NchooseK is an experiment in providing portable programming across classical computers, quantum annealers, and circuit-model quantum computers. Its initial implementation is as an embedded domain-specific language—a Python module that provides a set of basic programming primitives, which the programmer combines using ordinary Python code.

NchooseK is based on a single primitive, nck, which establishes a constraint, "k of these n Boolean values must be True". For example, nck([A, B, C], {1}) dictates that exactly one of variables A, B, and C must be True and the rest must be False. k can be a set containing multiple values: nck([A, B, C], {0, 3}) dictates that either all three of A, B, and C are False or all three are True.

Variables can appear multiple times in the first argument. All instances of a variable will receive the same True/False value. As an example, nck([A, B, B], {2}) has a single solution: A = False and B = True. Any other assignment of True and False would result in 0, 1, or 3 of [A, B, B] being True.

A program can—and typically does—specify multiple nck constraints. nck([A, B, C], {1}); nck([B, C, D], {1}); nck([C, D, E], {1}) dictates that exactly one of {A, B, C}, exactly one of [B, C, D], and exactly one of [C, D, E] must be True. Hence, one possible solution sets A and E True and the rest of the variables False; another possible solution sets only C True and the rest False.

Constraints can be either "hard" (the default) or "soft". Hard constraints must be satisfied for a solution to be valid. Soft constraints will be satisfied if possible but can be violated if necessary. Indicate a soft constraint by appending a soft=True argument to an nck constraint.

That's it! NchooseK may seem simplistic, but our hypothesis is that it is sufficiently general as to express a wide variety of computational problems yet sufficiently simple as to facilitate implementation across highly disparate computational platforms.

pip install --use-feature=in-tree-build .

Documentation is forthcoming. For the time being, please refer to the examples in the examples subdirectory. The main idea is to instantiate an nchoosek.Environment, which is basically a name space. The environment's register_port method defines a variable, and the environment's nck method establishes a constraint given a list of ports and a set of allowable numbers of True ports.

Different solvers eventually will be supported. Currently, only three exist: z3, which uses Microsoft Research's classical Z3 Theorem Prover, ocean, which uses D-Wave's Ocean to run either classically or on a quantum computer, and qiskit, which uses IBM's Qiskit to run either classically or on a quantum computer. Specify one of those in your NCHOOSEK_SOLVER environment variable or as the optional solver argument to the environment's solve method (default: z3). Invoke the solve method on the environment to solve for the value of every variable in the environment. solve accepts solver-specific parameters, which also can be provided via the NCHOOSEK_PARAMS environment variable.

As a convenience, the environment's new_type method defines a reusable constraint that can be applied to different sets of inputs.

Ellis Wilson, Frank Mueller and Scott Pakin, "Combining Hard and Soft Constraints in Quantum Constraint-Satisfaction Systems," in SC22: International Conference for High Performance Computing, Networking, Storage, and Analysis. Dallas, Texas, USA, Nov. 2022, pp. 161–174. URL: https://www.computer.org/csdl/proceedings-article/sc/2022/544400a161/1I0bSO944Eg.

Ellis Wilson, Frank Mueller and Scott Pakin, "Mapping Constraint Problems onto Quantum Gate and Annealing Devices," 2021 IEEE/ACM Second International Workshop on Quantum Computing Software (QCS), St. Louis, Missouri, USA, Nov. 2021, pp. 110–117, DOI: 10.1109/QCS54837.2021.00016.

Harsh Khetawat, Ashlesha Atrey, George Li, Frank Mueller, and Scott Pakin, "Implementing NChooseK on IBM Q Quantum Computer Systems". In: Michael Kirkedal Thomsen and Mathias Soeken (eds.), Proceedings of the 11th International Conference on Reversible Computation (RC 2019), Lausanne, Switzerland. Lecture Notes in Computer Science, vol. 11497. Springer, Cham. DOI: 10.1007/978-3-030-21500-2_13.

Copyright © 2021 Triad National Security, LLC. All rights reserved.

This program was produced under U.S. Government contract 89233218CNA000001 for Los Alamos National Laboratory (LANL), which is operated by Triad National Security, LLC for the U.S. Department of Energy/National Nuclear Security Administration. All rights in the program are reserved by Triad National Security, LLC, and the U.S. Department of Energy/National Nuclear Security Administration. The Government is granted for itself and others acting on its behalf a nonexclusive, paid-up, irrevocable worldwide license in this material to reproduce, prepare derivative works, distribute copies to the public, perform publicly and display publicly, and to permit others to do so.

This program is open source under the BSD-3 License. Its LANL-internal identifier is C21038.

Scott Pakin, [email protected]