Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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 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.

Abstract: 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.