Reconstructing Cut Quantum Circuits Maximising Fidelity between Quantum States

Quantum circuit cutting is an emerging field of quantum computing allowing quantum circuits requiring a relatively large number of qubits to be executed on a quantum computer which has a smaller number of qubits. Current works focus mainly on choosing the optimal position to cut circuits, in order to minimise classical reconstruction costs. They do not consider the detrimental effects of cutting circuits on the entanglement shared between the circuit qubits. This paper presents, so far as the authors are aware, the first works to globally reconstruct circuit cutting fragments by maximising the underlying fidelity between quantum states used within circuit computation. Consequently, the original entanglement present that was broken, is reformed. Gradient-based techniques are used to design an optimisation protocol for how to maximise the fidelity between highly multipartite-entangled states. Using adaptive gradient descent this work presents how unit fidelities can be achieved with a relatively small number of optimisation iterations.