One-Way Quantum Computer

Noriaki Horiuchi

Eesa Nikahd, Mahboobeh Houshmand, Morteza Saheb Zamani +1 more

Robert Raussendorf, Jim Harrington, Kovid Goyal

Vincent Danos A, Elham Kashefi, Prakash Panangaden +1 more

Measurement-based quantum computation (MBQC) has emerged as a new approach to quantum computation where the notion of measurement is the main driving force of computation. This is in contrast with the more traditional circuit model that takes unitary operations as fundamental. Among measurement-based quantum computation methods the recently introduced one-way quantum computer stands out as basic and fundamental. The key idea is to start from an entangled state and then use measurements and one-qubit unitaries, which may be dependent on the outcomes of measurements, to guide the computation. The main point is that one never has to perform unitaries on more than one qubit at a time after the initial preparation of an entangled state. The “programs” that one writes in this model are traditionally called “patterns.” In this chapter, we develop a rigorous mathematical model underlying measurement-based quantum computation. We give syntax, operational semantics, denotational semantics, and an algebra of programs derived from the denotational semantics. We also present a rewrite theory and prove a general standardization theorem that allows all programs to be put in a semantically equivalent standard form. Standardization has far-reaching consequences: a new physical architecture based on performing all the entanglement in the beginning, parallelization by exposing the dependency structure of measurements, and expressiveness theorems. We use our general measurement calculus not just to formalize the one-way model but also several other measurement-based models, e.g., Teleportation, Phase, and Pauli models, and present compositional embeddings of them into and from the one-way model.

Philip John Walther, Kevin J. Resch, Terry Rudolph +5 more

Yingheng Li, Aditya Pawar, Zewei Mo +3 more

Measurement-based quantum computing (MBQC) is a promising quantum computing paradigm that performs computation through "one-way" measurements on entangled quantum qubits. It is widely used in photonic quantum computing (PQC), where the computation is carried out on photonic cluster states (i.e., a 2-D mesh of entangled photons). In MBQC-based PQC, the cluster state depth (i.e., the length of one-way measurements) plays an important role in the overall execution time and circuit error. In this paper, we propose FMCC, a compilation framework that employs dynamic programming with heuristics to efficiently minimize the cluster state depth. Experimental results on six quantum applications show that FMCC achieves 51.7%, 57.4%, and 56.8% average depth reductions in small, medium, and large qubit counts compared to the state-of-the-art MBQC compilations.