Abstract Equivariant quantum neural networks are designed to preserve symmetries in quantum machine-learning data, but this property is usually verified only before hardware compilation. We show that a transpiler can preserve the expected unitary symmetry relation while compiling symmetry-related inputs into circuits with different two-qubit gate counts and physical-qubit layouts, so ideal-circuit equivariance does not guarantee symmetry at the level of compiled circuit structure. We formalise this gap with a three-level compliance hierarchy and a taxonomy separating topology-input ansätze, where the symmetry changes the gate topology the compiler sees, from parameter-input ansätze, where it changes only numerical gate parameters and provably leaves controlled- Z counts unchanged under topology-based transpilation. Auditing four published ansatz families, we observe the effect only in the topology-input case. For the Skolik permutation-equivariant weighted-graph ansatz compiled to the IBM Heron Fez simulator target at twelve qubits, sparse graph inputs produce a mean relative controlled- Z asymmetry of 7.3% across fifty random vertex permutations, with a worst case of 22.5%. The effect persists across all four Qiskit optimisation levels and is not removed by matched-layout compilation, implicating routing-stage sensitivity to the ordered sparse-edge gate sequence. A density sweep shows that the asymmetry is comparable across intermediate graph densities and vanishes for complete graphs, where the ansatz degenerates into the parameter-input class, and stochastic baselines attribute the realised differences to heuristic routing sensitivity rather than to differing optimal compiled costs. Finally, we propose compile-once-and-relabel, a deployment pattern that removes controlled- Z count asymmetry by construction and reduces compilation cost for orbit-based workflows.
Abstract Equivariant quantum neural networks are designed to preserve symmetries in quantum machine-learning data, but this property is usually verified only before hardware compilation. We show that a transpiler can preserve the expected unitary symmetry relation while compiling symmetry-related inputs into circuits with different two-qubit gate counts and physical-qubit layouts, so ideal-circuit equivariance does not guarantee symmetry at the level of compiled circuit structure. We formalise this gap with a three-level compliance hierarchy and a taxonomy separating topology-input ansätze, where the symmetry changes the gate topology the compiler sees, from parameter-input ansätze, where it changes only numerical gate parameters and provably leaves controlled- Z counts unchanged under topology-based transpilation. Auditing four published ansatz families, we observe the effect only in the topology-input case. For the Skolik permutation-equivariant weighted-graph ansatz compiled to the IBM Heron Fez simulator target at twelve qubits, sparse graph inputs produce a mean relative controlled- Z asymmetry of 7.3% across fifty random vertex permutations, with a worst case of 22.5%. The effect persists across all four Qiskit optimisation levels and is not removed by matched-layout compilation, implicating routing-stage sensitivity to the ordered sparse-edge gate sequence. A density sweep shows that the asymmetry is comparable across intermediate graph densities and vanishes for complete graphs, where the ansatz degenerates into the parameter-input class, and stochastic baselines attribute the realised differences to heuristic routing sensitivity rather than to differing optimal compiled costs. Finally, we propose compile-once-and-relabel, a deployment pattern that removes controlled- Z count asymmetry by construction and reduces compilation cost for orbit-based workflows.
Abstract Variational quantum algorithms are the leading candidate for advantage on near-term quantum hardware. When training a parametrized quantum circuit in this setting to solve a specific problem, the choice of ansatz is one of the most important factors that determines the trainability and performance of the algorithm. In quantum machine learning (QML), however, the literature on ansatzes that are motivated by the training data structure is scarce. In this work, we introduce an ansatz for learning tasks on weighted graphs that respects an important graph symmetry, namely equivariance under node permutations. We evaluate the performance of this ansatz on a complex learning task, namely neural combinatorial optimization, where a machine learning model is used to learn a heuristic for a combinatorial optimization problem. We analytically and numerically study the performance of our model, and our results strengthen the notion that symmetry-preserving ansatzes are a key to success in QML.
Deploying quantum neural networks (QNNs) on sparse hardware requires preserving task accuracy while reducing compiler-induced two-qubit gates, SWAPs, and depth. We present ConQUESTA (\underline{C}onstrained \underline{Qu}antum \underline{E}ntangler \underline{S}election with \underline{T}opology \underline{A}wareness), a post training pruning framework that combines task saliency with compiler cost, screens candidate entanglers, and searches complete pruning masks under an explicit accuracy constraint. Unlike one-shot ranking, each mask is transpiled as a whole across multiple coupling topologies. Across 4-, 6-, and 8-qubit QNNs and eight model seeds at 55% pruning, ConQUESTA achieves mean resource reductions of 61.6% on Breast Cancer, 72.0% on Digits01, and 82.2% on Iris, exceeding the strongest matched simple baseline by 3.5, 1.7, and 8.9 percentage points, respectively. Fixed-mask recovery raises feasibility from 16/24 to 22/24 runs. In a fixed-k=4 scaling study on a scaling probe of 4 to 12-qubits, the raw mask space grew from 495 to 12.1M while the evaluated masks increase only from 189 to 305. Resource-weight changes alter depth/routing priorities with at most a 0.44-point mean validation shift.
