We propose a general method for preparing stabilizer states with reduced two-qubit gate count and depth compared to the state of the art. The method starts from a graph state representation of the stabilizer state and iteratively reduces the number of edges in the graph using two-qubit Clifford gates to produce a unitary preparation circuit. We explore various heuristic search and AI-based approaches to optimally choose Clifford gates at each step, the most sophisticated of which is a combination of reinforcement learning and Monte Carlo tree search that we call QuSynth. We apply our method to synthesize code states of various quantum error correcting codes including the 23-qubit Golay code and the 144-qubit gross code, the latter of which is significantly beyond the qubit number that is accessible to prior optimal circuit synthesis methods. We demonstrate that our techniques are capable of reducing the required two-qubit gates by up to a factor of 2.5 compared to previous approaches while retaining low circuit depth.
We propose a general method for preparing stabilizer states with reduced two-qubit gate count and depth compared to the state of the art. The method starts from a graph state representation of the stabilizer state and iteratively reduces the number of edges in the graph using two-qubit Clifford gates to produce a unitary preparation circuit. We explore various heuristic search and AI-based approaches to optimally choose Clifford gates at each step, the most sophisticated of which is a combination of reinforcement learning and Monte Carlo tree search that we call QuSynth. We apply our method to synthesize code states of various quantum error correcting codes including the 23-qubit Golay code and the 144-qubit gross code, the latter of which is significantly beyond the qubit number that is accessible to prior optimal circuit synthesis methods. We demonstrate that our techniques are capable of reducing the required two-qubit gates by up to a factor of 2.5 compared to previous approaches while retaining low circuit depth.
This paper presents a deep reinforcement learning approach for synthesizing unitaries into quantum circuits. Unitary synthesis aims to identify a quantum circuit that represents a given unitary while minimizing circuit depth, total gate count, a specific gate count, or a combination of these factors. While past research has focused predominantly on continuous gate sets, synthesizing unitaries from the parameter-free Clifford+T gate set remains a challenge. Although the time complexity of this task will inevitably remain exponential in the number of qubits for general unitaries, reducing the runtime for simple problem instances still poses a significant challenge. In this study, we apply the tree-search method Gumbel AlphaZero to solve the problem for a subset of exactly synthesizable Clifford+T unitaries. Our method effectively synthesizes circuits for up to five qubits generated from randomized circuits with up to 60 gates, outperforming existing tools like QuantumCircuitOpt and MIN-T-SYNTH in terms of synthesis time for larger qubit counts. Furthermore, it surpasses Synthetiq in successfully synthesizing random, exactly synthesizable unitaries. These results establish a strong baseline for future unitary synthesis algorithms.
Preparing arbitrary logical states is a central primitive for universal fault-tolerant quantum computation and the cost of encoded-state preparation contributes directly to the overall resource overhead. This makes the synthesis of efficient general-state encoding circuits an important problem, particularly with respect to two-qubit gate count and circuit depth. Yet the synthesis of such encoders has been studied less extensively than general Clifford circuit synthesis or the preparation of specific logical Pauli-eigenstates. In this work, we develop methods for synthesizing efficient encoders for arbitrary stabilizer codes. We formulate encoder synthesis as a search over stabilizer tableaus and introduce greedy and rollout-based algorithms that exploit the freedom among stabilizer-equivalent realizations of the same encoding isometry. For code families with a modular structure, such as generalized concatenated and holographic codes, we show how large encoders can be assembled from optimized local constituent encoders, and we use SMT-based exact synthesis to obtain optimal local circuits for small instances. We further evaluate the proposed methods on a broad set of stabilizer codes, including holographic and quantum low-density parity-check (qLDPC) codes, and compare them against recent encoder-synthesis methods and existing constructions from the literature, obtaining improvements of up to 43% in two-qubit gate count and up to 70% in depth. Our results support the optimization of encoded-state preparation in several fault-tolerant quantum-computing schemes, and all methods are openly available as part of the Munich Quantum Toolkit.
Efficiently implementing Clifford circuits is crucial for quantum error correction and quantum algorithms. Linear reversible circuits, equivalent to circuits composed of CNOT\xspace gates, have important applications in classical computing. In this work we present methods for CNOT\xspace and general Clifford circuit synthesis which can be used to minimise either the entangling two-qubit gate count or the circuit depth. We present three families of algorithms - optimal synthesis which works on small circuits, A* synthesis for intermediate-size circuits and greedy synthesis for large circuits. We benchmark against existing methods, including rustiq, tket and qiskit and show that our approach results in circuits with lower two-qubit gate count. For encoding circuits, our methods outperform previous reinforcement learning results and find a lower two-qubit gate count circuit for the Golay code than previously known. The algorithms have been implemented in a GitHub repository for use by the classical and quantum computing community.
Quantum unitary synthesis addresses the problem of translating abstract quantum algorithms into sequences of hardware-executable quantum gates. Solving this task exactly is infeasible in general due to the exponential growth of the underlying combinatorial search space. Existing approaches suffer from misaligned optimization objectives, substantial training costs and limited generalization across different qubit counts. We mitigate these limitations by using supervised learning to approximate the minimum description length of residual unitaries and combining this estimate with stochastic beam search to identify near optimal gate sequences. Our method relies on a lightweight model with zero-shot generalization, substantially reducing training overhead compared to prior baselines. Across multiple benchmarks, we achieve faster wall-clock synthesis times while exceeding state-of-the-art methods in terms of success rate for complex circuits.
Quantum Circuit Pre-Synthesis: Learning Local Edits to Reduce T-count
Compiling quantum circuits into Clifford+T gates is a central task for fault-tolerant quantum computing using stabilizer codes. In the near term, T gates will dominate the cost of fault tolerant implementations, and any reduction in the number of such expensive gates could mean the difference between being able to run a circuit or not. While exact synthesis is exponentially hard in the number of qubits, local synthesis approaches are commonly used to compile large circuits by decomposing them into substructures. However, composing local methods leads to suboptimal compilations in key metrics such as T-count or circuit depth, and their performance strongly depends on circuit representation. In this work, we address this challenge by proposing \textsc{Q-PreSyn}, a strategy that, given a set of local edits preserving circuit equivalence, uses a RL agent to identify effective sequences of such actions and thereby obtain circuit representations that yield a reduced T-count upon synthesis. Experimental results of our proposed strategy, applied on top of well-known synthesis algorithms, show up to a 20% reduction in T-count on circuits with up to 25 qubits, without introducing any additional approximation error prior to synthesis.
With recent advancements in quantum computing technology, optimizing quantum circuits and ensuring reliable quantum state preparation have become increasingly vital. Traditional methods often demand extensive expertise and manual calculations, posing challenges as quantum circuits grow in qubit- and gate-count. Therefore, harnessing machine learning techniques to handle the growing variety of gate-to-qubit combinations is a promising approach. In this work, we introduce a comprehensive reinforcement learning environment for quantum circuit synthesis, where circuits are constructed utilizing gates from the the Clifford+T gate set to prepare specific target states. Our experiments focus on exploring the relationship between the depth of synthesized quantum circuits and the circuit depths used for target initialization, as well as qubit count. We organize the environment configurations into multiple evaluation levels and include a range of well-known quantum states for benchmarking purposes. We also lay baselines for evaluating the environment using Proximal Policy Optimization. By applying the trained agents to benchmark tests, we demonstrated their ability to reliably design minimal quantum circuits for a selection of 2-qubit Bell states.