HAMILTONIAN SIMULATION IN THE INTERACTION PICTURE

• US 20190318053A1
• Filed: 04/12/2019
• Published: 10/17/2019
• Est. Priority Date: 04/12/2018
• Status: Active Grant

• Current Assignee: Microsoft Technology Licensing LLC (Microsoft Corporation)
• Original Assignee: Microsoft Technology Licensing LLC (Microsoft Corporation)
• Inventors: Low, Guang Hao, Wiebe, Nathan O.
• Granted Patent: US 11,809,959 B2
• Time in Patent Office: Days
• CPC Class Codes: G06F 2111/10 Numerical modelling
• CPC Class Codes: G06F 30/20 Design optimisation, verification or simulation optimisation, verification or simulation of circuit designs G06F30/30
• CPC Class Codes: G06N 10/00 Quantum computing, i.e. information processing based on quantum-mechanical phenomena
• CPC Class Codes: G06N 10/20 Models of quantum computing, e.g. quantum circuits or universal quantum computers

Abstract

In this disclosure, quantum algorithms are presented for simulating Hamiltonian time-evolution e^−i(A+B)t in the interaction picture of quantum mechanics on a quantum computer. The interaction picture is a known analytical tool for separating dynamical effects due to trivial free-evolution A from those due to interactions B. This is especially useful when the energy-scale of the trivial component is dominant, but of little interest. Whereas state-of-art simulation algorithms scale with the energy ∥A+B∥≤∥A∥+∥B∥ of the full Hamiltonian, embodiments of the disclosed approach generally scale linearly with the sum of the Hamiltonian coefficients from the low-energy component B and poly-logarithmically with those from A.

Claims

1. A method, comprising:

configuring a quantum computer to simulate a quantum system, wherein a Hamiltonian in the simulation is represented in the interaction picture; and

performing a simulation of the quantum system using the quantum computer.

2. The method of claim 1, wherein the simulation of the quantum system is a subroutine that is repeated two or more times.

3. The method of claim 1, wherein the simulation is performed using linear combinations of unitaries.

4. The method of claim 3, wherein the simulation uses linear combinations of unitaries performed on a diagonally dominant matrix.

5. The method of claim 4, wherein the simulation using linear combinations of unitaries is performed on the diagonally dominant components of the diagonally dominant matrix.

6. The method of claim 1, wherein the quantum system is modelled by a Hubbard model.

7. The method of claim 1, wherein the quantum system describes a physical chemical system or molecule.

8. The method of claim 1, wherein the Hamiltonian is sparse and the simulation uses the state of an auxiliary qubit to encode the matrix elements of the Hamiltonian instead of using graph decomposition techniques.

9. The method of claim 1, further comprising compressing ancillas for quantum simulation of a time-dependent Hamiltonian.

10. A method, comprising:

implementing a quantum algorithm on a quantum computer for simulating a general sparse time-dependent quantum system, wherein the quantum algorithm does not use graph decomposition techniques.

11. The method of claim 10, wherein a quantum Hamiltonian used in the simulation is represented in the interaction picture.

12. The method of claim 10, wherein the simulation uses linear combinations of unitaries performed on a diagonally dominant matrix.

13. The method of claim 10, wherein a quantum Hamiltonian used in the simulation is represented in the interaction picture and is chosen to be a diagonal matrix.

14. The method of claim 10, wherein the quantum system is modelled by a Hubbard model, a physical chemical system, or a molecule.

15. The method of claim 10, further comprising compressing ancillas used to index a time for the simulation.

16. A quantum system, comprising:

a classical computer; and

a quantum computer,

wherein the classical computer is configured to configure the quantum computer to simulate a quantum system within the interaction picture.

17. The system of claim 16, wherein the simulation is performed in using linear combinations of unitaries.

18. The system of claim 16, wherein the simulation uses linear combinations of unitaries performed on a diagonally dominant matrix.

19. The system of claim 16, wherein the quantum system is modelled by a Hubbard model.

20. The system of claim 16, wherein the simulation is performed at least in part by compressing ancillas used to index evolution time within a quantum simulation of a time-dependent Hamiltonian.