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Testing Quantum Satisfiability
Ashley Montanaro1,2, Changpeng Shao3, Dominic Verdon1,4
1School of Mathematics, University of Bristol, Bristol, BS8 1UG UK.
Communications in Mathematical Physics
|September 3, 2025
Summary
Quantum k-SAT, a problem likely hard for quantum computers, can be solved efficiently under specific conditions. This research shows that with a property testing guarantee, quantum k-SAT instances are solvable in randomized polynomial time.
Area of Science:
- Quantum computing
- Computational complexity theory
- Quantum information science
Background:
- Quantum k-SAT is QMA-complete for k >= 3, indicating its computational hardness.
- Solving quantum k-SAT is challenging for quantum computers.
Purpose of the Study:
- To investigate the solvability of quantum k-SAT under a property testing promise.
- To develop a randomized polynomial-time algorithm for quantum k-SAT.
Main Methods:
- Leveraging a classical result by Alon and Shapira.
- Analyzing subproblems on constant-sized qubit subsystems.
- Employing a property testing framework for instance classification.
Main Results:
- Quantum k-SAT is solvable in randomized polynomial time if instances are guaranteed to be either satisfiable or far from product-state satisfiable.
- Satisfiable instances have product-state solutions for most small subproblems.
- Instances far from product-state satisfiable have unsatisfiable subproblems.
Conclusions:
- The property testing promise simplifies the quantum k-SAT problem.
- Randomly checking product-state satisfiability on subsystems offers a viable solution strategy.
- This approach potentially makes hard quantum computational problems tractable.
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