Quantum Circuits: Divide and Compute with Maximum Likelihood Tomography

We introduce maximum likelihood fragment tomography (MLFT) as an improved circuit cutting technique for running "clustered" quantum circuits on quantum devices with a limited number of qubits. In addition to minimizing the classical computing overhead of circuit cutting methods, MLFT finds the most likely probability distribution for the output of a quantum circuit, given the measurement data obtained from the circuit's fragments. Unlike previous circuit cutting methods, MLFT guarantees that all reconstructed probability distributions are strictly non-negative and normalized. We demonstrate the benefits of MLFT for accurately estimating the output of a fragmented quantum circuit with numerical experiments on random unitary circuits. Finally, we provide numerical evidence and theoretical arguments that circuit cutting can estimate the output of a clustered circuit with higher fidelity than full circuit execution, thereby motivating the use of circuit cutting as a standard tool for running clustered circuits on quantum hardware.

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