Efficient reduction of resources for the simulation of fermionic Hamiltonians on quantum hardware

Patent metadata

Field	Value
Publication number	US-10599989-B2
Application number	US-201916372462-A
Country	US
Kind code	B2
Filing date	Apr 2, 2019
Priority date	Aug 17, 2016
Publication date	Mar 24, 2020
Grant date	Mar 24, 2020

Abstract

A technique relates to reducing qubits required on a quantum computer. A Fermionic system is characterized in terms of a Hamiltonian. The Fermionic system includes Fermions and Fermionic modes with a total number of 2M Fermionic modes. The Hamiltonian has a parity symmetry encoded by spin up and spin down parity operators. Fermionic modes are sorted such that the first half of 2M modes corresponds to spin up and the second half of 2M modes corresponds to spin down. The Hamiltonian and the parity operators are transformed utilizing a Fermion to qubit mapping that transforms parity operators to a first single qubit Pauli operator on a qubit M and a second single qubit Pauli operator on a qubit 2M. The qubit M having been operated on by the first single qubit Pauli operator and the qubit 2M having been operated on by the second single qubit Pauli operator are removed.

First claim

What is claimed is:

1. A computer-implemented method of reducing a number of qubits required on a quantum computer, the method comprising:
characterizing a system in terms of a Hamiltonian, the system including particles and particle modes, wherein the Hamiltonian has a parity symmetry encoded by a first characteristic and a second characteristic for parity operators;
sorting the particle modes on the Hamiltonian, such that a first part of the particle modes corresponds to the first characteristic and a second part of the particle modes corresponds to the second characteristic;
transforming the parity operators utilizing a particle to qubit mapping, wherein the particle to qubit mapping transforms the parity operators to a first qubit operator on a first qubit and a second qubit operator on a second qubit; and
removing the first qubit having been operated on by the first qubit operator and the second qubit having been operated on by the second qubit operator.

2. The method of claim 1 , wherein the particle to qubit mapping is a generalized Jordan-Wigner transformation.

3. The method of claim 1 , wherein the first qubit operator on the first qubit is a matrix on the first qubit.

4. The method of claim 1 , wherein the second qubit operator on the second qubit is a product of two matrices at sites of the first qubit and the second qubit.

5. The method of claim 1 , wherein removing the first qubit having been operated on by the first qubit operator comprises replacing the first qubit with eigenvalues of +1 or −1 according to a parity of the first qubit.

6. The method of claim 5 , wherein removing the second qubit having been operated on by the second qubit operator comprises replacing the second qubit with eigenvalues of +1 or −1 according to a parity of the second qubit.

7. The method of claim 6 , wherein the parities of the first qubit and the second qubit are known in advance.

8. The method of claim 1 , wherein the particle modes define a total number of 2M Fermionic modes, the first qubit defines qubit M, and the second qubit defines qubit 2M.

9. The method of claim 1 , wherein the first characteristic defines a first spin direction and the second characteristic defines a second spin direction; and
wherein the first qubit operator defines a first single qubit Pauli operator and the second qubit operator defines a second single qubit Pauli operator; and
wherein the system comprises a Fermionic system.

10. A computer-implemented method of reducing a number of qubits required on a quantum computer, the method comprising:
characterizing a system in terms of a Hamiltonian, the system including particles and particle modes;
transforming the Hamiltonian utilizing a particle to qubit mapping;
finding symmetry operators of the Hamiltonian;
transforming the symmetry operators into single qubit operators; and
removing every qubit that the single qubit operators are acting upon.

11. The method of claim 10 , wherein the particle to qubit mapping comprises a generalized Jordan-Wigner transformation.

12. The method of claim 10 , wherein the particle to qubit mapping comprises a standard Jordan-Wigner transformation.

13. The method of claim 10 , wherein finding symmetry operators of the Hamiltonian comprises performing a parity check matrix on the Hamiltonian to determine the symmetry operators.

14. The method of claim 13 , wherein finding symmetry operators of the Hamiltonian further comprises:
if no symmetry operators are found, determining that no further reduction can be performed; and
if the symmetry operators are found, determining a commuting set of the symmetry operators.

15. The method of claim 14 , wherein transforming the symmetry operators into the single qubit operators comprises constructing a transformation for the commuting set of the symmetry operators to map to the commuting set of the symmetry operators to the single qubit operators.

16. The method of claim 15 , wherein a Clifford transformation is the transformation constructed for the commuting set of the symmetry operators to map to the commuting set of the symmetry operators to the single qubit operators.

17. The method of claim 10 , wherein the particle modes comprise Fermionic modes and the particles comprises Fermions.

18. The method of claim 10 , wherein the symmetry operators comprise Pauli symmetry operators and the single qubit operators comprise single qubit Pauli operators.

19. A computer-implemented method of reducing a number of qubits required on a quantum computer, the method comprising:
characterizing a system in terms of a Hamiltonian, the system including particles and modes with a total number of M modes, wherein the Hamiltonian has particle number symmetry and N particles;
transforming the Hamiltonian utilizing a particle to qubit mapping that transforms from M modes to M qubits, wherein the M qubits are represented by M-bit strings in a computational basis; and
applying a compression map to the Hamiltonian such that the Hamiltonian having the M qubits is mapped to a transformed Hamiltonian with Q qubits where Q<M, wherein the compression map maps the M-bit strings labeling the M qubits in the computational basis with Hamming weight N to Q-bit strings.

20. The method of claim 19 , wherein the computational basis is a 0 and 1 for each of the M qubits.

Assignees

• IBM

Inventors

• Bravyi Sergey
• Gambetta Jay M
• Mezzacapo Antonio
• Temme Paul Kristan

Classifications

• G06F30/392

  Floor-planning or layout, e.g. partitioning or placement · CPC title

• G06F17/16 Primary

  Matrix or vector computation {, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization (matrix transposition G06F7/78)} · CPC title

• G06N10/00 Primary

  Quantum computing, i.e. information processing based on quantum-mechanical phenomena · CPC title

• G06F17/5072

  Physics · mapped topic

• G06N10/40 Primary

  Physical realisations or architectures of quantum processors or components for manipulating qubits, e.g. qubit coupling or qubit control · CPC title