Quantum calculating thermalization rate and boltzmann sampling

1 . A computer-implemented method, comprising:

mapping, by a classical sampling system comprising a classical processor, a Fokker-Planck equation to a quantum problem comprising a first quantum operator;

generating, by the classical sampling system, a job request associated with the quantum problem;

based on the mapping and the job request, determining, by a quantum sampling system comprising a quantum processor, a second quantum operator as a function of a lowest eigenvalue of the first quantum operator, wherein the second quantum operator is a supersymmetric Hamiltonian that provides a supersymmetry-based ground state with the lowest eigenvalue based on an effective Hamiltonian, being the first quantum operator, and that provides the supersymmetry-based ground state, wherein the supersymmetric Hamiltonian is based on a supersymmetric quantum formulation of the Fokker-Planck equation, wherein determining the second quantum operator comprises implementing a kinetic portion of the supersymmetric Hamiltonian using a quantum Fourier transform that enables execution of a quantum logic circuit comprising qubits in polynomial time, and wherein the quantum logic circuit relates to unitary dynamics relating to the supersymmetric Hamiltonian; and

determining, by the quantum sampling system a thermalization rate as a function of the second quantum operator, wherein determining the thermalization rate comprises determining the thermalization rate as the supersymmetry-based ground state of the supersymmetric Hamiltonian; and

determining, by the quantum sampling system, quantum information from which a reaction rate constant and a saddle point of a reaction based on the supersymmetric Hamiltonian that provides the supersymmetry-based ground state with the lowest eigenvalue is subsequently determined.

2 . The computer-implemented method of claim 1 , further comprising:

encoding, by the classical sampling system a continuous variable of a classical computing problem into a quantum register of the quantum processor, wherein an encoded continuous variable is generated based on the encoding, wherein the quantum problem is generated based on the encoded continuous variable applied to the quantum register, and wherein the quantum register comprises a group of qubits;

performing, by the quantum sampling system a quantum computing operation on the encoded continuous variable in the quantum register, wherein the thermalization rate is determined based on the quantum computing operation performed on the encoded continuous variable; and

determining, by the quantum sampling system a quantum solution to the quantum problem based on the performing of the quantum computing operation on the encoded continuous variable, wherein the quantum solution comprises the thermalization rate, and wherein a solution to the classical computing problem is determined based on the quantum solution related to the encoded continuous variable.

3 . The computer-implemented method of claim 1 ,

wherein the first quantum operator is the effective Hamiltonian, and wherein the computer-implemented method further comprises:

determining, by the quantum sampling system a stationary solution of the Fokker-Planck equation as a ground state of the effective Hamiltonian, based on a connection between classical stochastic dynamics and a Schrodinger equation.

4 . The computer-implemented method of claim 1 , further comprising:

loading, by the classical sampling system a defined ansatz using a variational process, wherein the defined ansatz is able to minimize a cost function given by an expectation value associated with the effective Hamiltonian in connection with sampling of a Boltzmann probability distribution and a second expectation value associated with the supersymmetric Hamiltonian in connection with the determining of the reaction rate constant, wherein the Boltzmann probability distribution is related to the quantum problem and a classical computing problem corresponding to the quantum problem, and wherein a stationary solution of the Fokker-Planck equation is the Boltzmann probability distribution.

5 . The computer-implemented method of claim 1 , further comprising:

sampling, by the quantum sampling system a Boltzmann probability distribution related to the quantum problem and a classical computing problem corresponding to the quantum problem based on the supersymmetric Hamiltonian that provides the supersymmetry-based ground state with the lowest eigenvalue and based on an encoded continuous variable that is associated with the classical computing problem and is applied to a quantum register of the quantum processor, wherein a stationary solution of the Fokker-Planck equation is the Boltzmann probability distribution; and

determining, by the quantum sampling system a first estimation of a quantum solution to the quantum problem based on the sampling of the Boltzmann probability distribution and the thermalization rate.

6 . The computer-implemented method of claim 5 , further comprising:

modifying, by the s quantum sampling system the first estimation of the quantum solution to the quantum problem based on applying a quantum phase estimation engine to the first estimation of the quantum solution to the quantum problem;

determining, by the quantum sampling system a second estimation of the quantum solution to the quantum problem based on the modifying of the first estimation of the quantum solution, wherein the quantum solution to the quantum problem is determined based on the second estimation of the quantum solution to the quantum problem.

7 . The computer-implemented method of claim 6 , further comprising:

reducing, by the quantum sampling system, using the quantum phase estimation engine to facilitate solving the quantum problem, an amount of time utilized to determine the thermalization rate by a defined time reduction factor as compared to calculation of the thermalization rate using a classical computer, and wherein the defined time reduction factor ranges from greater than one up to approximately four.

