arXiv subjects

Mathias Weiden

Publications and source records attributed to Mathias Weiden.

12 recordsLinked to original sources

arXiv2026

Multi-Qubit Dyadic Phase Fixing for Fault-Tolerant Quantum Compilation

Fault-tolerant quantum computing requires translating application-level quantum circuits into the Clifford+$T$ gate set, where the $T$ gate is the dominant resource cost. Phase kickback is an ancilla-based technique that can dramatically reduce $T$-count for rotations with dyadic angles, but has previously been limited to highly structured circuit families. We present Dyadic Phase Fixing (DPF), a general multi-qubit synthesis tool that extends phase kickback to general quantum circuits. DPF uses numerical unitary synthesis to greedily extract dyadic angle rotations from any input circuit. Combined with a decision matrix to automatically size the final phase gradient register, our end-to-end workflow achieves up to 70% reduction in $T$-count compared to \texttt{gridsynth} and up to 60% compared to Repeat-Until-Success synthesis on a diverse set of benchmarks. We map these compiled circuits to a surface-code architecture to evaluate space-time volume, demonstrating up to a 60\% reduction in this metric as well. However, for some circuits and mapping strategies the two metrics diverge significantly, demonstrating that $T$-count alone is a useful but incomplete proxy for fault-tolerant program costs.

quant-ph↗

arXiv2026

T Count as a Numerically Solvable Minimization Problem

We present a formulation of the problem of finding the smallest T -Count circuit that implements a given unitary as a binary search over a sequence of continuous minimization problems, and demonstrate that these problems are numerically solvable in practice. We reproduce best-known results for synthesis of circuits with a small number of qubits, and push the bounds of the largest circuits that can be solved for in this way. Additionally, we show that circuit partitioning can be used to adapt this technique to be used to optimize the T -Count of circuits with large numbers of qubits by breaking the circuit into a series of smaller sub-circuits that can be optimized independently.

quant-ph↗

arXiv2026

TopoLS: Lattice Surgery Compilation via Topological Program Transformations

Lattice surgery is a leading approach for implementing fault-tolerant logical operations in surface code quantum computing, but compiling efficient lattice surgery layouts remains challenging. Existing compilers are largely circuit-centric and operate directly on gate sequences, limiting their ability to exploit the topological flexibility of merge-split operations and minimize space--time volume. We present TopoLS, a topology-centric compiler that uses ZX diagrams as an intermediate representation for lattice surgery compilation. TopoLS combines semantic-preserving ZX-level program transformations, including spider fusion and topology-aware slicing, with a Monte Carlo Tree Search (MCTS)-based synthesis procedure that constructs pipe-diagram embeddings by jointly optimizing placement and routing in 3D space--time. To scale to large circuits, TopoLS further introduces topology-aware partitioning that decomposes the compilation task into bounded subproblems and limits the routing frontier during embedding. Across evaluated benchmarks, TopoLS achieves an average $46\%$ reduction in space--time volume over prior circuit-centric compilers, with improvements ranging from $25\%$ to $90\%$, and exhibits strong empirical scalability on large benchmark families. Compared with SAT-based formulations that become intractable on larger instances, TopoLS offers a practical end-to-end solution for optimized lattice surgery compilation. TopoLS has been integrated into the TQEC ecosystem, enabling downstream circuit-level simulation and resource estimation workflows.

quant-ph↗

arXiv2026

AlphaSyndrome: Tackling the Syndrome Measurement Circuit Scheduling Problem for QEC Codes

Quantum error correction (QEC) is essential for scalable quantum computing, yet repeated syndrome-measurement cycles dominate its spacetime and hardware cost. Although stabilizers commute and admit many valid execution orders, different schedules induce distinct error-propagation paths under realistic noise, leading to large variations in logical error rate. Outside of surface codes, effective syndrome-measurement scheduling remains largely unexplored. We present AlphaSyndrome, an automated synthesis framework for scheduling syndrome-measurement circuits in general commuting-stabilizer codes under minimal assumptions: mutually commuting stabilizers and a heuristic decoder. AlphaSyndrome formulates scheduling as an optimization problem that shapes error propagation to (i) avoid patterns close to logical operators and (ii) remain within the decoder's correctable region. The framework uses Monte Carlo Tree Search (MCTS) to explore ordering and parallelism, guided by code structure and decoder feedback. Across diverse code families, sizes, and decoders, AlphaSyndrome reduces logical error rates by 80.6% on average (up to 96.2%) relative to depth-optimal baselines, matches Google's hand-crafted surface-code schedules, and outperforms IBM's schedule for the Bivariate Bicycle code.

