US 2021/0232960 A1 · METHODS AND SYSTEMS FOR SOLVING A PROBLEM ON A QUANTUM COMPUTER

Abstract

A method of solving a problem can include providing a fermionic Hamiltonian, transformation of the fermionic Hamiltonian to qubit operators, transformation of the fermionic Hamiltonian in qubit operators to a mean-field Hamiltonian, and embedding the Hamiltonian onto a quantum computer. Such systems and methods may improve upon existing methods for solving electronic structure problems on a computer by adapting the problem to available hardware, reducing computational cost, and reducing the number of required qubits to solve electronic structure problems for larger number of atoms.

Claims143

Dependent claims

(canceled)

The method of claim 107, wherein the parameterization of the qubit Hamiltonian in Pauli Z rotations comprises an Ising-type Hamiltonian.

The method of claim 107, wherein the parameterization of the qubit Hamiltonian in Pauli Z rotations comprises a higher order binary optimization (HOBO) problem.

(canceled)

The method of claim 78, wherein the qubit Hamiltonian is a mean-field Hamiltonian.

The method of claim 78, wherein the qubit Hamiltonian comprises a transformation of a fermionic Hamiltonian.

(canceled)

The method of claim 78, wherein the action of embedding comprises transferring a value of at least one term selected from a bias term and a coupling term to the quantum computer.

(canceled)

The method of claim 78, wherein the action of identifying comprises transforming a fermionic Hamiltonian to the qubit Hamiltonian using at least one of a Jordan-Wigner transformation, the Bravyi-Kitaev method and the Parity method.

(canceled)

The method of claim 142, wherein a number of instances used of operating at least one quantum logic gate scales linearly with a number of fermions in the qubit Hamiltonian.

(canceled)

A quantum computer comprising:

a plurality of qubits;
a qubit-coupled cluster Hamiltonian embedded on the quantum computer, wherein at least one eigenvalue thereof is a variational upper bound to an exact state energy;
and
at least one quantum logic gate operation for implementation on the quantum computer, comprising:
at least one entangler comprising at least one Pauli Word;
and
a selected one of the at least one entangler comprising selected at least ones of the Pauli Words that reduce a value of the at least one eigenvalues.

4 more elements

(canceled)

The method of claim 143, wherein the at least one operator comprises a commutation relation of the qubit Hamiltonian.

The method of claim 143, wherein the at least one operator is at least one of a number operator and a total spin operator.

(canceled)

A method of solving a problem on a quantum computer, the method comprising actions of:

identifying a qubit Hamiltonian parameterized by at least one entangler and having at least one eigenvalue, wherein the at least one entangler is ranked by a first order energy derivative and the at least one eigenvalue comprises a variational upper bound to an exact state energy;
selecting a qubit-coupled cluster Hamiltonian comprising a selected one of the at least one entangler that reduces a value of a selected one of the at least one eigenvalue;
embedding the selected qubit-coupled cluster Hamiltonian on the quantum computer to optimize an amplitude of the selected entangler that reduces the value of the selected one of the at least one eigenvalue;
evaluating the amplitude of the selected entangler to select a different qubit-coupled cluster Hamiltonian comprising a different selected one of the at least one entangler that reduces a value of a different selected one of the at least one eigenvalue;
and
repeating the actions of embedding and evaluating until a solution is obtained.

3 more elements

The method of claim 0, wherein the action of selecting comprises parameterizing at least one coordinate of the qubit-coupled cluster Hamiltonian by a spin coherent state.

The method of claim 0, further comprising folding an optimization domain in at least one of an amplitude space and a phase space before the action of selecting.

(canceled)

The method of claim 0, wherein the solution is at least one of a global minimum and a local minimum.

(canceled)

A computer, comprising:

a processor;
a machine-readable, non-transitory storage medium for storing instructions that, when executed by the processor, cause the computer to perform a method of solving a problem, comprising actions of:
identifying a qubit Hamiltonian parameterized by at least one entangler and having at least one eigenvalue, wherein the at least one entangler is ranked by a first order energy derivative and the at least one eigenvalue comprises a variational upper bound to an exact state energy, wherein one or more coordinates in the qubit Hamiltonian comprises a parameterization in a spin coherent state,
selecting a qubit-coupled cluster Hamiltonian comprising a selected one of the at least one entangler that reduces a value of a selected one of the at least one eigenvalue;
embedding the selected qubit-coupled cluster Hamiltonian on a quantum computer to optimize an amplitude of the selected entangler that reduces the value of the selected one of the at least one eigenvalue;
evaluating the amplitude of the selected entangler to select a different qubit-coupled cluster Hamiltonian comprising a different selected one of the at least one entangler that reduces a value of a different selected one of the at least one eigenvalue;
and
repeating the actions of embedding and evaluating until a solution is obtained.

5 more elements

(canceled)

A computer-implemented method of solving a problem comprising:

providing a qubit Hamiltonian, wherein at least one eigenvalue thereof is a variational upper bound to an exact state energy;
parameterizing at least one coordinate in the qubit Hamiltonian by a spin coherent state;
and
providing a solution to the problem that comprises at least one of the at least one eigenvalue of the qubit Hamiltonian.

1 more element

(canceled)

A computer comprising:

a processor;
a machine-readable, non-transitory storage medium for storing instructions that, when executed by the computer, cause the computer to perform a method of solving a problem, comprising actions of:
providing a qubit Hamiltonian, wherein at least one eigenvalue thereof is a variational upper bound to an exact stage energy;
parameterizing at least one coordinate in the qubit Hamiltonian by a spin coherent state;
and
providing a solution to the problem that comprises at least one of the at least one eigenvalue of the qubit Hamiltonian.

3 more elements

Dependencies are inferred from the claim text.

Methods and systems for solving a problem on a quantum computer

Life of this patent

Methods and systems for solving a problem on a quantum computer

Life of this patent

Abstract

Claims143