8 . The computer-implemented method of claim 1 , further comprising:

evaluating, by the quantum sampling system, the first quantum operator;

performing, by the quantum sampling system, a first eigenstate projection quantum method;

projecting, by the quantum sampling system, an initial quantum state, being a function of the first quantum operator, into an energy subspace of the first quantum operator;

reading out, by the quantum sampling system, of a qubit register a first readout configuration of the energy subspace; and

initializing, by the quantum sampling system, employing the quantum processor, another eigenstate projection method employing the first readout configuration as a starting state of the another eigenstate projection method.

9 . A system, comprising:

a classical sampling system comprising a classical processor; and

a quantum sampling system comprising a quantum processor; and

wherein the classical sampling system is configured to:

map a Fokker-Planck equation to a quantum problem comprising a first quantum operator; and

generate a job request associated with the quantum problem; and

wherein the quantum sampling system is configured to:

based on the mapping and the job request, determine a second quantum operator as a function of a lowest eigenvalue of the first quantum operator, wherein the second quantum operator is a supersymmetric Hamiltonian that provides a supersymmetry-based ground state with the lowest eigenvalue based on an effective Hamiltonian, being the first quantum operator, and that provides the supersymmetry-based ground state, wherein the supersymmetric Hamiltonian is based on a supersymmetric quantum formulation of the Fokker-Planck equation, wherein determining the second quantum operator comprises implementing a kinetic portion of the supersymmetric Hamiltonian using a quantum Fourier transform that enables execution of a quantum logic circuit comprising qubits in polynomial time, and wherein the quantum logic circuit relates to unitary dynamics relating to the supersymmetric Hamiltonian;

determine a thermalization rate as a function of the second quantum operator, wherein determining the thermalization rate comprises determining the thermalization rate as the supersymmetry-based ground state of the supersymmetric Hamiltonian; and

determine quantum information from which a reaction rate constant and a saddle point of a reaction based on the supersymmetric Hamiltonian that provides the supersymmetry-based ground state with the lowest eigenvalue is subsequently determined.

10 . The system of claim 9 , wherein the classical sampling system is further configured to:

encode a continuous variable of a classical computing problem into a quantum register of the quantum processor of the quantum sampling system, wherein an encoded continuous variable is generated based on the encoding, wherein the quantum problem relates to the classical computing problem, wherein the quantum problem is generated based on the encoded continuous variable applied to the quantum register, and wherein the quantum register comprises a group of qubits.

11 . The system of claim 10 , wherein the quantum sampling system is further configured to:

perform a quantum computing operation on the encoded continuous variable in the quantum register, wherein the thermalization rate is determined based on the quantum computing operation performed on the encoded continuous variable; and

determine a quantum solution to the quantum problem based on the performing of the quantum computing operation on the encoded continuous variable, wherein the quantum solution comprises the thermalization rate, and wherein a solution to the classical computing problem is determined based on the quantum solution related to the encoded continuous variable.

12 . The system of claim 9 , wherein the first quantum operator is the effective Hamiltonian, and wherein the quantum sampling system is further configured to:

determine a stationary solution of the Fokker-Planck equation as a ground state of the effective Hamiltonian based on a connection between classical stochastic dynamics and a Schrodinger equation.

13 . The system of claim 12 , wherein the classical sampling system is further configured to:

load a defined ansatz using a variational process, wherein the defined ansatz facilitates mitigating a cost function given by a first expectation value associated with the effective Hamiltonian in connection with sampling of a Boltzmann probability distribution and a second expectation value associated with the supersymmetric Hamiltonian in connection with the determining of the reaction rate constant, wherein the Boltzmann probability distribution is related to the quantum problem and a classical computing problem that corresponds to the quantum problem, and wherein the stationary solution of the Fokker-Planck equation is the Boltzmann probability distribution.

14 . The system of claim 12 , wherein the quantum sampling system is further configured to:

sample a Boltzmann probability distribution related to the quantum problem and a classical computing problem that corresponds to the quantum problem based on the supersymmetric Hamiltonian that provides the supersymmetry-based ground state with the lowest eigenvalue and based on an encoded continuous variable that is associated with the classical computing problem and is applied to a quantum register of the quantum processor, wherein the stationary solution of the Fokker-Planck equation is the Boltzmann probability distribution; and

determine a first estimation of a quantum solution to the quantum problem based on the sampling of the Boltzmann probability distribution and the thermalization rate.

