Translating one-way quantum computation to the circuit model: methods and applications

Marek Sawerwain

Mahboobeh Houshmand, Morteza Saheb Zamani, Mehdi Sedighi +1 more

François Chapeau‐Blondeau

Jisho Miyazaki, Michal Hajdušek, Mio Murao

In measurement-based quantum computation (MBQC), elementary quantum operations can be more parallelized than the quantum circuit model by employing a larger Hilbert space of graph states used as the resource. Thus MBQC can be regarded as a method of quantum computation where the temporal resource described by the depth of quantum operations can be reduced compared to the quantum circuit model by using the extra spatial resource described by graph states. To analyze the trade-off relationship of the spatial and temporal resources, we consider a method to obtain quantum circuit decompositions of general unitary transformations represented by MBQC on graph states with a certain underlying geometry called generalized flow. We present a method to translate any MBQC with generalized flow into quantum circuits without extra spatial resource. We also show an explicit way to unravel acausal gates without postselection that appear in the quantum circuit decomposition derived by a translation method [V. Danos and E. Kashefi, Phys. Rev. A 74, 052310 (2006)] and that represents an effect of the reduction of the temporal resource in MBQC. Finally, by considering a way to deterministically simulate these acausal gates, we investigate a general framework to analyze the trade-off between the spatial and temporal resources for quantum computation.

Gunajit Kalita

Mahboobeh Houshmand, Mehdi Sedighi, Morteza Saheb Zamani +1 more

One-way quantum computation (1WQC) is a model of universal quantum computations in which a specific highly entangled state called acluster stateallows for quantum computation by single-qubit measurements. The needed computations in this model are organized as measurement patterns. The traditional approach to obtain a measurement pattern is by translating a quantum circuit that solely consists of CZ andJ(α) gates into the corresponding measurement patterns and then performing some optimizations by using techniques proposed for the 1WQC model. However, in these cases, the input of the problem is a quantum circuit, not an arbitrary unitary matrix. Therefore, in this article, we focus on the first phase—that is, decomposing a unitary matrix into CZ andJ(α) gates. Two well-known quantum circuit synthesis methods, namely cosine-sine decomposition and quantum Shannon decomposition are considered and then adapted for a library of gates containing CZ andJ(α), equipped with optimizations. By exploring the solution space of the combinations of these two methods in a bottom-up approach of dynamic programming, a multiobjective quantum circuit synthesis method is proposed that generates a set of quantum circuits. This approach attempts to simultaneously improve the measurement pattern cost metrics after the translation from this set of quantum circuits.