arXiv subjects

Chae-Yeun Park

Publications and source records attributed to Chae-Yeun Park.

At least 19 recordsLinked to original sources

arXiv2026

Coherent-disorder-driven complexity transitions in a quantum-advantage architecture

While decoherence is known to erode classical hardness in quantum random sampling, the impact of coherent spatial disorder remains an open question. We study a square-lattice instantaneous quantum polynomial-time (IQP) architecture subject to two-qubit gate-angle disorder and single-qubit dephasing using exact tensor-network simulations up to 576 qubits. For finite systems without dephasing, increasing disorder drives two consecutive crossovers toward classical simulability: the output distribution first loses anticoncentration, and then the tensor-network simulation cost drops from exponential to polynomial as entanglement is suppressed. The finite-size scaling collapses are consistent with continuous transitions in the large-system limit. Dephasing further reduces the complexity. We characterize the computationally hard regime through scaling laws that provide quantitative error-budget bounds for realistic near-term devices.

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arXiv2026

Strictly Local Tile-Code Architectures on Two-Dimensional Planar Lattices

Tile codes are a family of planar quantum low-density parity-check (qLDPC) codes with weight-6 stabilizers and open boundary conditions, offering an encoding efficiency $kd^2/n$ of up to four times that of the surface code. In this work, we develop an exhaustive search algorithm for finding SWAP-based routing schemes that implement syndrome extraction for four tile-code families using only nearest-neighbor interactions on a two-dimensional square lattice, matching the connectivity of the surface code. Using explicitly constructed routed syndrome-extraction circuits decoded with BP+OSD, we estimate the circuit-level thresholds of these code families. For the SI1000 noise model, the threshold without such a connectivity constraint is obtained in a range 0.23%-0.31%, while it decreases to 0.11%-0.13% with routing, representing a reduction factor of around two to three. Despite this threshold penalty, our resource-footprint analysis shows that routed tile codes require fewer physical qubits per logical qubit than the surface code at sufficiently low physical error rates: Under the SI1000 noise model, we find a crossover near $p^*\approx 0.08\%$, below which routed tile codes become more qubit-efficient, with an advantage that grows monotonically as the physical error rate decreases.

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arXiv2026

HyQuRP: Hybrid quantum-classical neural network with rotational and permutational equivariance

Group-equivariant quantum machine learning has emerged as a promising paradigm by incorporating symmetry into quantum models. However, constructing models simultaneously equivariant to both rotational and permutational symmetries in a principled manner remains a bottleneck. In this work, we develop a general framework for dual-equivariant gates under rotations and permutations and analyze the dimension of the resulting gate space using group representation theory. Based on this, we introduce HyQuRP, a hybrid quantum-classical neural network with dual equivariance. On 3D point cloud classification benchmarks in the sparse-point regime, HyQuRP outperforms strong classical and quantum baselines. For example, when six subsampled points are used, HyQuRP ($\sim$1.5K parameters) achieves 76.13% accuracy on the 5-class ModelNet benchmark, compared with 72.54%, 71.09%, and 71.03% for Tensor Field Network, PointNet, and PointMamba with similar parameter counts. These results highlight HyQuRP's strong data efficiency and suggest the potential of equivariant quantum machine learning approaches in symmetry-sensitive tasks.

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arXiv2026

Toward the Goldilocks blind compression of quantum states

Quantum autoencoders (QAEs) are learning architectures that compress quantum data into a low-dimensional latent state while preserving the information needed for reconstruction. We study blind single-copy compression of quantum states through a $k$-qubit bottleneck and investigate the minimal circuit width required to attain the information-theoretic optimum under average infidelity. Between the conventional architecture, which is narrow but nonuniversal, and fully general \emph{completely positive and trace preserving} (CPTP) realizations, which are universal but overparameterized, we identify a \emph{Goldilocks} regime. We prove that for every distribution of pure $n$-qubit states, there exists a QAE with exactly $k$ encoder ancillas and $n$ decoder ancillas that achieves the optimal fidelity over all CPTP encoder--decoder pairs. The encoder-side statement is sharp in that we construct source families for which every optimal scheme necessarily uses at least $k$ encoder ancillas, thereby determining the universal encoder threshold exactly. On the decoder side, we show that isometric decoders are exactly optimal for several analytically tractable source families, but we also exhibit an explicit counterexample demonstrating that decoder isometry is not universally sufficient. Nevertheless, numerical experiments indicate that the performance gap is practically negligible.

