Abstract: Methods, systems, and apparatus for quantum data processing. In one aspect, a method includes storing, in a quantum memory, multiple copies of a quantum state, comprising, for each copy of the quantum state, i) probing, by an initialized quantum sensor, a target system to obtain an evolved quantum state of the quantum sensor, ii) transducing the evolved quantum state of the quantum sensor into a quantum state of a quantum buffer, iii) logically encoding the quantum state of the quantum buffer into a quantum error correcting code, and iv) moving the logically encoded quantum state of the quantum buffer into the quantum memory; loading the multiple copies of the quantum state in the quantum memory into a quantum computer; processing, by the quantum computer, the multiple copies of the quantum state to obtain a purified quantum state; and measuring the purified quantum state to determine properties of the target system.

Abstract: Methods, systems, and apparatus for quantum data processing. In one aspect, a method includes storing, in a quantum memory, multiple copies of a quantum state, comprising, for each copy of the quantum state, i) probing, by an initialized quantum sensor, a target system to obtain an evolved quantum state of the quantum sensor, ii) transducing the evolved quantum state of the quantum sensor into a quantum state of a quantum buffer, iii) logically encoding the quantum state of the quantum buffer into a quantum error correcting code, and iv) moving the logically encoded quantum state of the quantum buffer into the quantum memory; loading the multiple copies of the quantum state in the quantum memory into a quantum computer; processing, by the quantum computer, the multiple copies of the quantum state to obtain a purified quantum state; and measuring the purified quantum state to determine properties of the target system.

Abstract: Methods, systems and apparatus for correcting a result of a quantum computation.

Abstract: Methods, systems and apparatus for correcting a result of a quantum computation.

Abstract: Methods, systems and apparatus for determining an error-mitigated expectation value of a target observable with respect to a noisy quantum state. In one aspect a method includes obtaining multiple copies of the noisy quantum state; performing measurements on tensor products of M copies of the noisy quantum state to compute an expectation value of the target observable with respect to an entangled quantum state, wherein M?1 and eigenvalues corresponding to non-dominant eigenvectors of the noisy quantum state in the spectral decomposition of the entangled quantum state are suppressed exponentially in M; and using the computed expectation value of the target observable with respect to an entangled quantum state to determine the error-mitigated expectation value of the target observable with respect to the noisy quantum state.

Abstract: Quantum computing systems and methods for determining a state of a physical system are provided. In some examples, a method can include obtaining a defined function associated with the physical system, the defined function encoding an estimated value of at least one property to be simulated by a quantum computing system as a gradient of the defined function. The method can include implementing a quantum circuit on a plurality of qubits in a quantum computing system to perform a quantum operation (e.g., the Gilyén quantum gradient algorithm) on the plurality of qubits. The quantum operation is operable to determine the gradient of the defined function. The method can include determining the estimated value for the at least one property based at least on at least one of the plurality of qubits after implementation of the quantum operation.

Abstract: Systems and methods for quantum error mitigation are provided. A method can include accessing a quantum system; implementing a plurality of quantum circuits; obtaining a plurality of measurements performed for each of the quantum circuits; determining an estimated average value of an observable of interest (O)f for the quantum circuits based at least in part on the plurality of measurements; and determining an estimated noiseless value of an observable of interest (O)? based at least in part on the estimated average value of the observable of interest (O)f using a single-point full depolarizing error model. Each of the plurality of quantum circuits can be implemented by a different sequence of quantum gates as compared to each of the other quantum circuits in the plurality to thereby implement one or more circuit gauges and can be an equivalent logical operation as each of the other quantum circuits in the plurality.

Abstract: Methods, systems, and apparatus for quantum data processing. In one aspect, a method includes storing, in a quantum memory, multiple copies of a quantum state, comprising, for each copy of the quantum state, i) probing, by an initialized quantum sensor, a target system to obtain an evolved quantum state of the quantum sensor, ii) transducing the evolved quantum state of the quantum sensor into a quantum state of a quantum buffer, iii) logically encoding the quantum state of the quantum buffer into a quantum error correcting code, and iv) moving the logically encoded quantum state of the quantum buffer into the quantum memory; loading the multiple copies of the quantum state in the quantum memory into a quantum computer; processing, by the quantum computer, the multiple copies of the quantum state to obtain a purified quantum state; and measuring the purified quantum state to determine properties of the target system.

Abstract: Methods, systems and apparatus for measuring the energy of a quantum chemical system. In one aspect, a method includes obtaining a Hamiltonian describing the chemical system, where the Hamiltonian is expressed in an orthonormal basis; decomposing the Hamiltonian into a sum of terms where each term comprises a respective operator that effects a respective single particle basis rotation, and one or more particle density operators; repeatedly, for each group comprising terms with a same operator that effects a respective single particle basis rotation, measuring expectation values of the terms included in the group, comprising: performing the respective single particle basis rotation on a qubit system encoding a state of the chemical system; and measuring Jordan-Wigner transformations of the one or more particle density operators in the group to obtain a respective measurement result for the group; and determining the energy of the chemical system using the obtained measurement results.

Abstract: Methods, systems, and apparatus for quantum machine learning. In one aspect, a method includes obtaining, by a quantum computing device, a training dataset of quantum data points; computing, by the quantum computing device, a kernel matrix that represents a similarity between the quantum data points included in the training dataset, comprising computing a value of a kernel function for each pair of quantum data points in the training dataset, wherein the kernel function is based on reduced density matrices for the quantum data points; and providing, by the quantum computing device, the kernel matrix to a classical processor, wherein the classical processor performs a training algorithm using the kernel matrix to construct a machine learning model.

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 correcting a result of a quantum computation.

Abstract: Methods, systems and apparatus for error correction of fermionic quantum simulation. In one aspect, a method includes representing a fermionic system as a graph of vertices and edges, where each vertex represents a fermionic system fermionic mode and each edge represents an interaction between two respective fermionic modes; allocating a qubit to each edge in the graph to form a qubit system; determining qubit operators that satisfy a set of fermionic commutation and dependence relations, where the qubit operators are non-uniform with respect to the graph vertices; determining stabilizer operators corresponding to products of quadratic Majorana operators on respective loops in the graph, where a common eigenspace of the defined stabilizer operators defines a code subspace that encodes states of the fermionic system to be simulated; and simulating the fermionic system by evolving the qubit system under a qubit Hamiltonian that includes the determined qubit operators and stabilizer operators.

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: Methods, systems and apparatus for simulating a physical system described by an electronic structure Hamiltonian expressed in an orthonormal basis. In one aspect, a method includes decomposing the electronic structure Hamiltonian into a sum of sub-Hamiltonians, wherein each sub-Hamiltonian in the sum of sub-Hamiltonians is expressed in one of multiple bases; simulating evolution of the physical system using the decomposed electronic structure Hamiltonian; and using the simulated evolution of the physical system using the decomposed electronic structure Hamiltonian to determine properties of the physical system.

Abstract: Methods, systems and apparatus for targeting many-body states on a quantum computer. In one aspect, a method includes an adaptive phase shift method that includes preparing the quantum system in an initial state, wherein the initial state has non-zero overlap with the target eigenstate; preparing an ancilla qubit in a zero computational basis state; and iteratively applying a quantum eigenstate locking circuit to the quantum system and ancilla qubit until the state of the quantum system approximates the target eigenstate, wherein the quantum eigenstate locking circuit comprises a phase gate that, at each n-th iteration, is updated using a current average energy estimate of the quantum system.