Plane wave dual basis for quantum simulation
AssigneeGoogle Inc.
InventorRyan Babbush
Life of this patent
Estimating the term…
Abstract
Methods, systems and apparatus for simulating quantum systems. In one aspect, a method includes the actions of obtaining a first Hamiltonian describing the quantum system, wherein the Hamiltonian is written in a plane wave basis comprising N plane wave basis vectors; applying a discrete Fourier transform to the first Hamiltonian to generate a second Hamiltonian written in a plane wave dual basis, wherein the second Hamiltonian comprises a number of terms that scales at most quadratically with N; and simulating the quantum system using the second Hamiltonian.
Claims20
A method performed by quantum computing hardware, the method comprising:
- measuring a kinetic energy and potential energy of a physical quantum system, comprising:
- configuring a first plurality of qubits included in the quantum computing hardware according to a first qubit Hamiltonian, wherein the first qubit Hamiltonian comprises a kinetic energy operator in a plane wave basis;
- simulating, by the quantum computing hardware, the quantum system using the first qubit Hamiltonian;
- configuring a second plurality of qubits included in the quantum computing hardware according to a second qubit Hamiltonian, wherein the second qubit Hamiltonian comprises a potential energy operator in a plane wave dual basis;
- and
- simulating, by the quantum computing hardware, the quantum system using the first qubit Hamiltonian and the second qubit Hamiltonian.
An apparatus comprising:
- quantum computing hardware comprising:
- a quantum system comprising one or more qubits, and
- one or more control devices configured to operate the quantum system;
- wherein the apparatus is configured to perform operations comprising:
- measuring a kinetic energy and potential energy of a physical quantum system, comprising:
- configuring a first plurality of qubits included in the quantum computing hardware according to a first qubit Hamiltonian, wherein the first qubit Hamiltonian comprises a kinetic energy operator in a plane wave basis;
- simulating, by the quantum computing hardware, the quantum system using the first qubit Hamiltonian;
- configuring a second plurality of qubits included in the quantum computing hardware according to a second qubit Hamiltonian, wherein the second qubit Hamiltonian comprises a potential energy operator in a plane wave dual basis;
- and
- simulating, by the quantum computing hardware, the quantum system using the first qubit Hamiltonian and the second qubit Hamiltonian.
Dependencies are inferred from the claim text.