Qubit Routing Using Graph Neural Network Aided Monte Carlo Tree Search

Abstract

Near-term quantum hardware can support two-qubit operations only on the qubits that can interact with each other. Therefore, to execute an arbitrary quantum circuit on the hardware, compilers have to first perform the task of qubit routing, i.e., to transform the quantum circuit either by inserting additional SWAP gates or by reversing existing CNOT gates to satisfy the connectivity constraints of the target topology. The depth of the transformed quantum circuits is minimized by utilizing the Monte Carlo tree search (MCTS) to perform qubit routing by making it both construct each action and search over the space of all actions. It is aided in performing these tasks by a Graph neural network that evaluates the value function and action probabilities for each state. Along with this, we propose a new method of adding mutex-lock like variables in our state representation which helps factor in the parallelization of the scheduled operations, thereby pruning the depth of the output circuit. Overall, our procedure (referred to as QRoute) performs qubit routing in a hardware agnostic manner, and it outperforms other available qubit routing implementations on various circuit benchmarks.

Deep Reinforcement Learning for Mapping Quantum Circuits to 2D Nearest‐Neighbor Architectures

“…In 2020, Pozzi et al [29] extended the method proposed by Herbert et al [28] , using double deep Q-learning and prioritized experience replay to optimize the quantum circuit mapping. Zhou et al [30] in 2020 and Sinha et al [31] in 2022 also combined the Monte Carlo tree algorithm for qubit routing in the quantum circuit mapping process. Although these methods provided a more suitable way to add SWAP gates for quantum circuit 2DNN architecture mapping, they ignored the impact of the initial placement of logical qubits in the mapping process.…”

“…And recently Peham et al [34] compared the performance of various advanced quantum circuit mapping algorithms on benchmarks of known optimal mapping, and concluded that even the most advanced algorithms are not capable of optimal solutions therefore exists to improve upon them. Inspired by the Monte Carlo tree search algorithm [31] and the graph isomorphism search algorithm, [35] this paper proposes a 2DNN architecture mapping method of quantum circuits based on deep reinforcement learning. In our proposed DRL scheme, a new state representation and learning paradigm is adopted, which helps to improve the SWAP gate addition of the output quantum circuit and has faster algorithm running speed.…”

“…[ 30 ] in 2020 and Sinha et al. [ 31 ] in 2022 also combined the Monte Carlo tree algorithm for qubit routing in the quantum circuit mapping process. Although these methods provided a more suitable way to add SWAP gates for quantum circuit 2DNN architecture mapping, they ignored the impact of the initial placement of logical qubits in the mapping process.…”

ISAAQ: Ising Machine Assisted Quantum Compiler

“…To address this challenge, previous studies have proposed approximate solutions that use methods like A* search [19][20][21], Monte Carlo tree search [22,23], simulated annealing [24][25][26], reinforcement learning [27,28], and heuristics [7,14,[29][30][31][32][33][34][35][36][37][38][39][40]. Some of these approximate solutions have been implemented in qiskit [41] and tket [42], and have good scalability with respect to the problem size (i.e., the number of qubits and gates).…”

SpinQ: Compilation strategies for scalable spin-qubit architectures

“…• 1 additional shuttle operation for each Z rotation gate Depth overhead.FIG. 7: Shuttle-based SWAP for two-qubit gate routing: With this technique, two diagonally neighbouring qubits exchange their position by consecutively performing two horizontal and two vertical shuttles.equal to the minimum number of time steps of a circuit when executing gates in parallel[9,10,[45][46][47]. We calculate depth overhead as the percentage relation of additional depth produced by the mapper to the circuit depth after decomposition.…”