Abstract: Examples of the present disclosure are directed to a method for operating a quantum computing system (QCS) to load classical data. The method includes configuring a quantum circuit to implement a target classical function that is defined over a string of input bits. The target classical function is decomposed into a set of parity sub-functions. A set of quantum registers of the QCS is initialized with a superposition of input states corresponding to the string of input bits. A sequence of Quantum Read-Only Memory (QROM) operations is executed on the set of quantum registers to generate a set of outputs. Each QROM operation of the sequence of QROM operations encodes a separate parity sub-function of the set of parity sub-functions. Each output of the set of outputs is routed to a separate output register of a set of output registers of the QCS.

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: 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 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: 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 simulating a quantum system. In one aspect, a method includes performing a first quantized quantum algorithm on an initial quantum state to simulate time evolution of a fermionic system and generate a time evolved quantum state; and measuring, by the quantum computer, the time evolved quantum state to obtain one or more reduced density matrices in first quantization, the measuring including performing a classical shadows method that applies separate random Clifford channels to each qubit register of multiple qubit registers that represent respective occupied orbitals in the fermionic system.

Abstract: Methods, systems, and apparatus for hybrid quantum-classical quantum Monte Carlo.

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: Methods, systems, and apparatus for enhancing classical shadows using matchgate quantum circuits. In one aspect, a method for computing a classical shadow of an n-qubit quantum state includes repeatedly sampling, by a classical computer, a unitary operator from an ensemble of random unitaries, wherein the ensemble of random unitaries comprises a generalized matchgate group; for each sampled unitary operator: applying, by a quantum computer, a quantum circuit to the n-qubit quantum state to obtain an evolved quantum state, wherein the quantum circuit implements the sampled unitary operator, measuring, by the quantum computer, the evolved quantum state to obtain a respective bit string, and storing, by the classical computer, a record of the respective bit string and the sampled unitary operator; and providing the records as a classical shadow of the quantum state.

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.