Systems and methods employing new evolution schedules in an analog computer with applications to determining isomorphic graphs and post-processing solutions
A second problem Hamiltonian may replace a first problem Hamiltonian during evolution of an analog processor (e.g., quantum processor) during a first iteration in solving a first problem. This may be repeated during a second, or further successive iterations on the first problem, following re-initialization of the analog processor. An analog processor may evolve under a first non-monotonic evolution schedule during a first iteration, and second non-monotonic evolution schedule under second, or additional non-monotonic evolution schedule under even further iterations. A first graph and second graph may each be processed to extract final states versus a plurality of evolution schedules, and a determination made as to whether the first graph is isomorphic with respect to the second graph. An analog processor may evolve by decreasing a temperature of, and a set of quantum fluctuations, within the analog processor until the analog processor reaches a state preferred by a problem Hamiltonian.
1. A system for use in quantum processing, comprising:
at least one non-transitory processor-readable medium that stores at least one of processor executable instructions or data; and
at least one processor communicatively coupled to the least one non-transitory processor-readable medium, and which, in response to execution of the at least one of processor executable instructions or data:
for a first computational problem, during a first iteration of a plurality of iterations:
receives a problem Hamiltonian for the first computational problem;
receives an initial solution to the first computational problem;
receives an evolution schedule;
initializes an analog processor to a first final state based on the initial solution, the analog processor comprising:
a plurality of quantum devices;
a plurality of local bias devices to provide controllable local biases to the plurality of quantum devices; and
a plurality of couplers to provide controllable communicative coupling between respective pairs of quantum devices in the plurality of quantum devices;
causes the analog processor to evolve backwards within the evolution schedule from the initial solution towards a state preferred by an initial Hamiltonian reaching a first turning point;
causes the analog processor to evolve forwards within the evolution schedule from the first turning point towards a second final state preferred by the problem Hamiltonian; and
reads out the second final state thereby determining a second result of the first computational problem.
2. The system of claim 1 wherein, in response to execution of the at least one of processor executable instructions or data, the at least one processor:
for the first computational problem, during a second iteration of the plurality of iterations, the second iteration different from the first iteration:
re-initializes an analog processor to the first final state based on the initial solution;
causes the analog processor to re-evolve backwards within the evolution schedule from the initial solution towards a state preferred by an initial Hamiltonian reaching a second turning point;
causes the analog processor to re-evolve forwards within the evolution schedule from the second turning point towards a third final state preferred by the problem Hamiltonian; and
reads out the third final state thereby determining a third result of the first computational problem.
3. The system of claim 2 wherein, in response to execution of the at least one of processor executable instructions or data, the at least one processor:
records the second result and a value correlated with the first turning point; and
records the third result and a value correlated with the second turning point.
4. The system of claim 2 wherein, in response to execution of the at least one of processor executable instructions or data, the at least one processor:
returns the second result and a value correlated with the first turning point; and
returns the third result and a value correlated with the second turning point.
5. A computational method, comprising:
receiving a problem Hamiltonian for a first computational problem;
receiving an initial solution to the first computational problem;
receiving an evolution schedule;
for a first computational problem, during a first iteration of a plurality of iterations:
initializing an analog processor to a first final state based on the initial solution, wherein the analog processor comprises:
a plurality of quantum devices;
a plurality of local bias devices to provide controllable local biases to the plurality of quantum devices; and
a plurality of couplers to provide controllable communicative coupling between respective pairs of quantum devices in the plurality of quantum devices;
causing the analog processor to evolve backwards within the evolution schedule from the initial solution towards a state preferred by an initial Hamiltonian;
causing the analog processor to evolve forwards within the evolution schedule from a first turning point towards a second final state preferred by the problem Hamiltonian; and
reading out the second final state of the quantum devices to determine a second result of the first computational problem.
6. The method of claim 5 , further comprising
for the first computational problem, during a second iteration of the plurality of iterations, the second iteration different from the first iteration:
re-initializing an analog processor to the first final state based on the initial solution;
causing the analog processor to re-evolve backwards within the evolution schedule from the initial solution towards a state preferred by an initial Hamiltonian;
causing the analog processor to re-evolve forwards within the evolution schedule from a second turning point towards a third final state preferred by the problem Hamiltonian; and
reading out the third final state to determine a third result of the first computational problem.
7. The method of claim 6 , further comprising:
recording the second result and a value correlated with the first turning point; and
recording the third result and a value correlated with the second turning point.
8. The method of claim 6 , further comprising:
returning the second result and a value correlated with the first turning point; and
returning the third result and a value correlated with the second turning point.