| CPC G06N 10/60 (2022.01) [G06N 10/20 (2022.01); G06N 10/70 (2022.01)] | 15 Claims |
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1. A method implemented by one or more classical processors and quantum hardware for determining an average purity of multiple output quantum states of qubits of the quantum hardware, wherein the multiple output quantum states correspond to applications of respective random quantum circuits of a same circuit depth to a same initial quantum state, the method comprising:
applying, by the quantum hardware, the respective random quantum circuits of the same circuit depth to the same initial quantum state of the qubits of the quantum hardware by sending one or more control signals to change a state of the quantum hardware from the initial quantum state to a state in which logic gates included in the random quantum circuit are implemented by the qubits of the quantum hardware;
obtaining, by the one or more classical processors, measurement data corresponding to measurement results of the applications of the respective random quantum circuits to the same initial quantum state of qubits of the quantum hardware;
representing each output quantum state by a depolarizing channel with depolarizing channel parameter p that represents a probability that the output quantum state is a pure state;
computing the average purity of the output quantum states, comprising:
calculating, by the one or more classical processors and using the obtained measurement data, a plurality of data items, wherein each data item corresponds to a respective random quantum circuit of the same circuit depth and represents a probability that application of the respective random quantum circuit to the initial quantum state produces a respective measurement result, wherein a distribution of the probabilities represented by the plurality of data items comprises a scaled Porter Thomas distribution, wherein the scaled Porter Thomas distribution is scaled towards a uniform distribution by the depolarizing channel parameter p;
calculating, by the one or more classical processors, a variance of the scaled Porter Thomas distribution of the probabilities represented by the plurality of data items;
determining, by the one or more classical processors, a variance of an unscaled Porter-Thomas distribution having a dimension equal to a dimension D of each output quantum state; and
dividing, by the one or more classical processors, the calculated variance of the scaled Porter Thomas distribution by variance of the unscaled Porter-Thomas distribution with dimension D to determine the average purity.
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