Quantum Circuit Transformation: A Monte Carlo Tree Search Framework

Abstract

In Noisy Intermediate-Scale Quantum (NISQ) era, quantum processing units (QPUs) suffer from, among others, highly limited connectivity between physical qubits. To make a quantum circuit effectively executable, a circuit transformation process is necessary to transform it, with overhead cost the smaller the better, into a functionally equivalent one so that the connectivity constraints imposed by the QPU are satisfied. While several algorithms have been proposed for this goal, the overhead costs are often very high, which degenerates the fidelity of the obtained circuits sharply. One major reason for this lies in that, due to the high branching factor and vast search space, almost all these algorithms only search very shallowly and thus, very often, only (at most) locally optimal solutions can be reached. In this paper, we propose a Monte Carlo Tree Search (MCTS) framework to tackle the circuit transformation problem, which enables the search process to go much deeper. The general framework supports implementations aiming to reduce either the size or depth of the output circuit through introducing SWAP or remote CNOT gates. The algorithms, called MCTS-Size and MCTS-Depth, are polynomial in all relevant parameters. Empirical results on extensive realistic circuits and IBM Q Tokyo show that the MCTS-based algorithms can reduce the size (depth, resp.) overhead by, on average, 66% (84%, resp.) when compared with t|ket PLX − right 〉., an industrial level compiler.

On constructing benchmark quantum circuits with known near-optimal transformation cost

“…These heuristic algorithms can be further classified according to their optimisation objective. A few algorithms aim to maximise the fidelity or minimise the error rate [15], [2], [26], [9]; many aim to reduce the number of SWAP gates inserted [34], [11], [12], [33], [31]; and many others aim to reduce the depth of the output circuit [7], [30], [32] so that the highly limited qubit coherence time is respected.…”

“…The SAHS algorithm [33] first selects an initial mapping which best fits the input circuit C by using the simulated annealing method and then, in the routing process, simulates the search process one step further and selects the SWAP with the best consecutive SWAP to apply. The Monte Carlo Tree Search (MCTS) method for quantum circuit transformation, denoted as MCTS in this paper, was first introduced in [31] for gate size optimisation and extended in [32] for depth optimisation. The idea is to exploit the search space in a balanced way.…”

“…For the depth optimisation, each permutation (except the first one) is implemented by a set of parallel swaps, i.e., a SWAP circuit of depth 1. 4) architecture graph (AG): We consider three representative and state-of-the-art quantum devices, viz., IBM Q Tokyo (20 qubits), IBM Q Rochester (53 qubits), and Google's Sycamore (53 qubits), which are also considered in [25], [12], [32]. We note that the benchmarks designed for IBM Q Rochester are perhaps not near-optimal for Sycamore, and vice versa.…”

“…This critical procedure is known as quantum circuit transformation (QCT), qubit mapping, or layout synthesis, and is in a sense analogous to the classical layout synthesis task. QCT is an important component of quantum circuit compilation and has attracted broad interests from areas like quantum computing [4], [7], [17], [21], [28], electronic design automation [2], [9], [10], [24], [29], [31], [32], [33], [34], and computer architecture [11], [13], [15], [16], [26], [30]. In this paper, we address this procedure as, interchangeably, qubit mapping and (quantum) circuit transformation.…”

“…In terms of ρ gate and ρ depth above, it is appropriate to regard our benchmarks as having known near-optimal costs. We compared four state-of-the-art QCT algorithms, t|ket [7], SABRE [11], SAHS [33], and MCTS [31], [32] with a baseline Qiskit transpiler on our benchmarks and three sets of QUEKO benchmarks -'54Q bntf Sycamore', '20Q bss Tokyo', and '16Q bntf Aspen-4'. Fig.…”