cs.ET↗

arXiv2025

PureMagic: A Dynamic Scheduler for Lattice Surgery

Fault-tolerant quantum computation on surface codes requires magic states for universal computation. Traditional distillation factories deliver magic states deterministically but consume large areas of logical qubits, forcing static, peripheral placement. Magic state cultivation reduces magic state preparation to a single logical qubit, but is inherently stochastic, making static scheduling infeasible. We introduce PureMagic, a dynamic scheduler that eliminates dedicated bus patches by repurposing all ancilla patches for both routing and cultivation. When a patch is needed for routing, cultivation is interrupted and restarted afterward, naturally cutting off the long tail of cultivation times and ensuring no ancilla is ever idle. We also introduce a weight limit on Tableau transpilation that trades gate count for parallelism, which PureMagic is particularly well-suited to exploit. Across 29 benchmark circuits, PureMagic achieves 43% to 152% efficiency improvement over bus routing, uses 19% to 80% fewer logical qubits, and reduces average magic state preparation time by 4.5x. Compared to DASCOT, a state-of-the-art static scheduler, PureMagic is up to 21x more efficient when magic state preparation costs are included. PureMagic's scheduled volumes fall between the conservative and optimistic FLASQ theoretical lower bounds, demonstrating near-optimal use of ancilla resources.

quant-ph↗

arXiv2025

Application Scale Quantum Circuit Compilation with Controlled Error

Compilation and optimization of quantum circuits are critical components in the execution of algorithms on quantum computers. These components must successfully balance two competing priorities: minimizing the number of expensive resources, such as two-qubit gates or arbitrary angle single-qubit rotations, and minimizing the approximation error of the compiled circuit to the ideal target unitary describing the quantum algorithm. We develop a practical workflow for managing and optimizing this tradeoff, which enables quantum circuit compilation and optimization at scales of hundreds of qubits. Our workflow is able to tackle circuits at such large scales while providing rigorous guarantees on circuit output error by leveraging circuit partitioning and the notion of averaging over circuit ensembles. We demonstrate our workflow on several benchmark algorithmic circuits acting on up to 380 qubits, and show that it can simultaneously achieve substantial reductions in resource-intensive gates and control output errors, offering a practical and scalable strategy for both near-term and fault-tolerant quantum computing.

quant-ph↗

arXiv2025

Making Neural Networks More Suitable for Approximate Clifford+T Circuit Synthesis

Machine Learning with deep neural networks has transformed computational approaches to scientific and engineering problems. Central to many of these advancements are precisely tuned neural architectures that are tailored to the domains in which they are used. In this work, we develop deep learning techniques and architectural modifications that improve performance on reinforcement learning guided quantum circuit synthesis-the task of constructing a circuit that implements a given unitary matrix. First, we propose a global phase invariance operation which makes our architecture resilient to complex global phase shifts. Second, we demonstrate how augmenting data with small random unitary perturbations during training enables more robust learning. Finally, we show how encoding numerical data with techniques from image processing allow networks to better detect small but significant changes in data. Our work enables deep learning approaches to better synthesize quantum circuits that implement unitary matrices.

quant-ph↗

arXiv2024

High-Precision Multi-Qubit Clifford+T Synthesis by Unitary Diagonalization

Resource-efficient and high-precision approximate synthesis of quantum circuits expressed in the Clifford+T gate set is vital for Fault-Tolerant quantum computing. Efficient optimal methods are known for single-qubit RZ unitaries, otherwise the problem is generally intractable. Search-based methods, like simulated annealing, empirically generate low resource cost approximate implementations of general multi-qubit unitaries so long as low precision (Hilbert-Schmidt distances of e>10^-2) can be tolerated. These algorithms build up circuits that directly invert target unitaries. We instead leverage search-based methods to first approximately diagonalize a unitary, then perform the inversion analytically. This lets difficult continuous rotations be bypassed and handled in a post-processing step. Our approach improves both the implementation precision and run time of synthesis algorithms by orders of magnitude when evaluated on unitaries from real quantum algorithms. On benchmarks previously synthesizable only with analytical techniques like the Quantum Shannon Decomposition, diagonalization uses an average of 95% fewer non-Clifford gates.

quant-ph↗

arXiv2024

Quantum Hardware Roofline: Evaluating the Impact of Gate Expressivity on Quantum Processor Design

