# US 12,008,433 B2 · Variational quantum state preparation > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 12,008,433 B2 - Document ID: US12008433B2 - Status: Granted - Kind: B2 - Application number: 16/967,339 - Filed: 2019-08-07 - Published: 2021-06-10 - Granted: 2024-06-11 - Earliest claimed: 2018-08-07 - Assignees: Google Inc. - Applicants: Google LLC - Inventors: Ryan Babbush; Ian David Kivlichan - Web page: https://patentgrep.com/patent/US12008433B2 ## CPC - G06N 10/20: Models of quantum computing, e.g. quantum circuits or universal quantum computers - G06N 10/60: Quantum algorithms, e.g. based on quantum optimisation, quantum Fourier or Hadamard transforms - G06F 15/16: Combinations of two or more digital computers each having at least an arithmetic unit, a program unit and a register, e.g. for a simultaneous processing of several programs {(coordinating program control therefor G06F9/52; in regulating and control system G05B)} - B82Y 10/00: Nanotechnology for information processing, storage or transmission, e.g. quantum computing or single electron logic - G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) - B82Y: SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES ## Abstract Methods, systems and apparatus for performing quantum state preparation. In one aspect, a method includes the actions of defining a target quantum state of a quantum system, wherein time evolution of the quantum system is governed by a target Hamiltonian, and defining a total Hamiltonian that interpolates between an initial Hamiltonian and the target Hamiltonian, wherein the total Hamiltonian is equal to the initial Hamiltonian at an initial time and is equal to the target Hamiltonian at a final time; approximating the time evolution of the total Hamiltonian using a truncated linear combination of unitary simulations to generate a truncated time evolution operator; evolving a ground state of the initial Hamiltonian according to the truncated time evolution operator for a truncated number of time steps to generate an intermediate state; and variationally adjusting the intermediate state to determine a wavefunction that approximates the target quantum state of the quantum system. ## Claims ### Claim 1 A computer-implemented method for performing quantum state preparation, the method comprising: defining (i) a target quantum state of a quantum system, wherein time evolution of the quantum system is governed by a target Hamiltonian, and (ii) a total Hamiltonian that interpolates between an initial Hamiltonian and the target Hamiltonian, wherein the total Hamiltonian is equal to the initial Hamiltonian at an initial time and is equal to the target Hamiltonian at a final time; determining a wavefunction that approximates the target quantum state of the quantum system and satisfies a first predetermined error tolerance, the determining comprising: approximating the time evolution of the total Hamiltonian using a truncated linear combination of unitary simulations to generate a truncated time evolution operator; evolving a ground state of the initial Hamiltonian according to the truncated time evolution operator for a truncated number of time steps to generate an intermediate state, wherein the intermediate state does not satisfy the first predetermined error tolerance; and variationally adjusting the intermediate state to determine a wavefunction that approximates the target quantum state of the quantum system and satisfies the first predetermined error tolerance. ### Claim 2 (depends on 1) The method of claim 1, wherein variationally adjusting the intermediate state to determine a wavefunction that approximates the target quantum state of the quantum system and satisfies the first predetermined error tolerance comprises: defining a variational ansatz wavefunction dependent on one or more variational parameters as being equal to the action of a parameterized quantum circuit applied to the intermediate state; performing a variational algorithm using the defined variational ansatz wavefunction to determine fixed values of the one or more variational parameters; and using the fixed values of the one or more variational parameters to define the wavefunction that approximates the target quantum state of the quantum system. ### Claim 3 (depends on 2) The method of claim 2, wherein the fixed values of the one or more variational parameters minimize an energy expectation of the target Hamiltonian. ### Claim 4 (depends on 1) The method of claim 1, wherein the linear combination of unitary simulations comprises a Taylor series simulation. ### Claim 5 (depends on 1) The method of claim 1, wherein the truncated number of time steps scales less than a sub logarithmically in error. ### Claim 6 (depends on 1) The method of claim 1, wherein the evolution of the ground state of the Hamiltonian is adiabatic. ### Claim 7 (depends on 1) The method of claim 1, further comprising iteratively increasing the truncated number of time steps until the defined wavefunction that approximates the target quantum state of the quantum system for each iteration converges. ### Claim 8 (depends on 1) The method of claim 1, wherein the truncation of the truncated linear combination of unitary simulations is dependent on a second predetermined error tolerance. ### Claim 9 (depends on 8) The method of claim 8, wherein the second predetermined error tolerance is dependent on limitations of computational hardware implementing the method. ### Claim 10 (depends on 8) The method of claim 8, wherein the truncation of the truncated linear combination of unitary simulations is dependent on the second predetermined error tolerance, wherein the second predetermined error tolerance is higher than the first predetermined error tolerance, and the truncated number of time steps scales sub logarithmically in the error. ### Claim 11 (depends on 1) The method of claim 1, wherein: the target Hamiltonian describes a physical quantum system, and the defined wavefunction that approximates the target quantum state of the quantum system is used to simulate the physical quantum system. ### Claim 12 (depends on 11) The method of claim 11, wherein simulating the physical quantum system comprises determining physical properties of the physical system. ### Claim 13 (depends on 1) The method of claim 1, further comprising: encoding a solution to an optimization task in the target quantum state; and using the defined wavefunction that approximates the target quantum state of the quantum system to determine an approximate solution to the optimization task. ### Claim 14 An apparatus comprising: quantum hardware; and one or more classical processors; wherein the apparatus is configured to perform operations comprising defining (i) a target quantum state of a quantum system of the quantum hardware, wherein time evolution of the quantum system is governed by a target Hamiltonian, and (ii) a total Hamiltonian that interpolates between an initial Hamiltonian and the target Hamiltonian, wherein the total Hamiltonian is equal to the initial Hamiltonian at an initial time and is equal to the target Hamiltonian at a final time; determining a wavefunction that approximates the target quantum state of the quantum system and satisfies a first predetermined error tolerance, the determining comprising: approximating the time evolution of the total Hamiltonian using a truncated linear combination of unitary simulations to generate a truncated time evolution operator; evolving a ground state of the initial Hamiltonian according to the truncated time evolution operator for a truncated number of time steps to generate an intermediate state, wherein the intermediate state does not satisfy the first predetermined error tolerance; and variationally adjusting the intermediate state to determine a wavefunction that approximates the target quantum state of the quantum system and satisfies the first predetermined error tolerance.