Encoding Trade-offs And Design Toolkits In Quantum Algorithms For Discrete Optimization: Coloring, Routing, Scheduling, And Other Problems

Nicolas PD Sawaya¹, Albert T Schmitz², and Stuart Hadfield^3,4

¹Intel Labs, Intel Corporation, Santa Clara, California 95054, USA [[email protected]]
²Intel Labs, Intel Corporation, Hillsboro, Oregon 97124, USA
³Quantum Artificial Intelligence Laboratory, NASA Ames Research Center, Moffett Field, California 94035, USA
⁴USRA Research Institute for Advanced Computer Science, Mountain View, California, 94043, USA

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Abstract

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.

Featured image: A graph-derived partial mixer (GDPM) for constraining a 3-qubit variable to 6 states while implementing e.g. QAOA.

► BibTeX data

@article{Sawaya2023encodingtradeoffs, doi = {10.22331/q-2023-09-14-1111}, url = {https://doi.org/10.22331/q-2023-09-14-1111}, title = {Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems}, author = {Sawaya, Nicolas PD and Schmitz, Albert T and Hadfield, Stuart}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1111}, month = sep, year = {2023}<br /> }

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Cited by

[1] Nicolas PD Sawaya, Daniel Marti-Dafcik, Yang Ho, Daniel P Tabor, David Bernal, Alicia B Magann, Shavindra Premaratne, Pradeep Dubey, Anne Matsuura, Nathan Bishop, Wibe A de Jong, Simon Benjamin, Ojas D Parekh, Norm Tubman, Katherine Klymko, and Daan Camps, “HamLib: A library of Hamiltonians for benchmarking quantum algorithms and hardware”, arXiv:2306.13126, (2023).

[2] Federico Dominguez, Josua Unger, Matthias Traube, Barry Mant, Christian Ertler, and Wolfgang Lechner, “Encoding-Independent Optimization Problem Formulation for Quantum Computing”, arXiv:2302.03711, (2023).

[3] Nicolas PD Sawaya and Joonsuk Huh, “Improved resource-tunable near-term quantum algorithms for transition probabilities, with applications in physics and variational quantum linear algebra”, arXiv:2206.14213, (2022).

The above citations are from SAO/NASA ADS (last updated successfully 2023-09-15 13:07:36). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2023-09-15 13:07:35).

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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