Mitigating errors in algorithms performed using quantum information processors
A method comprises, for each of a plurality of FLO circuits, (i) executing, one or more times using the quantum information processor, that FLO circuit to determine a first value of an observable; and (ii) classically simulating that FLO circuit to determine a second value of the observable. A training set comprises tuples, each tuple comprising parameter(s) for defining a FLO circuit, the corresponding first value of the observable determined for that FLO circuit, and the corresponding second value of the observable determined for that FLO circuit. The training set is used to determine a noise inversion function. The quantum information processor executes one or more times a quantum circuit for implementing at least a part of the algorithm to determine a noisy value of an observable. The noise inversion function is applied to the noisy value and a corrected value of the observable is determined.
1 . A method for mitigating errors caused by noise in an algorithm executed using a quantum information processor, wherein the algorithm is configured to simulate a fermionic system and comprises a target quantum circuit for implementing at least a part of the algorithm, and wherein the method comprises:
identifying a plurality of fermionic linear optics (FLO) circuits, wherein each FLO circuit of the plurality of FLO circuits approximates the target quantum circuit, wherein each of plurality of FLO circuits comprise a quantum circuit for which all gates are of the form exp [iHq], where Hq is a quadratic fermionic Hamiltonian;
for each FLO circuit of the plurality of FLO circuits:
executing, one or more times using the quantum information processor, that FLO circuit to determine a first value of an observable; and
classically simulating that FLO circuit to determine a second value of the observable; establishing a training set comprising a plurality of tuples, each tuple comprising:
a set of one or more parameters for defining a FLO circuit of the plurality of FLO circuits;
the corresponding first value of the observable determined for that FLO circuit; and
the corresponding second value of the observable determined for that FLO circuit;
determining, using the training set, a noise inversion function;
executing, one or more times using the quantum information processor, a quantum circuit for implementing at least a part of the algorithm to determine a noisy value of an observable;
applying the noise inversion function to the noisy value; and
determining, from an output of the noise inversion function, a corrected value of the observable.
2 . The method according to claim 1 , wherein the method further comprises determining the plurality of FLO circuits which approximate the quantum circuit.
3 . The method according to claim 2 , wherein determining the plurality of FLO circuits which approximate the quantum circuit comprises analysing the quantum circuit and determining a plurality of FLO circuits experiencing noise which approximates noise experienced by the quantum circuit.
4 . The method according to claim 1 , wherein the quantum circuit includes one or more FLO gates, and wherein FLO circuits of the plurality of FLO circuits preserve a location and/or parameters of one or more of those FLO gates.
5 . The method according to claim 1 , wherein FLO circuits of the plurality of FLO circuits consist of matchgates acting on consecutive qubits of the quantum information processor.
6 . The method according to claim 1 , wherein applying the noise inversion function to the noisy value comprises providing the noisy value and one or more parameters defining the quantum circuit as input to the noise inversion function.
7 . The method according to claim 1 , wherein determining the noise inversion function comprises performing a linear regression.
8 . The method according to claim 1 , wherein determining the noise inversion function comprises training a machine learning algorithm to learn a model for mapping the first value of the observable determined from one or more executions, using the quantum information processor, of the FLO circuit to the second value of the observable determined from a classical simulation of the FLO circuit.
9 . The method according to claim 1 , wherein the observable comprises an energy of a quantum state with respect to a given quantum Hamiltonian.
10 . The method according to claim 1 , wherein the algorithm comprises a variational quantum eigensolver (VQE) algorithm.
11 . A computer readable medium having instructions stored thereon which, when read by a processor of a computing apparatus, cause the computing apparatus to perform the method according to claim 1 .
12 . A computing apparatus comprising:
one or more memory units; and
one or more classical processors configured to execute instructions stored in the one or more memory units to perform the method according to claim 1 .
13 . The computing apparatus according to claim 12 , further comprising the quantum information processor configured to execute the quantum circuit for implementing the algorithm.
14 . The computing apparatus according to claim 13 , wherein the quantum information processor is further configured to execute a fermionic linear optics (FLO) circuit to determine a value of an observable.
15 . The computing apparatus according to claim 14 , further comprising interaction means for interacting with the quantum information processor.