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arXiv2026

All you need is spin: SU(2) equivariant variational quantum circuits based on spin networks

Variational algorithms require architectures that naturally constrain the optimization space to run efficiently. Geometric quantum machine learning achieves this goal by encoding group structure into parameterized quantum circuits to include the symmetries of a problem as an inductive bias. However, constructing such circuits is challenging as a concrete guiding principle has yet to emerge. In this paper, we propose the use of spin networks, a form of directed tensor network invariant under a group transformation, to devise SU(2) equivariant quantum circuit ansätze $\unicode{x2013}$ circuits possessing spin-rotation symmetry. By changing to the basis that block diagonalizes the SU(2) group action, these networks provide a natural building block for constructing parameterized equivariant quantum circuits. We prove that our construction is mathematically equivalent to other known constructions, such as those based on twirling and generalized permutations, but more direct to implement on quantum hardware. The efficacy of our constructed circuits is tested by solving the ground state problem of SU(2) symmetric Heisenberg models on the one-dimensional triangular lattice and the Kagome lattice. Our results highlight that our equivariant circuits boost the performance of quantum variational algorithms, indicating broader applicability to other real-world problems.

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arXiv2025

Quadratically Shallow Quantum Circuits for Hamiltonian Functions

Many quantum algorithms for ground-state preparation and energy estimation require the implementation of high-degree polynomials of a Hamiltonian to achieve better convergence rates. Their circuit implementation typically relies on quantum signal processing (QSP), whose circuit depth is proportional to the degree of the polynomial. Previous studies exploit the Chebyshev polynomial approximation, which requires a Chebyshev series of degree $O(\sqrt{n\ln(1/δ)})$ for an $n$-degree polynomial, where $δ$ is the approximation error. However, the approximation is limited to only a few functions, including monomials, truncated exponential, Gaussian, and error functions. In this work, we present the most generalized function approximation methods for $δ$-approximating linear combinations or products of polynomial-approximable functions with quadratically reduced-degree polynomials. We extend the list of polynomial-approximable functions by showing that the functions of cosine and sine can also be $δ$-approximated by quadratically reduced-degree Laurent polynomials. We demonstrate that various Hamiltonian functions for quantum ground-state preparation and energy estimation can be implemented with quadratically shallow circuits.

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arXiv2025

Backpropagation scaling in parameterised quantum circuits

The discovery of the backpropagation algorithm ranks among one of the most important moments in the history of machine learning, and has made possible the training of large-scale neural networks through its ability to compute gradients at roughly the same computational cost as model evaluation. Despite its importance, a similar backpropagation-like scaling for gradient evaluation of parameterised quantum circuits has remained elusive. Currently, the most popular method requires sampling from a number of circuits that scales with the number of circuit parameters, making training of large-scale quantum circuits prohibitively expensive in practice. Here we address this problem by introducing a class of structured circuits that are not known to be classically simulable and admit gradient estimation with significantly fewer circuits. In the simplest case -- for which the parameters feed into commuting quantum gates -- these circuits allow for fast estimation of the gradient, higher order partial derivatives and the Fisher information matrix. Moreover, specific families of parameterised circuits exist for which the scaling of gradient estimation is in line with classical backpropagation, and can thus be trained at scale. In a toy classification problem on 16 qubits, such circuits show competitive performance with other methods, while reducing the training cost by about two orders of magnitude.

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arXiv2024

Hardware-efficient ansatz without barren plateaus in any depth

Variational quantum circuits have recently gained much interest due to their relevance in real-world applications, such as combinatorial optimizations, quantum simulations, and modeling a probability distribution. Despite their huge potential, the practical usefulness of those circuits beyond tens of qubits is largely questioned. One of the major problems is the so-called barren plateaus phenomenon. Quantum circuits with a random structure often have a flat cost-function landscape and thus cannot be trained efficiently. In this paper, we propose two novel parameter conditions in which the hardware-efficient ansatz (HEA) is free from barren plateaus for arbitrary circuit depths. In the first condition, the HEA approximates to a time-evolution operator generated by a local Hamiltonian. Utilizing a recent result by [Park and Killoran, Quantum 8, 1239 (2024)], we prove a constant lower bound of gradient magnitudes in any depth both for local and global observables. On the other hand, the HEA is within the many-body localized (MBL) phase in the second parameter condition. We argue that the HEA in this phase has a large gradient component for a local observable using a phenomenological model for the MBL system. By initializing the parameters of the HEA using these conditions, we show that our findings offer better overall performance in solving many-body Hamiltonians. Our results indicate that barren plateaus are not an issue when initial parameters are smartly chosen, and other factors, such as local minima or the expressivity of the circuit, are more crucial.

