Quantum vertex model for reversible classical computing.

Area of Science:

• Computational Physics
• Statistical Mechanics
• Computer Science Theory

Background:

• Classical computation mapped to statistical mechanics models shows success but faces challenges with thermodynamic phase transitions.
• These phase transitions can hinder finding solutions, even for problems solvable in polynomial time.

Purpose of the Study:

• To develop a mapping of universal reversible classical computations onto a statistical mechanics model that avoids bulk thermodynamic phase transitions.
• To explore computational problem-solving using this novel model and thermal annealing techniques.

Main Methods:

• Mapping universal reversible classical computations to a planar vertex model.
• Utilizing thermal annealing, with and without 'learning,' to explore computational problems.
• Constructing a mapping of the vertex model onto the D-Wave machine's Chimera architecture.

Main Results:

• The proposed planar vertex model exhibits no bulk classical thermodynamic phase transition, irrespective of the computational circuit.
• The complexity of a computation is reflected in the relaxation dynamics of the system towards its ground state, where the solution is encoded.
• Demonstrated an approach for reversible classical computation using state-of-the-art quantum annealing implementations.

Conclusions:

• This novel mapping offers a pathway to overcome limitations posed by thermodynamic phase transitions in computational problem-solving.
• The approach provides a foundation for implementing reversible classical computation on quantum annealing hardware.