The how and why of translating between the circuit model and the one-way model of quantum computing

          @misc{ pirsa_PIRSA:24050004,
            doi = {10.48660/24050004},
            url = {https://pirsa.org/24050004},
            author = {Backens, Miriam},
            keywords = {Quantum Information},
            language = {en},
            title = {The how and why of translating between the circuit model and the one-way model of quantum computing},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {may},
            note = {PIRSA:24050004 see, \url{https://pirsa.org}}
          }
          

Abstract

In the one-way model of measurement based quantum computing, unlike the quantum circuit model, a computation is driven not by unitary gates but by successive adaptive single-qubit measurements on an entangled resource state. So-called flow properties ensure that a one-way computation, described by a measurement pattern, is deterministic overall (up to Pauli corrections on output qubits). Translations between quantum circuits and measurement patterns have been used to show universality of the one-way model, verify measurement patterns, optimise quantum circuits, and more. Yet while it is straightforward to translate a circuit into a measurement pattern, the question of algorithmic "circuit extraction" -- how to translate general measurement patterns with flow to ancilla-free circuits -- had long remained open for all but the simplest type of flow. In this talk, we will recap the one-way model of quantum computing and then explain how the problem of circuit extraction was resolved using the ZX-calculus as a common language for circuits and measurement patterns. We also discuss applications.