Simulating Quantum Systems with Quantum Computation

Abstract

In some aspects, a quantum simulation method includes generating a set of models representing a quantum system. The set of models includes subsystem models representing respective fragments of the quantum system. The quantum system is simulated by operating the set of models on a computer system that includes a classical processor unit and multiple unentangled quantum processor units (QPUs), and the unentangled QPUs operate the respective subsystem models. In some examples, density matrix embedding theory (DMET) is used to compute an approximate ground state energy for the quantum system.

1 . A quantum simulation method comprising:
 generating a set of models representing a quantum system, the set of models comprising subsystem models representing respective fragments of the quantum system; and   simulating the quantum system by operating the set of models on a computer system, the computer system comprising a classical processor unit and a plurality of unentangled quantum processor units (QPUs), wherein operating the set of models comprises using the unentangled QPUs to operate the respective subsystem models.   
     
     
         2 . The quantum simulation method of  claim 1 , wherein operating the set of models comprises using two or more of the unentangled QPUs to operate two or more of the subsystem models in parallel. 
     
     
         3 . The quantum simulation method of  claim 1 , wherein simulating the quantum system comprises using density matrix embedding theory (DMET) to compute an approximate ground state energy for the quantum system. 
     
     
         4 . The quantum simulation method of  claim 3 , wherein using the unentangled QPUs to operate the respective subsystem models comprises executing a variational quantum eigensolver (VQE) algorithm on each QPU to compute reduced density matrices (RDMs) for the respective fragments. 
     
     
         5 . The quantum simulation method of  claim 4 , comprising computing the approximate ground state energy from the RDMs. 
     
     
         6 . The quantum simulation method of  claim 4 , wherein the QPUs execute the VQE algorithm to compute two-particle reduced density matrices (2-RDMs) for the respective fragments. 
     
     
         7 . The quantum simulation method of  claim 4 , wherein the set of models comprises an approximate Hamiltonian for the quantum system, the approximate Hamiltonian comprises embedding potentials associated with the respective fragments, the subsystem models comprise embedded Hamiltonians for the respective fragments, and the QPUs compute the RDMs based on the embedded Hamiltonians. 
     
     
         8 . The quantum simulation method of  claim 7 , wherein simulating the quantum system comprises, by operation of the classical processor unit:
 computing an approximate ground state of the quantum system based on the approximate Hamiltonian having an initial set of values assigned to the embedding potentials; and   computing an updated set of values for the embedding potentials based on the RDMs computed by the QPUs.   
     
     
         9 . The quantum simulation method of  claim 7 , wherein simulating the quantum system comprises executing an iterative process, and each iteration of the iterative process comprises:
 computing an approximate ground state of the quantum system for the iteration based on the approximate Hamiltonian;   generating subsystem models for the iteration based on the approximate ground state for the iteration;   by operation of the unentangled QPUs, computing updated RDMs for the respective fragments based on the subsystem models for the iteration; and   computing an updated set of values for the embedding potentials based on the updated RDMs.   
     
     
         10 . A computer system comprising:
 a plurality of unentangled quantum processor units (QPUs);   one or more classical processor units configured to perform operations comprising:
 generating a set of models representing a quantum system, the set of models comprising subsystem models representing respective fragments of the quantum system; and 
 using the unentangled QPUs to operate the respective subsystem models. 
   
     
     
         11 . The computer system of  claim 10 , wherein using the unentangled QPUs comprises using two or more of the unentangled QPUs concurrently to operate two or more of the subsystem models in parallel. 
     
     
         12 . The computer system of  claim 10 , wherein the one or more classical processor units are configured to use the unentangled QPUs to operate the subsystem models in a simulation that computes an approximate ground state energy for the quantum system. 
     
     
         13 . The computer system of  claim 12 , wherein using the unentangled QPUs to operate the respective subsystem models comprises executing a variational quantum eigensolver (VQE) algorithm on each QPU to compute reduced density matrices (RDMs) for the respective fragments. 
     
     
         14 . The computer system of  claim 13 , wherein the one or more classical processor units are configured to compute the approximate ground state energy from the RDMs. 
     
     
         15 . The computer system of  claim 13 , wherein the QPUs are configured to execute the VQE algorithm to compute two-particle reduced density matrices (2-RDMs) for the respective fragments. 
     
     
         16 . The computer system of  claim 13 , wherein the set of models comprises an approximate Hamiltonian for the quantum system, the approximate Hamiltonian comprises embedding potentials associated with the respective fragments, and the subsystem models comprise embedded Hamiltonians for the respective fragments. 
     
     
         17 . The computer system of  claim 16 , wherein the one or more classical processor units are configured to perform operations comprising:
 computing an approximate ground state of the quantum system based on the approximate Hamiltonian having an initial set of values assigned to the embedding potentials; and   computing an updated set of values for the embedding potentials based on the RDMs computed by the QPUs.   
     
     
         18 . The computer system of  claim 16 , wherein the one or more classical processor units are configured to execute an iterative process, and each iteration of the iterative process comprises:
 computing an approximate ground state of the quantum system for the iteration based on the approximate Hamiltonian;   generating subsystem models for the iteration based on the approximate ground state for the iteration;   by operation of the unentangled QPUs, computing updated RDMs for the respective fragments based on the subsystem models for the iteration; and   computing an updated set of values for the embedding potentials based on the updated RDMs.   
     
     
         19 . A quantum simulation method comprising:
 identifying fragments of a quantum system to be simulated;   using one or more quantum processor units (QPUs) to generate reduced density matrices (RDMs) for the respective fragments; and   computing an approximate ground state energy of the quantum system based on the RDMs.   
     
     
         20 . The quantum simulation method of  claim 19 , wherein multiple RDMs are generated in parallel by multiple unentangled QPUs, each of the RDMs being generated by a respective one of the unentangled QPUs. 
     
     
         21 - 22 . (canceled)