Google Inc.

Vadim Smelyanskiy

Sergio Boixo Castrillo

Yuezhen Niu

Hartmut Neven

Rami Barends

Ryan Babbush

John Martinis

Yu Chen

Nan Ding

Alexander Nikolaevich Korotkov

Sergei V Isakov

Andre Petukhov

Julian Shaw Kelly

Masoud Mohseni

Zhang Jiang

Paul Victor Klimov

Charles Neill

Kevin Joseph Satzinger

Zijun Chen

Matthew James McEwen

Kostyantyn Yevgenovych Kechedzhi

Trevor Johnathan Mccourt

Juan Carlos Atalaya-Chavez

Xiao Mi

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 simulating quantum circuits including multiple quantum logic gates. In one aspect, a method includes the actions of representing the multiple quantum logic gates as functions of one or more classical Boolean variables that define a undirected graphical model with each classical Boolean variable representing a vertex in the model and each function of respective classical Boolean variables representing a clique between vertices corresponding to the respective classical Boolean variables; representing the probability of obtaining a particular output bit string from the quantum circuit as a first sum of products of the functions; and calculating the probability of obtaining the particular output bit string from the quantum circuit by directly evaluating the sum of products of the functions. The calculated partition function is used to (i) calibrate, (ii) validate, or (iii) benchmark quantum computing hardware implementing a quantum circuit.

Simulation of quantum circuits

Methods and apparatus for estimating the fidelity of quantum hardware. In one aspect, a method includes accessing a set of quantum gates; sampling a subset of quantum gates from the set of quantum gates, wherein the subset of quantum gates defines a quantum circuit; applying the quantum circuit to a quantum system and performing measurements on the quantum system to determine output information of the quantum system; calculating output information of the quantum system based on application of the quantum circuit to the quantum system; and estimating a fidelity of the quantum circuit based on the determined output information and the calculated output information of the quantum system.

Fidelity estimation for quantum computing systems

Errors that affect a quantum computer can be efficiently measured and characterized by placing the quantum computer in a highly-entangled state such as a Greenberger-Horne-Zeilinger (GHZ) state, accumulating quantum errors in the highly entangled state, and then measuring the accumulated errors. In some approaches, the error characterization includes measuring parity oscillations of the GHZ state and fitting a quantum error model to a power spectrum of the parity oscillations. The fitted quantum error model can be used to select a suitable fault-tolerant error correction scheme for the quantum computer given its environmental noise.

Characterization of time-correlated quantum errors through entanglement

Methods, systems and apparatus for implementing a quantum gate on a quantum system comprising a second qubit coupled to a first qubit and a third qubit. In one aspect, a method includes evolving a state of the quantum system for a predetermined time, wherein during evolving: the ground and first excited state of the second qubit are separated by a first energy gap ω; the first and second excited state of the second qubit are separated by a second energy gap equal to a first multiple of ω minus qubit anharmoniticity η; the ground and first excited state of the first qubit and third qubit are separated by a third energy gap equal to ω−η; and the first and second excited state of the first qubit and third qubit are separated by a fourth energy gap equal to the first multiple of the ω minus a second multiple of η.

Three qubit entangling gate through two-local Hamiltonian control

Methods, systems, and apparatus for implementing a unitary quantum gate on one or more qubits. In one aspect, a method includes the actions designing a control pulse for the unitary quantum gate, comprising: defining a universal quantum control cost function, wherein the control cost function comprises a qubit leakage penalty term representing i) coherent qubit leakage, and ii) incoherent qubit leakage across all frequency components during a time dependent Hamiltonian evolution that realizes the unitary quantum gate; adjusting parameters of the time dependent Hamiltonian evolution to vary a control cost according to the control cost function such that leakage errors are reduced; generating the control pulse using the adjusted parameters; and applying the control pulse to the one or more qubits to implement the unitary quantum gate.

Universal control for implementing quantum gates

Methods, systems and apparatus for generating plunge schedules for implementing iSWAP quantum logic gates between a first qubit and a second qubit. In one aspect, a plunge schedule that defines a trajectory of a detuning between a frequency of the first qubit and a frequency of the second qubit includes, during a first stage, non-adiabatically driving detuning between the frequency of the first qubit and the frequency of the second qubit through a first avoided crossing in a leakage channel, during a second stage, driving detuning between the frequency of the first qubit and the frequency of the second qubit through a second avoided crossing in a swap channel. during a third stage, allowing the first qubit and the second qubit to freely evolve and interact, during a fourth stage, implementing the second stage in reverse order, and during a fifth stage, implementing the first stage in reverse order.

Non-adiabatic implementation of an iSWAP quantum logic gate

Methods, systems and apparatus for implementing iSWAP quantum logic gates between a first qubit and a second qubit. In one aspect, a method includes implementing a cascade schedule that defines a trajectory of a detuning between a frequency of the first qubit and a frequency of the second qubit. Implementing the cascade schedule includes: during a first stage, adiabatically driving detuning between the frequency of the first qubit and the frequency of the second qubit through a first avoided crossing in a leakage channel; during a second stage, driving detuning between the frequency of the first qubit and the frequency of the second qubit through a second avoided crossing in a swap channel; during a third stage, evolving the first qubit and second qubit; during a fourth stage, implementing the second stage in reverse order; and during a fifth stage, implementing the first stage in reverse order.

Cascade protocol for iSWAP gate in a two-qubit system

The present disclosure provides systems and methods to measure quantum gate fidelity through swap spectroscopy. In particular, aspects of the present disclosure are directed to the derivation and use of a physical model that models non-Markovian quantum dynamics of interactions between one or more qubits of a quantum gate and one or more two-level-system (TLS) defects during operation of the quantum gate.

Systems and methods to measure quantum gate fidelity through swap spectroscopy

A quantum computing system configured for removal of leakage states can include quantum hardware including a first qubit and a second qubit, wherein the first qubit is configured to have a first transition frequency and wherein the second qubit is configured to have a second transition frequency, the first transition frequency being greater than the second transition frequency. The quantum computing system can include one or more quantum control devices configured to control operation of at least the first qubit and the second qubit, wherein the one or more quantum control devices are configured to implement a quantum gate operation on the first qubit and the second qubit based at least in part on the first transition frequency and the second transition frequency, and wherein the one or more quantum control devices are configured to periodically reset a quantum state of the first qubit.

Frequency configuration in quantum gates for leakage removal

Methods, systems, and apparatus for designing a quantum control trajectory for implementing a quantum gate using quantum hardware. In one aspect, a method includes the actions of representing the quantum gate as a sequence of control actions and applying a reinforcement learning model to iteratively adjust each control action in the sequence of control actions to determine a quantum control trajectory that implements the quantum gate and reduces leakage, infidelity and total runtime of the quantum gate to improve its robustness of performance against control noise during the iterative adjustments.

Quantum computation through reinforcement learning

Methods, systems and apparatus for implementing a quantum gate on a quantum system comprising a second qubit coupled to a first qubit and a third qubit. In one aspect, a method includes evolving a state of the quantum system for a predetermined time, wherein during evolving: the ground and first excited state of the second qubit are separated by a first energy gap &#x3c9;; the first and second excited state of the second qubit are separated by a second energy gap equal to a first multiple of &#x3c9; minus qubit anharmoniticity&#x2212;; the ground and first excited state of the first qubit and third qubit are separated by a third energy gap equal to &#x3c9;&#x2212;; and the first and second excited state of the first qubit and third qubit are separated by a fourth energy gap equal to the first multiple of the &#x3c9; minus a second multiple of.

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Mountain View, CA, United States of America

Vadim Smelyanskiy