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. 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 show 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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