Hamiltonian simulation is one of the most promising paths toward quantum advantage. Most prior approaches to Hamiltonian simulation circuit synthesis focus on local rewrite rules and low-level optimizations, and give limited attention to high-level scheduling of Pauli terms under varying constraints. In practice, different simulation algorithms require different orderings of the Pauli terms, yet many prior IR-based methods assume a fixed commutation structure, which limits their flexibility.
We present MonteQ, a novel quantum circuit synthesis framework for Hamiltonian simulation. MonteQ leverages a two-level design that combines low-level synthesis heuristics with an upper-level tree structure to explore sequences of Pauli rotations. To avoid enumerating this factorially large tree, the Monte Carlo Tree Search algorithm serves as workhorse for judiciously exploring promising paths to leaf nodes. With this two-level design, MonteQ supports both logical-level and hardware-aware synthesis by selecting different low-level heuristics. It also supports different ordering constraints on the Pauli rotations by adjusting the high-level tree structure. For example, MonteQ can preserve the target unitary by using a directed acyclic graph that records the commutation relations among the Pauli rotations, or it can relax unitary preservation constraint to uncover additional optimization options. Our experimental results show that MonteQ can achieve an improvement, as measured in CNOT gate counts, of up to 53% (30% on average) against state-of-the-art compilers like Rustiq on a set of representative synthesis tasks.
Hamiltonian simulation is one of the most promising paths toward quantum advantage. Most prior approaches to Hamiltonian simulation circuit synthesis focus on local rewrite rules and low-level optimizations, and give limited attention to high-level scheduling of Pauli terms under varying constraints. In practice, different simulation algorithms require different orderings of the Pauli terms, yet many prior IR-based methods assume a fixed commutation structure, which limits their flexibility.
We present MonteQ, a novel quantum circuit synthesis framework for Hamiltonian simulation. MonteQ leverages a two-level design that combines low-level synthesis heuristics with an upper-level tree structure to explore sequences of Pauli rotations. To avoid enumerating this factorially large tree, the Monte Carlo Tree Search algorithm serves as workhorse for judiciously exploring promising paths to leaf nodes. With this two-level design, MonteQ supports both logical-level and hardware-aware synthesis by selecting different low-level heuristics. It also supports different ordering constraints on the Pauli rotations by adjusting the high-level tree structure. For example, MonteQ can preserve the target unitary by using a directed acyclic graph that records the commutation relations among the Pauli rotations, or it can relax unitary preservation constraint to uncover additional optimization options. Our experimental results show that MonteQ can achieve an improvement, as measured in CNOT gate counts, of up to 53% (30% on average) against state-of-the-art compilers like Rustiq on a set of representative synthesis tasks.
Hamiltonian simulation is one of the most promising paths toward quantum advantage. Most prior approaches to Hamiltonian simulation circuit synthesis focus on local rewrite rules and low-level optimizations, and give limited attention to high-level scheduling of Pauli terms under varying constraints. In practice, different simulation algorithms require different orderings of the Pauli terms, yet many prior IR-based methods assume a fixed commutation structure, which limits their flexibility. We present MonteQ, a novel quantum circuit synthesis framework for Hamiltonian simulation. MonteQ leverages a two-level design that combines low-level synthesis heuristics with an upper-level tree structure to explore sequences of Pauli rotations. To avoid enumerating this factorially large tree, the Monte Carlo Tree Search algorithm serves as workhorse for judiciously exploring promising paths to leaf nodes. With this two-level design, MonteQ supports both logical-level and hardware-aware synthesis by selecting different low-level heuristics. It also supports different ordering constraints on the Pauli rotations by adjusting the high-level tree structure. For example, MonteQ can preserve the target unitary by using a directed acyclic graph that records the commutation relations among the Pauli rotations, or it can relax unitary preservation constraint to uncover additional optimization options. Our experimental results show that MonteQ can achieve an improvement, as measured in CNOT gate counts, of up to 53% (30% on average) against state-of-the-art compilers like Rustiq on a set of representative synthesis tasks.
