US 12,265,760 B2
Techniques for obtaining accurate diagonal electronic structure Hamiltonians
Ryan Babbush, Venice, CA (US); and Jarrod Ryan McClean, Marina Del Rey, CA (US)
Assigned to Google LLC, Mountain View, CA (US)
Appl. No. 16/976,229
Filed by Google LLC, Mountain View, CA (US)
PCT Filed Aug. 10, 2018, PCT No. PCT/US2018/046249
§ 371(c)(1), (2) Date Aug. 27, 2020,
PCT Pub. No. WO2019/203874, PCT Pub. Date Oct. 24, 2019.
Claims priority of provisional application 62/660,505, filed on Apr. 20, 2018.
Prior Publication US 2021/0035009 A1, Feb. 4, 2021
Int. Cl. G06F 30/20 (2020.01); G06N 10/20 (2022.01); G16C 10/00 (2019.01); G16C 60/00 (2019.01)
CPC G06F 30/20 (2020.01) [G06N 10/20 (2022.01); G16C 10/00 (2019.02); G16C 60/00 (2019.02)] 19 Claims
OG exemplary drawing
 
1. A method for simulating a physical system described by an electronic structure Hamiltonian expressed in an orthonormal basis, the method implemented by a system comprising a classical processor and quantum hardware, wherein the quantum hardware comprises a plurality of connected qubits and a plurality of control devices configured to apply quantum logic gates to the plurality of connected qubits, the method comprising:
decomposing, by the classical processor, the electronic structure Hamiltonian into a sum of sub-Hamiltonians, wherein each sub-Hamiltonian in the sum of sub-Hamiltonians:
is expressed in a respective basis of multiple different bases of the other sub-Hamiltonians in the sum of sub-Hamiltonians; and
comprises the product of i) a transformation operator effecting a respective basis rotation from an initial basis to the one basis of the multiple different bases, ii) a fermionic Hamiltonian expressed in the respective basis, the fermionic Hamiltonian comprising O(N2) terms with N representing system size, and iii) a Hermitian conjugate of the transformation operator effecting the respective basis rotation from the initial basis to the one basis of the multiple different bases, wherein the transformation operator and fermionic Hamiltonian comprise fermionic creation and annihilation operators;
simulating, using the quantum hardware, evolution of the physical system using the decomposed electronic structure Hamiltonian, comprising, for each sub-Hamiltonian that is expressed in a respective basis of the multiple different bases, applying a respective quantum circuit of quantum logic gates to an initial state of the plurality of qubits to implement a Trotter step of unitary evolution in the respective basis of the multiple different bases, wherein the quantum circuit requires linear qubit connectivity and has a depth that is linear in the system size; and
using, by the classical processor, the simulated evolution of the physical system using the decomposed electronic structure Hamiltonian to determine properties of the physical system.