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arXiv2024

Hybrid quantum programming with PennyLane Lightning on HPC platforms

We introduce PennyLane's Lightning suite, a collection of high-performance state-vector simulators targeting CPU, GPU, and HPC-native architectures and workloads. Quantum applications such as QAOA, VQE, and synthetic workloads are implemented to demonstrate the supported classical computing architectures and showcase the scale of problems that can be simulated using our tooling. We benchmark the performance of Lightning with backends supporting CPUs, as well as NVidia and AMD GPUs, and compare the results to other commonly used high-performance simulator packages, demonstrating where Lightning's implementations give performance leads. We show improved CPU performance by employing explicit SIMD intrinsics and multi-threading, batched task-based execution across multiple GPUs, and distributed forward and gradient-based quantum circuit executions across multiple nodes. Our data shows we can comfortably simulate a variety of circuits, giving examples with up to 30 qubits on a single device or node, and up to 41 qubits using multiple nodes.

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arXiv2024

Efficient ground state preparation in variational quantum eigensolver with symmetry-breaking layers

Variational quantum eigensolver (VQE) solves the ground state problem of a given Hamiltonian by finding the parameters of a quantum circuit ansatz that minimizes the Hamiltonian expectation value. Among possible quantum circuit ansätze, the Hamiltonian variational ansatz (HVA) is widely studied for quantum many-body problems as the ansatz with sufficiently large depth is theoretically guaranteed to express the ground state. However, since the HVA shares the same symmetry with the Hamiltonian, it is not necessarily good at finding the symmetry-broken ground states that prevail in nature. In this paper, we systematically explore the limitations of the HVA for solving symmetry-broken systems and propose an alternative quantum circuit ansatz with symmetry-breaking layers. With extensive numerical simulations, we show that the proposed ansatz finds the ground state in depth significantly shorter than the bare HVA when the target Hamiltonian has symmetry-broken ground states.

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arXiv2024

Hamiltonian variational ansatz without barren plateaus

Variational quantum algorithms, which combine highly expressive parameterized quantum circuits (PQCs) and optimization techniques in machine learning, are one of the most promising applications of a near-term quantum computer. Despite their huge potential, the utility of variational quantum algorithms beyond tens of qubits is still questioned. One of the central problems is the trainability of PQCs. The cost function landscape of a randomly initialized PQC is often too flat, asking for an exponential amount of quantum resources to find a solution. This problem, dubbed barren plateaus, has gained lots of attention recently, but a general solution is still not available. In this paper, we solve this problem for the Hamiltonian variational ansatz (HVA), which is widely studied for solving quantum many-body problems. After showing that a circuit described by a time-evolution operator generated by a local Hamiltonian does not have exponentially small gradients, we derive parameter conditions for which the HVA is well approximated by such an operator. Based on this result, we propose an initialization scheme for the variational quantum algorithms and a parameter-constrained ansatz free from barren plateaus.

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arXiv2023

The hardness of quantum spin dynamics

Recent experiments demonstrated quantum computational advantage in random circuit sampling and Gaussian boson sampling. However, it is unclear whether these experiments can lead to practical applications even after considerable research effort. On the other hand, simulating the quantum coherent dynamics of interacting spins has been considered as a potential first useful application of quantum computers, providing a possible quantum advantage. Despite evidence that simulating the dynamics of hundreds of interacting spins is challenging for classical computers, concrete proof is yet to emerge. We address this problem by proving that sampling from the output distribution generated by a wide class of quantum spin Hamiltonians is a hard problem for classical computers. Our proof is based on the Taylor series of the output probability, which contains the permanent of a matrix as a coefficient when bipartite spin interactions are considered. We devise a classical algorithm that extracts the coefficient using an oracle estimating the output probability. Since calculating the permanent is #P-hard, such an oracle does not exist unless the polynomial hierarchy collapses. With an anticoncentration conjecture, the hardness of the sampling task is also proven. Based on our proof, we estimate that an instance involving about 200 spins will be challenging for classical devices but feasible for intermediate-scale quantum computers with fault-tolerant qubits.

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arXiv2023

Complexity phase transitions in instantaneous quantum polynomial-time circuits

We study a subclass of the Instantaneous Quantum Polynomial-time (IQP) circuit with a varying density of two-qubit gates. In addition to a known anticoncentration regime, we identify novel parameter conditions where the model is classically simulable or the output distribution follows the Porter-Thomas distribution. By showing that those parameter regimes do not coincide, we argue the presence of more than two phases in the model. The learnability of the output distribution of this model is further studied, which indicates that an energy-based model fails to learn the output distribution even when it is not anticoncentrated. Our study reveals that a quantum circuit model can have multiple fine-grained complexity phases, suggesting the potential for quantum advantage even when the output distribution is far from the Porter-Thomas distribution.

