Quantum circuit for chemistry simulation

Patent metadata

Field	Value
Publication number	US-9819347-B2
Application number	US-201515118474-A
Country	US
Kind code	B2
Filing date	Feb 6, 2015
Priority date	Feb 12, 2014
Publication date	Nov 14, 2017
Grant date	Nov 14, 2017

Abstract

Quantum circuits for chemistry simulation are based on second quantization Hamiltonian coefficients for one-body and two-body interactions. Jordan-Wigner series that conserve parity can be defined so that selected CNOT gates are removed from the associated circuits. Basis change gates such as Hadamard or Y-gates can be coupled to some or all qubits of a quantum circuit or cancelled in view of corresponding gates in adjacent circuits. In some examples, CNOT gates can be moved to different circuit locations.

First claim

The invention claimed is:

1. A quantum circuit, comprising:
at least one reduced Jordan-Wigner circuit coupled to a plurality of qubits and including a plurality of CNOT gates corresponding to respective spin orbitals p,q,r,s, wherein p,q,r,s are integers such that p<q<r<s; and
a reduced Hamiltonian circuit coupled to p,q,r,s qubits associated with the p,q,r,s spin orbitals.

2. The quantum circuit of claim 1 , further comprising a plurality of reduced Hamiltonian circuits situated in series and having different basis change gates.

3. The quantum circuit of claim 2 , further comprising an output side reduced Jordan-Wigner string corresponding to the input side reduced Jordan-Wigner string, the output side reduced Jordan-Wigner string situated after the plurality of reduced Hamiltonian circuits.

4. The quantum circuit of claim 1 , wherein the basis change gates are Hadamard gates and Y-gates.

5. The quantum circuit of claim 1 , wherein CNOT gates of the reduced Jordan-Wigner circuit couple selected qubits in a set of qubits associated with spin orbitals p, . . . , s to each other.

6. The quantum circuit of claim 1 , wherein CNOT gates of the reduced Jordan-Wigner circuit are coupled to an entanglement qubit.

7. The quantum circuit of claim 1 , further comprising at least one one-body reduced Jordan-Wigner circuit coupled to the plurality of qubits and including a plurality of CNOT gates corresponding to respective spin orbitals p,q, wherein p,q are integers such that p<q; and
a one-body reduced Hamiltonian circuit coupled to p,q qubits associated with the p,q spin orbitals.

8. A method of defining a quantum circuit associated with at least a selected one-body or two-body Hamiltonian coefficient associated with second quantization, comprising:
defining a reduced Jordan-Wigner string associated with spin orbitals coupled by a Hamiltonian coefficient;
defining a reduced Hamiltonian circuit based at least on selected Hamiltonian coefficient; and
coupling the reduced Jordan-Wigner string to the reduced Hamiltonian on an input side.

9. The method of claim 8 , further comprising defining a series of reduced Hamiltonian circuits associated with at least two basis operators and one or more Hamiltonian coefficients, and coupling the reduced Jordan-Wigner string in series with the series of reduced Hamiltonian circuits on the input side.

10. The method of claim 8 , wherein the Hamiltonian coefficient is a one-body Hamiltonian coefficient or a two-body Hamiltonian coefficient.

11. The method of claim 8 , wherein the basis operators are defined by Hadamard gates, Y-gates, or combinations thereof.

12. The method of claim 11 , further comprising defining the reduced Hamiltonian circuit to include input side basis change gates corresponding to a selected set of spin orbitals, and output side basis change gates for at most one of the selected spin orbitals.

13. The method of claim 12 , defining the reduced Jordan-Wigner string as a series of CNOT gates coupled to an entanglement qubit.

14. The method of claim 12 , wherein the Hamiltonian coefficient is associated with a two body Hamiltonian coefficient coupling spin orbitals p,q,r,s, wherein p,q,r,s are integers such that p<q<r<s, and the reduced Jordan-Wigner string is an interior Jordan-Wigner string coupling the p,q,r,s spin orbitals.

15. The method of claim 14 , wherein the reduced Hamiltonian circuit is defined to include input side basis change gates for p,q,r,s qubits associated with the p,q,r,s spin orbitals.

16. The method of claim 15 , further comprising defining a plurality of reduced Hamiltonian circuits coupled in series based on selected Hamiltonian coefficients, and coupling a first reduced Hamiltonian circuit of the plurality to the reduced Jordan-Wigner string and a last reduced Hamiltonian circuit of the plurality to a final Jordan-Wigner string.

17. The method of claim 15 , wherein the reduced Jordan-Wigner string is associated with spin orbitals coupled by a Hamiltonian coefficient of the form H pqrs , and further comprising:
defining a reduced Hamiltonian circuit associated a Hamiltonian coefficient of the form H p′q′r′s′ ; and
defining a coupling of the reduced Hamiltonian circuits together with CNOT gates corresponding to respective Jordan-Wigner strings in which CNOT gates coupled to common qubits are omitted, wherein the Jordan-Wigner strings include CNOT gates coupled to an entanglement qubit.

18. The method of claim 17 , further comprising removing at least one CNOT gate associated with the Jordan-Wigner strings in the defined circuit.

19. The method of claim 8 , wherein at least one qubit in the reduced Hamiltonian circuit is situated so as to be processed without a basis change at one or both of an input or output of the reduced Hamiltonian circuit.

20. A computing device having computer executable instructions stored therein for performing a method, comprising:
defining a plurality of reduced Hamiltonian circuits associated with one-body and two-body interactions in a second quantized Hamiltonian;
determining a plurality of Jordan-Wigner series for coupling the reduced Hamiltonian circuits;
cancelling at least selected CNOT gates in the plurality of series that couple to common qubits; and
identifying common basis change gates in the defined reduced Hamiltonian circuits that are applied to a common qubit and removing the common basis change gates from the reduced Hamiltonian circuit definitions.

Assignees

• Microsoft Technology Licensing Llc

Inventors

• Hastings Matthew
• Wecker David

Classifications

• H03K19/195 Primary

  using superconductive devices · CPC title

• B82Y10/00

  Nanotechnology for information processing, storage or transmission, e.g. quantum computing or single electron logic · CPC title

• G06N99/002

  Physics · mapped topic

• G06N10/20

  Models of quantum computing, e.g. quantum circuits or universal quantum computers · CPC title

• G16C10/00 Primary

  Computational theoretical chemistry, i.e. ICT specially adapted for theoretical aspects of quantum chemistry, molecular mechanics, molecular dynamics or the like · CPC title