[Paper Review] Quantum Circuit Transformation: A Monte Carlo Tree Search Framework

Xiangzhen Zhou, Yuan Feng+1 more|arXiv (Cornell University)|Aug 21, 2020

Quantum Computing Algorithms and Architecture32 references23 citations

TL;DR

This paper proposes a Monte Carlo Tree Search (MCTS) framework for quantum circuit transformation in Noisy Intermediate-Scale Quantum (NISQ) devices, enabling deeper search to reduce circuit size and depth overhead. By integrating a scoring mechanism with discounted backpropagation and random simulations, the MCTS-Size and MCTS-Depth algorithms achieve up to 66% and 84% average reductions in CNOT count and circuit depth, respectively, outperforming industrial compilers like t|ket⟩.

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 tket, an industrial level compiler.

Motivation & Objective

• Address the challenge of high overhead in quantum circuit transformation due to limited qubit connectivity in NISQ devices.
• Overcome the shallow search depth of existing heuristic algorithms that limit optimization quality.
• Develop a scalable, polynomial-time framework to minimize either circuit size or depth during qubit mapping.
• Enable deeper exploration of the search space to find globally better solutions than locally optimal ones.
• Improve compilation fidelity by reducing SWAP and CNOT gate insertions through intelligent search.

Proposed method

• Propose a general MCTS framework for quantum circuit transformation, supporting both size and depth minimization.
• Design a scoring mechanism that balances immediate rewards (SWAP cost) and long-term value from random simulations.
• Introduce a discount factor in backpropagation to prioritize paths with lower cumulative cost to goal states.
• Implement two variants: MCTS-Size minimizes total gate count, MCTS-Depth minimizes circuit depth.
• Use a simulation module with deterministic greedy heuristics to guide rollout policy in large-scale circuits.
• Ensure polynomial runtime in all relevant parameters, enabling scalability to large quantum processors.

Experimental results

Research questions

• RQ1 Can MCTS enable deeper search in quantum circuit transformation than shallow heuristic methods?
• RQ2 Does integrating long-term simulation rewards with immediate cost lead to better circuit optimization?
• RQ3 Can the MCTS framework reduce both size and depth overhead more effectively than industrial compilers like t|ket⟩?
• RQ4 How does the choice of simulation strategy (random vs. deterministic greedy) affect performance on large architectures?
• RQ5 To what extent can MCTS-based transformation improve fidelity by minimizing gate insertions?

Key findings

• MCTS-Size reduces average CNOT gate overhead by 66% compared to t|ket⟩ on IBM Q20, Rochester, and Google Sycamore.
• MCTS-Depth reduces average circuit depth overhead by 84% compared to t|ket⟩ on the same hardware platforms.
• On the QUEKO benchmark, MCTS-Depth achieves a total depth ratio of 2.88, outperforming t|ket⟩ (3.76) but still below the optimal 1.0.
• The deterministic greedy simulation strategy outperforms random simulation on large architectures (e.g., 8×8 grid), especially for depth minimization.
• The MCTS framework scales effectively, with polynomial time complexity and the ability to stop early under resource constraints.
• Empirical results confirm consistent superiority over Qiskit, SABRE, and t|ket⟩ across diverse real-world circuits and QPU architectures.