| CPC G06N 10/20 (2022.01) [G06N 10/80 (2022.01)] | 20 Claims |
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1. A method for performing a parameterised quantum evolution for a quantum system associated with a hybrid computing system having a quantum computing system and a classical computing system, wherein the quantum computing system comprises a quantum system having one or more quantum devices,
the method comprising estimating a derivative of a parameter-dependent physical quantity that is dependent on a first control parameter θ of the parameterised quantum evolution by:
on the classical computing system:
determining a finite sub-multi-set S from the set of shift values
 wherein K is a bounding value defining the interval [φ−K, φ+K] which contains the Fourier spectrum of an expectation-value function ƒ(θ) of the first parameterised unitary quantum evolution, where φ is a phase-correction value;
determining a finite sub-multi-set of weighting values qs each weighting value corresponding to a shift value s from the sub-multi-set of shift values S;
wherein the sub-multi-set of shift values and the respective sub-multi-set of weighting values are determined in accordance with a targeted probability distribution
 calculating a sub-multi-set of trial control parameter values, each trial control parameter value generated by combining a respective shift value s from the sub-multi-set of shift values S with the first value of the first control parameter θ0;
calculating a sub-multi-set of summation factors ds, each summation factor ds=2πK(−1)2Ks+1/2 for a respective shift value s from the sub-multi-set of shift values S;
for each trial control parameter value:
communicating the trial control parameter value from the classical computing system to the quantum computing system; and
on the quantum computing system:
subjecting the quantum system to a parameterised unitary quantum evolution with the first control parameter of the parameterised unitary quantum evolution set to the trial control parameter value;
making a quantum measurement on the quantum state to obtain a parameter-dependent physical quantity Fs;
communicating the parameter-dependent physical quantity to the classical computing system; and
on the classical computing system:
calculating a phase-corrected measurement result Fsφ for each shift value s by calculating Fse−2πi(θ0−s)φ; and
calculating the estimate of the derivative of ƒφ(θ)=e−2πi(θ)φƒ(θ) with respect to the first control parameter through the summation
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