The design space of current quantum computers is expansive with no obvious winning solution. This leaves practitioners with a clear question: "What is the optimal system configuration to run an algorithm?". This paper explores hardware design trade-offs across NISQ systems to guide algorithm and hardware design choices. The evaluation is driven by algorithmic workloads and algorithm fidelity models which capture architectural features such as gate expressivity, fidelity, and crosstalk. We also argue that the criteria for gate design and selection should be extended from maximizing average fidelity to a more comprehensive approach that takes into account the gate expressivity with respect to algorithmic structures. We consider native entangling gates (CNOT, ECR, CZ, ZZ, XX, Sycamore, $\sqrt{\text{iSWAP}}$), proposed gates (B Gate, $\sqrt[4]{\text{CNOT}}$, $\sqrt[8]{\text{CNOT}}$), as well as parameterized gates (FSim, XY). Our methodology is driven by a custom synthesis driven circuit compilation workflow, which is able to produce minimal circuit representations for a given system configuration. By providing a method to evaluate the suitability of algorithms for hardware platforms, this work emphasizes the importance of hardware-software co-design for quantum computing.

quant-ph↗

arXiv2023

Improving Quantum Circuit Synthesis with Machine Learning

In the Noisy Intermediate Scale Quantum (NISQ) era, finding implementations of quantum algorithms that minimize the number of expensive and error prone multi-qubit gates is vital to ensure computations produce meaningful outputs. Unitary synthesis, the process of finding a quantum circuit that implements some target unitary matrix, is able to solve this problem optimally in many cases. However, current bottom-up unitary synthesis algorithms are limited by their exponentially growing run times. We show how applying machine learning to unitary datasets permits drastic speedups for synthesis algorithms. This paper presents QSeed, a seeded synthesis algorithm that employs a learned model to quickly propose resource efficient circuit implementations of unitaries. QSeed maintains low gate counts and offers a speedup of $3.7\times$ in synthesis time over the state of the art for a 64 qubit modular exponentiation circuit, a core component in Shor's factoring algorithm. QSeed's performance improvements also generalize to families of circuits not seen during the training process.

quant-ph↗

arXiv2023

Tackling the Qubit Mapping Problem with Permutation-Aware Synthesis

We propose a novel hierarchical qubit mapping and routing algorithm. First, a circuit is decomposed into blocks that span an identical number of qubits. In the second stage permutation-aware synthesis (PAS), each block is optimized and synthesized in isolation. In the third stage a permutation-aware mapping (PAM) algorithm maps the blocks to the target device based on the information from the second stage. Our approach is based on the following insights: (1) partitioning the circuit into blocks is beneficial for qubit mapping and routing; (2) with PAS, any block can implement an arbitrary input-output qubit mapping that reduces the gate count; and (3) with PAM, for two adjacent blocks we can select input-output permutations that optimize each block together with the amount of communication required at the block boundary. Whereas existing mapping algorithms preserve the original circuit structure and only introduce "minimal" communication via inserting SWAP or bridge gates, the PAS+PAM approach can additionally change the circuit structure and take full advantage of hardware-connectivity. Our experiments show that we can produce better-quality circuits than existing mapping algorithms or commercial compilers (Qiskit, TKET, BQSKit) with maximum optimization settings. For a combination of benchmarks we produce circuits shorter by up to 68% (18% on average) fewer gates than Qiskit, up to 36% (9% on average) fewer gates than TKET, and up to 67% (21% on average) fewer gates than BQSKit. Furthermore, the approach scales, and it can be seamlessly integrated into any quantum circuit compiler or optimization infrastructure.

quant-ph↗

arXiv2022

Wide Quantum Circuit Optimization with Topology Aware Synthesis

Unitary synthesis is an optimization technique that can achieve optimal multi-qubit gate counts while mapping quantum circuits to restrictive qubit topologies. Because synthesis algorithms are limited in scalability by their exponentially growing run time and memory requirements, application to circuits wider than 5 qubits requires divide-and-conquer partitioning of circuits into smaller components. In this work, we will explore methods to reduce the depth (program run time) and multi-qubit gate instruction count of wide (16-100 qubit) mapped quantum circuits optimized with synthesis. Reducing circuit depth and gate count directly impacts program performance and the likelihood of successful execution for quantum circuits on parallel quantum machines. We present TopAS, a topology aware synthesis tool built with the \emph{BQSKit} framework that preconditions quantum circuits before mapping. Partitioned subcircuits are optimized and fitted to sparse qubit subtopologies in a way that balances the often opposing demands of synthesis and mapping algorithms. This technique can be used to reduce the depth and gate count of wide quantum circuits mapped to the sparse qubit topologies of Google and IBM. Compared to large scale synthesis algorithms which focus on optimizing quantum circuits after mapping, TopAS is able to reduce depth by an average of 35.2% and CNOT gate count an average of 11.5% when targeting a 2D mesh topology. When compared with traditional quantum compilers using peephole optimization and mapping algorithms from the Qiskit or $t|ket\rangle$ toolkits, our approach is able to provide significant improvements in performance, reducing CNOT counts by 30.3% and depth by 38.2% on average.

quant-ph↗