Potts Model Computing Device Solving Multivalued Spin Problems
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional Ising model computing devices can only solve binary spin problems, making it difficult to address multivalued combinatorial optimization problems known as Potts problems, which require a device capable of computing the Potts model.
Innovation Solution
A Potts model computing device is developed that transforms the Potts model Hamiltonian into a form representable by binary Ising spins, allowing the use of optical pulses to simulate the Potts model, where multivalued spins are represented by multiple binary Ising spins and interactions are computed using a ring resonator and phase-sensitive amplifier to achieve a stable state.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If an Ising model computing device is used, then binary spin problems can be solved efficiently, but multivalued spin problems (Potts problems) cannot be solved directly
Solution Approach 1:
The Potts model with M states is segmented into multiple Ising models, where M = 2^Ms. Each Ising model handles a subset of the states, and the complete solution requires solving Ms sequential Ising problems. This segmentation allows the device to handle multivalued problems by breaking them down into binary problems that the Ising device can solve.
Solution Approach 2:
The invention adds a temporal dimension to the computation by solving Ms sequential Ising problems instead of one Potts problem. The transformation involves adding imaginary time evolution and introducing auxiliary variables (σ' and σ'') to embed the multivalued problem into a sequence of binary problems, effectively moving from a single-state problem to a multi-layer temporal structure.
2Productivity
If the Potts model is transformed into binary Ising spins, then multivalued problems can be solved using optical pulses, but the computation requires multiple sequential Ising model solutions
Solution Approach 1:
The solution employs periodic action by repeating the Ising model computation Ms times, each time with different coupling coefficients J^((k)) that correspond to different layers in the temporal evolution. This periodic repetition allows the system to converge to the correct multivalued solution through iterative refinement, with each cycle bringing the system closer to the ground state.
3Adaptability or versatility
If conventional Ising model computing devices are used, then binary optimization problems can be solved, but the device cannot directly handle problems requiring more than two spin values
Solution Approach 1:
The invention introduces intermediary variables (σ' and σ'') that act as mediators between the original spin variables and the auxiliary Ising model variables. These intermediaries facilitate the transformation by establishing relationships that allow the binary Ising device to indirectly represent and solve multivalued Potts problems through a series of binary decisions.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Enables the solution of multivalued spin problems by converting the Potts model into a series of binary Ising problems, allowing the Potts model computing device to efficiently compute multivalued spin values and solve complex problems like map coloring with multiple colors.
Implementation Method 1
a phase sensitive amplifier (PSA) 2 provided in a ring-shaped optical fiber which functions as a ring resonator 1 (binary optical parametric oscillator [OPO]; 0 or π phase optical parametric oscillator)
Data Source
Figure 1
Figure 2A
Figure 2B
AI summary
There is provided a Potts model computing device capable of computing a Potts problem that is a multivalued spin problem. The Potts model computing device includes: an Ising model computing device; a computation result storage and determination unit configured to store a value of a spin of the Ising model obtained in a case where a coupling coefficient is set in the Ising model computing device and to determine whether a computation is finished; and a coupling coefficient overwriting unit configured to update a coupling coefficient generated based on the stored value of the spin to the Ising model computing device. According to a value of a set of spins of the Ising model obtained as a computation result corresponding to a coupling coefficient set for an m-th time in the Ising model computing device, the coupling coefficient overwriting unit generates again a coupling coefficient to be set for an (m+1)-th iterative computation and sets the generated coupling coefficient to the Ising model computing device. In a case where a possible value of a multivalued spin is Si = 0, 1, 2, ..., M - 1 (M is a natural number) and M ≤ 2Ms, the computation result storage and determination unit determines that a computation is finished in a case where a number of iteration times of setting a coupling coefficient in the coupling coefficient overwriting unit reaches a number of iteration times corresponding to Ms (Ms is a natural number), and computes a value Si by substituting a value σim of a spin obtained as a computation result based on the coupling coefficient set for the m-th time computation into the following formula to compute a problem mapped to the Potts model using the Ising model: Si=∑m=1Ms1+σim2m−2