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arXiv2022

Expressive power of complex-valued restricted Boltzmann machines for solving non-stoquastic Hamiltonians

Variational Monte Carlo with neural network quantum states has proven to be a promising avenue for evaluating the ground state energy of spin Hamiltonians. However, despite continuous efforts the performance of the method on frustrated Hamiltonians remains significantly worse than those on stoquastic Hamiltonians that are sign-free. We present a detailed and systematic study of restricted Boltzmann machine (RBM) based variational Monte Carlo for quantum spin chains, resolving how relevant stoquasticity is in this setting. We show that in most cases, when the Hamiltonian is phase connected with a stoquastic point, the complex RBM state can faithfully represent the ground state, and local quantities can be evaluated efficiently by sampling. On the other hand, we identify several new phases that are challenging for the RBM Ansatz, including non-topological robust non-stoquastic phases as well as stoquastic phases where sampling is nevertheless inefficient. Furthermore, we find that an accurate neural network representation of ground states in non-stoquastic phases is hindered not only by the sign structure but also by their amplitudes.

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arXiv2022

PennyLane: Automatic differentiation of hybrid quantum-classical computations

PennyLane is a Python 3 software framework for differentiable programming of quantum computers. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework compatible with any gate-based quantum simulator or hardware. We provide plugins for hardware providers including the Xanadu Cloud, Amazon Braket, and IBM Quantum, allowing PennyLane optimizations to be run on publicly accessible quantum devices. On the classical front, PennyLane interfaces with accelerated machine learning libraries such as TensorFlow, PyTorch, JAX, and Autograd. PennyLane can be used for the optimization of variational quantum eigensolvers, quantum approximate optimization, quantum machine learning models, and many other applications.

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arXiv2021

Scalable Neural Decoder for Topological Surface Codes

With the advent of noisy intermediate-scale quantum (NISQ) devices, practical quantum computing has seemingly come into reach. However, to go beyond proof-of-principle calculations, the current processing architectures will need to scale up to larger quantum circuits which in turn will require fast and scalable algorithms for quantum error correction. Here we present a neural network based decoder that, for a family of stabilizer codes subject to depolarizing noise and syndrome measurement errors, is scalable to tens of thousands of qubits (in contrast to other recent machine learning inspired decoders) and exhibits faster decoding times than the state-of-the-art union find decoder for a wide range of error rates (down to 1%). The key innovation is to autodecode error syndromes on small scales by shifting a preprocessing window over the underlying code, akin to a convolutional neural network in pattern recognition approaches. We show that such a preprocessing step allows to effectively reduce the error rate by up to two orders of magnitude in practical applications and, by detecting correlation effects, shifts the actual error threshold, up to fifteen percent higher than the threshold of conventional error correction algorithms such as union find or minimum weight perfect matching, even in the presence of measurement errors. An in-situ implementation of such machine learning-assisted quantum error correction will be a decisive step to push the entanglement frontier beyond the NISQ horizon.

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arXiv2021

Classical restrictions of generic matrix product states are quasi-locally Gibbsian

We show that the norm squared amplitudes with respect to a local orthonormal basis (the classical restriction) of finite quantum systems on one-dimensional lattices can be exponentially well approximated by Gibbs states of local Hamiltonians (i.e., are quasi-locally Gibbsian) if the classical conditional mutual information (CMI) of any connected tripartition of the lattice is rapidly decaying in the width of the middle region. For injective matrix product states, we moreover show that the classical CMI decays exponentially, whenever the collection of matrix product operators satisfies a 'purity condition'; a notion previously established in the theory of random matrix products. We furthermore show that violations of the purity condition enables a generalized notion of error correction on the virtual space, thus indicating the non-generic nature of such violations. We make this intuition more concrete by constructing a probabilistic model where purity is a typical property. The proof of our main result makes extensive use of the theory of random matrix products, and may find applications elsewhere.

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arXiv2020

Geometry of learning neural quantum states

Combining insights from machine learning and quantum Monte Carlo, the stochastic reconfiguration method with neural network Ansatz states is a promising new direction for high-precision ground state estimation of quantum many-body problems. Even though this method works well in practice, little is known about the learning dynamics. In this paper, we bring to light several hidden details of the algorithm by analyzing the learning landscape. In particular, the spectrum of the quantum Fisher matrix of complex restricted Boltzmann machine states exhibits a universal initial dynamics, but the converged spectrum can dramatically change across a phase transition. In contrast to the spectral properties of the quantum Fisher matrix, the actual weights of the network at convergence do not reveal much information about the system or the dynamics. Furthermore, we identify a new measure of correlation in the state by analyzing entanglement in eigenvectors. We show that, generically, the learning landscape modes with least entanglement have largest eigenvalue, suggesting that correlations are encoded in large flat valleys of the learning landscape, favoring stable representations of the ground state.

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