In the noisy intermediate-scale quantum era, quantum processing units 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 quantum processing unit are satisfied. Although 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 of these algorithms only search very shallowly, and thus, very often, only (at most) locally optimal solutions can be reached. In this article, 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 (respectively, depth) overhead by, on average, 66% (respectively, 84%) when compared with t ∣ket⟩ , an industrial-level compiler.
Quantum simulation is the foundation for the design of many algorithms which share subroutines known as quantum simulation kernels. Optimizing the compilation of these kernels is crucial, involving two key components: 1) circuit synthesis and 2) qubit mapping. However, existing circuit synthesis methods either overlook qubit connectivity constraints (QCCs) or prioritize minimizing gate count over optimizing circuit depth. Similarly, current qubit mapping techniques do not work well with circuit synthesis methods. To address these limitations, we propose PauliForest, which comprises a connectivity-aware circuit synthesis algorithm and a Pauli-oriented qubit mapping algorithm. The synthesis algorithm employs heuristic strategies to generate shallower circuits, while the qubit mapping algorithm seamlessly collaborates with the circuit synthesis process. Compared to the state-of-the-art Paulihedral compiler, our approach significantly reduces both CNOT gate counts (by 13%) and circuit depths (by 25%). Experiments on a noisy simulator and a real superconducting quantum computer show that our algorithm can improve the fidelity of quantum circuit execution compared to Paulihedral.
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.
Quantum circuit synthesis is one of the major areas of current research in the field of quantum computing.Analogous to its Boolean counterpart, the task involves constructing arbitrary quantum gates using only those available within a small set of universal gates that can be realized physically.However, unlike the latter, there are an infinite number of single qubit quantum gates, all of which constitute the special unitary group SU(2).Realizing any given single qubit gate using a given universal gate family is a complex task.Although gates can be synthesized to arbitrary degree of precision as long as the set of finite strings of the gate family is a dense subset of SU(2), it is desirable to accomplish the highest level of precision using only the minimum number of universal gates within the string approximation.Almost all algorithms that have been proposed for this purpose are based on the Solovay-Kitaev algorithm.The crux of the Solovay-Kitaev algorithm is the use of a procedure to decompose a given quantum gate into a pair of group commutators with the pair being synthesized separately.The Solovay-Kitaev algorithm involves group commutator decomposition in a recursive manner, with a direct approximation of a gate into a string of universal gates being performed only at the last level, i.e. in the leaf nodes of the search tree representing the execution of the Solovay-Kitaev algorithm.The main contribution of this research is in integrating conventional optimization procedures within the Solovay-Kitaev algorithm.Two specific directions of research have been studied.Firstly, optimization is incorporated within the group commutator decomposition, so that a more optimal pair of group commutators are obtained.As the degree of precision of the synthesized gate is explicitly minimized by means of this optimization procedure, the enhanced algorithm allows for more accurate quantum gates to be synthesized than what the original Solovay-Kitaev algorithm achieves.Simulation results with random gates indicate that the obtained accuracy is an order of magnitude better than before.Two versions of the new algorithm are examined, with the optimization in the first version being invoked only at the bottom level of Solovay-Kitaev algorithm and when carried out across all levels of the search tree in the next.Extensive simulations show that the second version yields better results despite equivalent computation times.Theoretical analysis of the proposed algorithm is able to provide a more formal, quantitative explanation underlying the experimentally observed phenomena.The other direction of investigation of this research involves formulating the group commutator decomposition in the form of bi-criteria optimization.This phase of research relaxed the equality constraint in the previous approach and with relaxation, a bi-criteria optimization is proposed.This optimization algorithm is new and has been devised primarily when the objective needs to be relaxed in different stages.This bi-criteria approach is able to provide comparably accurate synthesis as the previous approach.
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.