15 . The system of claim 14 , wherein the quantum sampling system is further configured to:

refine, using a quantum phase estimation engine of the quantum sampling system, the first estimation of the quantum solution to the quantum problem, based on the first estimation of the quantum solution to the quantum problem and a quantum phase estimation function, wherein the quantum phase estimation engine determines a second estimation of the quantum solution to the quantum problem based on the refining of the first estimation of the quantum solution, wherein the second estimation enhances accuracy of estimation of the quantum solution over the first estimation; and

determine the quantum solution to the quantum problem based on the second estimation of the quantum solution to the quantum problem.

16 . The system of claim 9 , wherein the quantum sampling system is further configured to:

evaluate the first quantum operator;

performs a first eigenstate projection quantum method;

project an initial quantum state, being a function of the first quantum operator, into an energy subspace of the first quantum operator;

read out of a qubit register a first readout configuration of the energy subspace; and

initialize another eigenstate projection method employing the first readout configuration as a starting state of the another eigenstate projection method.

17 . A computer program product that facilitates performing Boltzmann probability distribution sampling and determining a thermalization rate using quantum computing operations, the computer program product comprising a non-transitory computer readable storage medium having program instructions embodied therewith, the program instructions being executable by a system comprising a classical sampling system comprising a classical processor and a quantum sampling system comprising a quantum processor to cause the system to:

map, by the classical sampling system, a Fokker-Planck equation to a quantum problem comprising a first quantum operator;

generate, by the classical sampling system, a job request associated with the quantum problem;

based on the mapping and the job request, determine, by the quantum sampling system, a second quantum operator as a function of a lowest eigenvalue of the first quantum operator;

determine, by the quantum sampling system, the thermalization rate as a function of the second quantum operator;

evaluate, by the quantum sampling system, the first quantum operator;

perform, by the quantum sampling system, a first eigenstate projection quantum method;

project, by the quantum sampling system, an initial quantum state, being a function of the first quantum operator, into an energy subspace of the first quantum operator;

read out, by the quantum sampling system, of a qubit register a first readout configuration of the energy subspace; and

initialize, by the quantum sampling system, another eigenstate projection method employing the first readout configuration as a starting state of the another eigenstate projection method.

18 . The computer program product of claim 17 , wherein the program instructions are further executable by the system to cause the system to:

encode, by the classical sampling system, a continuous variable of a classical computing problem into a quantum register of the quantum processor, wherein an encoded continuous variable is generated based on the encoding, wherein the quantum problem is generated based on the encoded continuous variable applied to the quantum register, and wherein the quantum register comprises a group of qubits;

perform, the quantum sampling system, a quantum computing operation on the encoded continuous variable in the quantum register, wherein the thermalization rate is determined based on the quantum computing operation performed on the encoded continuous variable; and

determine, by the quantum sampling system, a quantum solution to the quantum problem based on the performing of the quantum computing operation on the encoded continuous variable, wherein the quantum solution comprises the thermalization rate, and wherein a solution to the classical computing problem is determined based on the quantum solution related to the encoded continuous variable.

19 . The computer program product of claim 17 , wherein the first quantum operator is an effective Hamiltonian, wherein the second quantum operator is a supersymmetric Hamiltonian that provides a supersymmetry-based ground state with the lowest eigenvalue based on the effective Hamiltonian that provides a ground state, wherein the supersymmetric Hamiltonian is based on a supersymmetric quantum formulation of the Fokker-Planck equation, wherein determining the thermalization rate comprises determining the thermalization rate as the ground state of the supersymmetric Hamiltonian, and wherein the program instructions are further executable by the system to cause the system to:

determine, by the quantum sampling system, a stationary solution of the Fokker-Planck equation as the ground state of the effective Hamiltonian, based on a connection between classical stochastic dynamics and a Schrodinger equation;

determine, by the quantum sampling system, a reaction rate constant and a saddle point of a reaction based on the supersymmetric Hamiltonian that provides the supersymmetry-based ground state with the lowest eigenvalue, wherein the reaction rate constant is a function of the thermalization rate; and

sample, by the quantum sampling system, a Boltzmann probability distribution related to the quantum problem and a classical computing problem corresponding to the quantum problem based on the supersymmetric Hamiltonian that provides the supersymmetry-based ground state with the lowest eigenvalue and based on an encoded continuous variable that is associated with the classical computing problem and is applied to a quantum register of the quantum processor, wherein the stationary solution of the Fokker-Planck equation is the Boltzmann probability distribution.

20 . The computer program product of claim 17 , wherein the program instructions are further executable by the system to cause the system to:

determine, by the quantum sampling system, a first estimation of a quantum solution to the quantum problem based on the sampling of the Boltzmann probability distribution and the thermalization rate.