Nonlinear calibration of a quantum computing apparatus

Abstract

Methods, systems, and apparatus for nonlinear calibration of quantum computing apparatus. In one aspect, elements in a set of experimental data correspond to a respective configuration of control biases for the quantum computing apparatus. An initial physical model comprising one or more model parameters of the quantum computing apparatus is defined. The model is iteratively adjusted to determine a revised physical model, where at each iteration: a set of predictive data corresponding to the set of experimental data is generated, and elements in the predictive data represent a difference between the two smallest eigenvalues of a Hamiltonian characterizing the system qubits for the previous iteration, and are dependent on at least one model parameter of the physical model for the previous iteration; and the model for the previous iteration is adjusted using the obtained experimental data and the generated set of predictive data for the iteration.

What is claimed is: 
     
         1 . A computer-implemented method for generating a revised physical model, the revised physical model representing a system of qubits and being suitable for use in simulating the system of qubits, the system of qubits operable via a set of control biases, the method comprising:
 obtaining an initial physical model representing the system of qubits, the initial physical model comprising a Hamiltonian matrix, wherein the Hamiltonian matrix is dependent on one or more model parameters and the set of control biases;   generating and storing matrix components included in a functional representation of the Hamiltonian matrix;   iteratively adjusting the initial physical model to determine a revised physical model representing the system of qubits, comprising, for each iteration:
 minimizing a cost function with respect to at least one of the one or more model parameters included in the functional representation of the Hamiltonian matrix, comprising: 
 computing a symbolic derivative of a scalar function of the at least one model parameter; 
 retrieving one or more of the stored matrix components; and 
 computing a gradient of the cost function with respect to the at least one model parameter using the symbolic derivative and retrieved one or more stored matrix components; and 
 
   providing parameters of the revised physical model as calibrated parameter values for controlling the system of qubits.   
     
     
         2 . The method of  claim 1 , further comprising using the revised physical model to model a behavior of the system of qubits. 
     
     
         3 . The method of  claim 2 , wherein using the revised physical model to model the behavior of the system of qubits comprises:
 fixing the revised physical model; and   determining one or more control bias configurations that, when applied to the qubits, cause the system of qubits to have one or more target properties.   
     
     
         4 . The method of  claim 1 , wherein the system of qubits comprises a quantum annealer circuit. 
     
     
         5 . The method of  claim 1 , wherein the cost function is dependent on differences between elements of a set of experimental data and elements of a set of predictive data, wherein elements in the set of experimental data (i) correspond to a respective configuration of control biases, and (ii) comprise a measurement result of an observable of the system of qubits for the respective configuration of control biases. 
     
     
         6 . The method of  claim 5 , wherein elements in the set of predictive data for the iteration represent a difference between two smallest eigenvalues of the Hamiltonian matrix included in the physical model for a previous iteration, and are dependent on the at least one model parameter of the physical model for the previous iteration. 
     
     
         7 . The method of  claim 5 , further comprising, for each iteration, generating the set of predictive data for an iteration comprises, comprising, for each configuration of control biases:
 defining the Hamiltonian matrix included in the physical model for a previous iteration, the Hamiltonian matrix being dependent on the configuration of control biases and the at least one model parameter;   determining a two smallest eigenvalues of the defined Hamiltonian matrix; and   generating an element of the set of predictive data for the configuration of control biases representing the difference between the determined two smallest eigenvalues of the defined Hamiltonian matrix.   
     
     
         8 . The method of  claim 1 , wherein the initial physical model is obtained through application of experimental techniques to estimate the at least one model parameter. 
     
     
         9 . The method of  claim 6 , wherein the cost function is represented by
         C       λ   ¯           =         1     2   N           ∑     i   =   1     N               E           z   ¯     i             −         E   m             z   ¯     i     ;         λ   ¯               2                 where   λ  represents the at least one model parameter, N represents a number of configurations of control biases  z   i  in the set of control biases, E(z̅ i ) represents experimental data corresponding to control bias configuration i and E m (z̅ i ;  λ ) represents predictive data corresponding to control bias configuration i. 
     
     
         10 . The method of  claim 1 , wherein computing gradients of the cost function with respect to the at least one model parameter comprises applying matrix perturbation theory. 
     
     
         11 . The method of  claim 10 , wherein applying matrix perturbation theory comprises using eigenvalues and eigenvectors of the Hamiltonian matrix included in the physical model. 
     
     
         12 . The method of  claim 1 , wherein the Hamiltonian matrix included in the physical model comprises an effective Hamiltonian describing interactions between the qubits. 
     
     
         13 . The method of  claim 12 , wherein the effective Hamiltonian is defined using a physical approximation. 
     
     
         14 . The method of  claim 12 , wherein the Hamiltonian matrix included in the physical model describes more interacting components than the effective Hamiltonian. 
     
     
         15 . The method of  claim 5 , wherein the observable comprises-Hamiltonians describing the system of qubits for respective configurations of control biases, and wherein the set of experimental data comprises measured energy spectrum values of the system of qubits for respective configurations of control biases. 
     
     
         16 . The method of  claim 15 , wherein the set of predictive data comprises predicted energy spectrum values of the system of qubits for respective configurations of control biases. 
     
     
         17 . The method of  claim 1 , wherein the qubits comprise superconducting qubits. 
     
     
         18 . The method of  claim 17 , wherein the control biases comprise voltages or currents. 
     
     
         19 . The method of  claim 1 , wherein the at least one model parameter comprises a physical parameter defining the system of qubits. 
     
     
         20 . An apparatus comprising:
 a classical computing device; and   a quantum computing device, wherein the quantum computing device comprises a system of qubits operable via a set of control biases;   wherein the classical computing device and quantum computing device are configured to perform operations comprising:
 obtaining an initial physical model representing the system of qubits, the initial physical model comprising a Hamiltonian matrix, wherein the Hamiltonian matrix is dependent on one or more model parameters and the set of control biases; 
 generating and storing matrix components included in a functional representation of the Hamiltonian matrix; 
 iteratively adjusting the initial physical model to determine a revised physical model representing the system of qubits, comprising, for each iteration:
 minimizing a cost function with respect to at least one of the one or more model parameters included in the functional representation of the Hamiltonian matrix, comprising: 
 computing a symbolic derivative of a scalar function of the at least one model parameter; 
 retrieving one or more of the stored matrix components; and 
 computing a gradient of the cost function with respect to the at least one model parameter using the symbolic derivative and retrieved one or more stored matrix components; and 
 
 
providing parameters of the revised physical model as calibrated parameter values for controlling the system of qubits.