Variational quantum circuits (VQCs) are typically evaluated at the logical design level when analyzing trainability. However, execution on real quantum devices requires hardware-aware compilation (transpilation) to satisfy qubit connectivity and native gate-set constraints. In this paper, we examine how transpilation can alter the gradient statistics. Using parameter-shift differentiation and gradient variance estimation, we compare logical and transpiled circuits across three representative ansatz families: EfficientSU2 (dense entanglement), TTN (tree tensor network), and RealAmplitudes (linear entanglement). We observe architecture-dependent trainability shifts where densely entangling circuits exhibit pronounced gradient reshaping in shallow regimes, structured tensor-network circuits remain comparatively robust, and linear architectures show mixed behavior. Deep circuits across all families display minimal sensitivity to hardware-aware compilation. These findings demonstrate that transpilation acts as an implicit structural transformation of the optimization landscape, motivating compilation-aware analysis and co-design for VQCs.
Parameterised quantum circuits are commonly assessed using measures such as expressibility, gradient behaviour, and entanglement. While useful, these measures do not indicate whether a circuit respects the symmetry it was designed to respect. This is especially important in equivariant quantum machine learning, where symmetry is central to the model. We introduce PsiAudit, an open-source Python toolkit for auditing symmetry-aware quantum neural network ansätze before training. Given an ansatz, a target symmetry, and a state trajectory, PsiAudit reports how the circuit occupies symmetry sectors, maintains coherence between them, fluctuates across the trajectory, and complies with the target symmetry. These outputs are combined into a configurable dashboard-style summary. PsiAudit supports phase, spin, and permutation symmetries, with the permutation audit implemented using Hamming-weight orbits. Tests on five ansatz families, across twenty random seeds and four to eight qubits, show, in the tested setting, that PsiAudit can identify inactive equivariant circuits, recover structure when multiple symmetry sectors are activated, and distinguish ansätze that appear similar under standard diagnostics. The toolkit also includes a unitary-level compliance check, reproducible examples, and a notebook for regenerating the reported results.
Mapping quantum programs to restricted physical chips requires SWAP operations, incurring depth and error penalties. In symmetric programs, this routing overhead breaks theoretical symmetry because identical logical roles experience unequal shuffling. While often attributed to hardware topology alone, we show this is a two-level phenomenon. A qubit patch's shape dictates if it can host a balanced assignment. When balance is possible, the actual imbalance is set by the logical-to-physical assignment, meaning a balanced assignment can distribute routing costs perfectly evenly at no extra depth. Through exhaustive search on a 57-qubit "heavy-hex" lattice, we prove these topological constraints. For a four-part ring, 108 of 124 connected patches admit a cost-free balanced assignment, with the 16 exceptions being star-shaped. For a six-part ring, cost-free balance is impossible on compact patches. For a fully connected four-part symmetry, balance is structurally impossible at any depth. Simulations using realistic error rates show that, relative to the worst-case concentrated assignment, balanced assignments reduce symmetry-breaking by 92.7% (95% CI [+89.8%, +95.3%]) for the raw metric and 87.0% (95% CI [+79.6%, +94.1%]) for the decoherence-corrected measure (p = 2.45 x 10^-32). Substrate error heterogeneity accounts for at most 10.8% of this effect. Notably, switching to the compiler's highest generic optimization level did not yield a statistically significant change in routing imbalance, highlighting the need for targeted symmetry-aware passes. When patch geometry permits, routing imbalance is a compiler choice rather than a hardware limitation. Thus, symmetry-aware assignment should be a primary objective for compiler optimization and chip design.
Quantum computing is a quickly growing field with great potential for future technology. Quantum computers in the current noisy intermediate-scale quantum (NISQ) era face two major limitations - qubit count and error vulnerability. Although quantum error correction (QEC) methods exist, they are not applicable to the current size of computers, requiring thousands of qubits, while current NISQ systems have hundreds at most. It is therefore imperative to improve the reliability of the circuits as much as possible to make them robust to the errors that will occur. One common approach is to adjust the compilation process of a circuit to create a final circuit with improved reliability. However, there are many decisions to be made when compiling that affect the final performance of the circuit, two of the most critical ones being the mapping of logical to physical qubits (the qubit allocation problem) and the movement of qubits to satisfy two-qubit gate adjacency requirements (the qubit routing problem). We focus on solving the qubit allocation problem and identifying initial layouts that reduce error. To identify these layouts, we combine reinforcement learning with a graph neural network (GNN)-based Q-network for analyzing both the connections and error rates of the graph-like backend of superconducting quantum computers to make mapping decisions, creating a Graph Neural Network Assisted Compilation (GNAQC) strategy. We provide both the circuit and the properties of the target backend as input to guide the decision-making process. We work with the IBM Qiskit API to compile and simulate our quantum circuits. We train the architecture using a set of four backends and six circuits and find that GNAQC generally outperforms pre-existing qubit allocation algorithms, increasing final relative output fidelity by roughly 12.7%.