Methods and apparatuses for resource-optimized fermionic local simulation on quantum computer for quantum chemistry

1 . A method to reduce complexity in a simulation of a chemical system, comprising:

performing, by a classical processor, a first perturbation operation for obtaining a first set of ansatz terms and first initial amplitudes associated with the first set of ansatz terms;

iteratively performing, by the classical processor, the following operations until an energy of the chemical system converges to an energy conversion criterion:

a variational quantum eigensolver (VQE) simulation for minimizing energy of the chemical system based on the first set of ansatz terms and the first initial amplitudes,

a second perturbation operation for calculating at least one of perturbative corrections in the energy of the chemical system or wavefunction based on one or more ansatz wavefunctions,

a determining operation of whether the energy of the chemical system has converged to the energy conversion criterion after the second perturbation operation, and

a third perturbation operation when the energy of the chemical system has not converged to the energy conversion criterion, the third perturbation operation obtaining a next set of ansatz terms and next initial amplitudes associated with the next set of ansatz terms to be provided to the VQE operation in a next cycle of the iteration, and the third perturbation operation being selected based on a size of an amplitude of the calculated perturbative corrections; and

generating, by the classical processor when the energy of the chemical system has converged to the energy conversion criterion and based a current cycle of the iteration, an output of a ground-state energy estimate of the chemical system that is a ground-state energy estimate of particles of the chemical system; and

compiling, by the classical processor, a circuit according to the simulation of the chemical system that is based on the ground-state energy estimate of the particles, wherein the compiling comprises mapping, to qubit indices, ansatz terms that cause the chemical system to converge by:

translating Fermionic operators comprised in the ansatz terms into qubit operations using one or more fermion-to-qubit transformations;

assigning the qubit operations that can be executed by a quantum processor to the qubit indices, wherein the qubit indices indicate a placement and application of gates within the circuit; and

executing, by the quantum processor, the circuit to determine at least one of a chemical reaction, bonding property and energetic state of the chemical system.

2 . The method of claim 1 , wherein the first perturbation operation comprises predicting the first set of ansatz terms and the first initial amplitudes associated with the first set of ansatz terms.

3 . The method of claim 2 , wherein the predicting is performed based on a second order Møller-Plesset (MP2) perturbation.

4 . The method of claim 1 , wherein the third perturbation operation comprises predicting the next set of ansatz terms and the next initial amplitudes associated with the next set of ansatz terms.

5 . The method of claim 4 , wherein the predicting comprises increasing ansatz sizes of the next set of ansatz terms.

6 . A non-transitory computer readable medium for reducing complexity in a simulation of a chemical system, the non-transitory computer readable medium having instructions stored therein that, when executed by a classical processor, cause the classical processor to:

perform a first perturbation operation for obtaining a first set of ansatz terms and first initial amplitudes associated with the first set of ansatz terms;

iteratively perform the following operations until an energy of the chemical system converges to an energy conversion criterion:

a variational quantum eigensolver (VQE) simulation for minimizing energy of the chemical system based on the first set of ansatz terms and the first initial amplitudes,

a second perturbation operation for calculating at least one of perturbative corrections in the energy of the chemical system or wavefunction based on one or more ansatz wavefunctions,

a determining operation of whether the energy of the chemical system has converged to the energy conversion criterion after the second perturbation operation, and

a third perturbation operation when the energy of the chemical system has not converged to the energy conversion criterion, the third perturbation operation obtaining a next set of ansatz terms and next initial amplitudes associated with the next set of ansatz terms to be provided to the VQE operation in a next cycle of the iteration, and the third perturbation operation being selected based on a size of an amplitude of the calculated perturbative corrections; and

generate, when the energy of the chemical system has converged to the energy conversion criterion and based a current cycle of the iteration, an output of a ground-state energy estimate of the chemical system that is a ground-state energy estimate of particles of the chemical system; and

compile a circuit according to the simulation of the chemical system that is based on the ground-state energy estimate of the particles, wherein the compiling comprises mapping, to qubit indices, ansatz terms that cause the chemical system to converge by:

translating Fermionic operators comprised in the ansatz terms into qubit operations using one or more fermion-to-qubit transformations;

assigning the qubit operations that can be executed by a quantum processor to the qubit indices, wherein the qubit indices indicate a placement and application of gates within the circuit, and wherein the circuit is executed by the quantum processor to determine at least one of a chemical reaction, bonding property and energetic state of the chemical system.

7 . The non-transitory computer readable medium of claim 6 , wherein the instructions to perform the first perturbation operation comprise instructions for predicting the first set of ansatz terms and the first initial amplitudes associated with the first set of ansatz terms.

8 . The non-transitory computer readable medium of claim 7 , wherein the predicting is performed based on a second order Møller-Plesset (MP2) perturbation.

9 . The non-transitory computer readable medium of claim 6 , wherein the instructions to perform the third perturbation operation comprise instructions for predicting the next set of ansatz terms and the next initial amplitudes associated with the next set of ansatz terms.

10 . The non-transitory computer readable medium of claim 9 , wherein the predicting comprises increasing ansatz sizes of the next set of ansatz terms.