Very large scale quantum circuit optimisation using alternative circuit representations

Quantum computations are often described by diagrams, such as quantum circuits, tensor networks or ZX-diagrams. Optimizing quantum circuits implies implementing methods for manipulating the diagrams according to well-defined sets of rules. Quantum circuit optimization using the diagrammatic representation is a highly complex, combinatorial problem even for heuristic methods and it does not easily scale to large-scale circuits.

Our approach to achieve scalable quantum circuit optimisation is: 1) to represent an input circuit with an alternative, not necessarily lossless, representation, 2) to perform optimization on the novel representation, and, 3) finally, to reinterpret an output circuit corresponding to the optimized, functionally equivalent, version of the input circuit. We check the functionally equivalence of the output circuit.

This work we present is, to the best of our knowledge, the first method that is able to easily compile and optimize very wide and deep quantum circuits. We implement our method and benchmark it on representative circuits, including fault-tolerant ones. Compared to state of the art compilers and optimizers, our method can handle circuits of at least one hundred qubits.