Google Inc.

Zhang Jiang

Ryan Babbush

Jarrod Ryan McClean

Vadim Smelyanskiy

Yu Chen

Yuezhen Niu

Charles Neill

Alexander Nikolaevich Korotkov

Kostyantyn Yevgenovych Kechedzhi

Jonathan Arthur Gross

Nicholas Charles Rubin

Xiao Mi

Dripto Mazumdar Debroy

Wojtek Jerzy Mruczkiewicz

Charles James Neill

Jarrod Ryan Mcclean

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.

Increasing representation accuracy of quantum simulations without additional quantum resources

Quantum computing systems and methods are provided. In one example, a quantum computing system includes a quantum system having one or more quantum system qubits and one or more ancilla qubits. The quantum computing system includes one or more quantum gates implemented by the quantum computing system. The quantum gate(s) are operable to configure the one or more ancilla qubits into a known state. The quantum computing system includes a quantum measurement circuit operable to perform a plurality of measurements on the one or more quantum system qubits using the one or more ancilla qubits. The quantum computing system includes one or more processors operable to determine a reduced density matrix for a subset of the quantum system based on a set of the plurality of measurements that include a number of repeated measurements performed using the quantum measurement circuit.

Systems and methods for quantum tomography using an ancilla

Systems and methods for composite quantum gate calibration for a quantum computing system are provided. In some implementations, a method includes accessing a unitary gate model describing a composite quantum gate. The unitary gate model includes a plurality of gate parameters. The method includes implementing the composite quantum gate for a plurality of gate cycles on the quantum system to amplify the plurality of gate parameters. The method includes obtaining a measurement of a state of the quantum system after implementing the composite quantum gate for the plurality of gate cycles. The method includes determining at least one of the plurality of gate parameters based at least in part on the measurement of the state of the quantum system. The method includes calibrating the composite quantum gate for the quantum computing system based at least in part on the plurality of gate parameters.

Composite quantum gate calibration

Methods, systems and apparatus for preparing arbitrary superposition quantum states of a quantum register on a quantum computer, the quantum state comprising a superposition of L computational basis states. In one aspect, a register of log L qubits is prepared in a weighted sum of register basis states, where each register basis state indexes a corresponding quantum state computational basis state, and the amplitude of each register basis state in the weighted sum of register basis states is equal to the amplitude of the corresponding computational basis state in the superposition of L computational basis states. A unitary transformation that maps the register basis states to the corresponding L computational basis states is then implemented, including, for each index 1 to L, controlling, by the register of log L qubits, transformation of the quantum system register state for the index to the corresponding computational basis state for the index.

Preparing superpositions of computational basis states on a quantum computer

Methods, systems and apparatus for correcting a result of a quantum computation. In one aspect, a method includes selecting a quantum error correcting code for the quantum computation, wherein the quantum error correcting code is defined by multiple stabilizer generators; determining a set of symmetry operators, comprising: selecting a subset of the stabilizer generators, determining, for each selected stabilizer generator, a sum between an identity operator and the stabilizer generator, and multiplying the determined sums together to form a summation of terms, wherein each term in the summation is equal to a respective symmetry operator; measuring a projective correction of a physical observable over an output quantum state of the quantum computation using the determined set of symmetry operators, wherein the physical observable corresponds to the result of the quantum computation; and determining a corrected result of the quantum computation using the measured projective correction of the physical observable.

Decoding errors using quantum subspace expansion

The disclosure is directed to characterizing a quantum logic circuit (QLC), via a set of intrinsic parameters. One method includes selecting control vectors that are associated with phase shifts for the intrinsic parameters such that experimental unitary operators for the QLC are defined. Each experimental unitary operator is based on the intrinsic parameters and phase shifts associated with a corresponding control vector. For each control vector, eigenvalues for the corresponding unitary operator are estimated based on qubit measurements performed subsequent to tuning the QLC in accordance with the control vector. The eigenvalues correspond to quasienergy levels of the qubits. Values for the set of intrinsic parameters may be determined based on the eigenvalues.

Characterization of quantum logic circuits

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.

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El Segundo, CA, United States of America

Zhang Jiang