Abstract: Methods, systems and apparatus for preparing a target quantum state of a quantum system, where the target quantum state is stationary with respect to a parameterized many-body qubit operator. In one aspect a method includes preparing an initial quantum state as an input state for a first iteration; iteratively evolving the initial quantum state and subsequent input quantum states as inputs for subsequent iterations until an approximation of the target stationary quantum state is obtained, comprising, for each iteration: computing, by quantum computation, parameter values of the many-body qubit operator for the iteration; computing, by quantum computation, an evolution time for the iteration, comprising evaluating changes in elements of a 2-RDM for the iteration; and evolving the initial quantum state or the subsequent input quantum state for the iteration using the computed parameter values and evolution time to generate a subsequent input quantum state for the subsequent iteration.

Abstract: Methods, systems, and apparatus for verified quantum phase estimation. In one aspect, a method includes repeatedly performing a experiment. Performing one repetition of the experiment includes: applying a second unitary to a system register of N qubits prepared in a target computational basis state; applying, conditioned on a state of a control qubit, a first unitary to the system register; applying an inverse of the second unitary to the system register and measuring each qubit to determine an output state of the system register; measuring the control qubit to obtain a corresponding measurement result m; and post-selecting on the target computational basis state by, in response to determining that the output state indicates that each qubit was in the target computational basis state prior to measurement, incrementing a first or second classical variable by (?1)m. Phases or expectation values of the first unitary are estimated based on the classical variables.

Abstract: Methods, systems and apparatus for simulating physical systems. In one aspect, a method includes the actions of selecting a first set of basis functions for the simulation, wherein the first set of basis functions comprises an active and a virtual set of orbitals; defining a set of expansion operators for the simulation, wherein expansion operators in the set of expansion operators approximate fermionic excitations in an active space spanned by the active set of orbitals and a virtual space spanned by the virtual set of orbitals; performing multiple quantum computations to determine a matrix representation of a Hamiltonian characterizing the system in a second set of basis functions, computing, using the determined matrix representation of the Hamiltonian, eigenvalues and eigenvectors of the Hamiltonian; and determining properties of the physical system using the computed eigenvalues and eigenvectors.

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.

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.