Google Inc.

Sergio Boixo Castrillo

Vadim Smelyanskiy

Yuezhen Niu

Hartmut Neven

Ryan Babbush

John Martinis

Rami Barends

Nan Ding

Sergei V Isakov

Andre Petukhov

Craig Gidney

Yu Chen

Jimmy C Chau

Adam Zalcman

Alan Kar-Lun Ho

Methods, systems and apparatus for estimating quantum processor performance. In one aspect, a method includes defining a benchmarking circuit configured to operate on an array of qubits, wherein the benchmarking circuit comprises one or more cycles of quantum gates, each cycle comprising a respective layer of randomly sampled single-qubit gates and a layer of multiple instances of a same multi-qubit gate; partitioning the defined benchmarking circuit into two or more sub-circuits, comprising: defining one or more boundaries between qubits in the array of qubits, removing instances of the multi-qubit gate that cross the defined one or more boundaries to create the two or more sub-circuits; performing a benchmarking process using the partitioned benchmarking circuit to estimate a respective circuit fidelity of each of the sub-circuits; and multiplying the estimated circuit fidelities of each of the sub-circuits to obtain an estimate of the fidelity of the quantum processor.

Patch and elided fidelity estimation

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

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

Systems and methods for quantum random number generation are provided. In some implementations, a method can include obtaining data indicative of a quantum circuit used by the quantum random number generation system to generate a quantum entropy source for determining a random number. The quantum entropy source can include a plurality of output samples. Each output sample can be obtained by measuring an output of the quantum circuit. The method can include performing one or more simulations of the quantum circuit to obtain a simulated output distribution of the quantum circuit without access to data associated with the random number. The method can include providing data indicative of the simulated output distribution for use in a verification process for the quantum random number generation system. The verification process can determine the use of the quantum computing system in generation of the quantum entropy source.

Verified quantum random number generation for cryptographic applications

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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Rancho Palos Verdes, CA, United States of America

Sergio Boixo Castrillo