Third, we design low-depth graph-derived partial mixers (GDPMs) up to 16-level quantum variables, demonstrating that compact (binary) encodings are more amenable to QAOA than previously understood. We expect this toolkit of programming abstractions and low-level building blocks to aid in designing quantum algorithms for discrete combinatorial problems.
Sawaya, Nicolas P. D., et al. "Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems." Quantum, vol. 7, Sep. 2023. https://doi.org/10.22331/q-2023-09-14-1111
Sawaya, Nicolas P. D., Schmitz, Albert T., & Hadfield, Stuart (2023). Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems. Quantum, 7. https://doi.org/10.22331/q-2023-09-14-1111
Sawaya, Nicolas P. D., Schmitz, Albert T., and Hadfield, Stuart, "Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems," Quantum 7 (2023), https://doi.org/10.22331/q-2023-09-14-1111
@article{osti_2422948,
author = {Sawaya, Nicolas P. D. and Schmitz, Albert T. and Hadfield, Stuart},
title = {Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems},
annote = {Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing this field of research, this manuscript has three distinct purposes. First, we present an intuitive method for synthesizing and analyzing discrete (i.e., integer-based) optimization problems, wherein the problem and corresponding algorithmic primitives are expressed using a discrete quantum intermediate representation (DQIR) that is encoding-independent. This compact representation often allows for more efficient problem compilation, automated analyses of different encoding choices, easier interpretability, more complex runtime procedures, and richer programmability, as compared to previous approaches, which we demonstrate with a number of examples. Second, we perform numerical studies comparing several qubit encodings; the results exhibit a number of preliminary trends that help guide the choice of encoding for a particular set of hardware and a particular problem and algorithm. Our study includes problems related to graph coloring, the traveling salesperson problem, factory/machine scheduling, financial portfolio rebalancing, and integer linear programming. Third, we design low-depth graph-derived partial mixers (GDPMs) up to 16-level quantum variables, demonstrating that compact (binary) encodings are more amenable to QAOA than previously understood. We expect this toolkit of programming abstractions and low-level building blocks to aid in designing quantum algorithms for discrete combinatorial problems.},
doi = {10.22331/q-2023-09-14-1111},
url = {https://www.osti.gov/biblio/2422948},
journal = {Quantum},
issn = {ISSN 2521-327X},
volume = {7},
place = {United States},
publisher = {Quantum Science Open Community},
year = {2023},
month = {09}}
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 381, Issue 2241https://doi.org/10.1098/rsta.2021.0410