Quantum Circuits: Divide and Compute with Maximum Likelihood Tomography

We introduce the method of maximum likelihood fragment tomography (MLFT) as an improved circuit cutting technique for running clustered quantum circuits on quantum devices with limited quantum resources. In addition to minimizing the classical computing overhead of circuit cutting methods, MLFT finds the most likely probability distribution over measurement outcomes at the output of a quantum circuit, given the data obtained from running 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 with classical simulations of clustered 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.