Qubit allocation as a combination of subgraph isomorphism and token swapping

Abstract

In 2016, the first quantum processors have been made available to the general public. The possibility of programming an actual quantum device has elicited much enthusiasm. Yet, such possibility also brought challenges. One challenge is the so called Qubit Allocation problem: the mapping of a virtual quantum circuit into an actual quantum architecture. There exist solutions to this problem; however, in our opinion, they fail to capitalize on decades of improvements on graph theory. In contrast, this paper shows how to model qubit allocation as the combination of Subgraph Isomorphism and Token Swapping. This idea has been made possible by the publication of an approximative solution to the latter problem in 2016. We have compared our algorithm against five other qubit allocators, all independently designed in the last two years, including the winner of the IBM Challenge. When evaluated in łTokyo", a quantum architecture with 20 qubits, our technique outperforms these state-of-the-art approaches in terms of the quality of the solutions that it finds and the amount of memory that it uses, while showing practical runtime. CCS Concepts: • Computer systems organization → Quantum computing; • Software and its engineering → Compilers; • Theory of computation → Parameterized complexity and exact algorithms.

Qubit Allocation

“…The dissertation contains a plethora of experiments that compare different versions of our qubit allocators with state-of-the-art algorithms. In this section, we chose to show results involving seven different algorithms: ibm, jku, chw, and sbr; plus the two variations of BMT [Siraichi et al 2019]: bmtS and bmtF and wpm . The latter three algorithms are contributions of the dissertation.…”

“…It counts 39 citations accumulated in 19 months-only one of them from our research group. • Published the "Bounded Mapping Tree" algorithm in the Conference of Object-Oriented Programming, Systems, Languages & Applications (OOPSLA'19-Qualis A1) [Siraichi et al 2019]. In this paper we established approximation bounds to qubit allocation, and developed what, to the best of our knowledge, is one of the most effective qubit allocators available today; • Second best tool in CBSoft 2018 Tools Session, with the paper "Enfield: An Open-QASM Compiler" [Siraichi and Tonetti 2018].…”

NISQ circuit compilation is the travelling salesman problem on a torus

“…QCC has also been considered a search problem according to [27], which includes a detailed review of the methods used for determining the complexity class. It has been recently discussed that the complexity of QCC optimisation is NP-hard [17] by comparing QCC with the optimisation of fault-tolerant quantum circuits protected by the surface code [9].…”

“…The first two are practically already methodological parts of established quantum circuit design frameworks such as Cirq and Qiskit. A theoretical analysis of the first two was provided in [27]. The third operation is based on circular CNOT circuits as introduced in [19].…”

Quantum Circuit Transformation: A Monte Carlo Tree Search Framework

“…As there are now standard decomposition processes (see, e.g., [Nielsen and Chuang 2002, Chapter 4]), in this paper, we focus on the transformation process, and assume that gates in the input logical circuit have been well decomposed into elementary gates that are supported by the QPU. Furthermore, we assume that an initial mapping is given, which can be obtained by employing, say, the greedy strategy [Cowtan et al 2019;Paler 2019;Zulehner et al 2018], the reverse traversal technique [Li et al 2019], the simulated annealing based algorithm [Zhou et al 2020b], or the subgraph isomorphism based methods Siraichi et al 2019b].…”