arXiv subjects

Joonsuk Huh

Publications and source records attributed to Joonsuk Huh.

At least 19 recordsLinked to original sources

arXiv2026

Efficient Multi-Controlled Gate Implementation in Trapped-Ion Systems

Multi-controlled gates are essential primitives in quantum algorithms, yet implementing them via standard gate-level decompositions remains resource-intensive. We develop efficient pulse-level implementations of multi-controlled gates in trapped-ion systems using the Cirac-Zoller scheme. We first show that the Cirac-Zoller construction admits a freedom in the sign choice of red-sideband (RSB) pulses, which leaves the logical operation invariant up to a local Pauli-$Z$ correction. By exploiting this freedom, we construct equivalent realizations of multi-controlled gates and develop pulse cancellation for more efficient implementations of successive gates. We perform numerical simulations and show that pulse cancellation reduces the gate time and improves the state fidelity. Furthermore, we propose ancilla-free circuits for general $N$-controlled gates that use a single-controlled gate primitive and $\mathcal{O}(N)$ RSB pulses. As a key application, we apply our pulse cancellation to the linear combination of unitaries (LCU) method for block encoding. We show that the RSB-pulse cost of the select operator over $L$ unitaries can be reduced from $\mathcal{O}(L\log L)$ to $\mathcal{O}(L)$, which improves the efficiency and scalability of LCU-based quantum circuits.

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arXiv2026

Combinatorial Matrix Functions in Ising Models and Quantum Circuit Representation

Permanents, hafnians, and loop-hafnians are combinatorial matrix functions defined on the perfect matchings of graphs. These matrix functions arise in the quantum amplitudes for output photon configurations in linear optical networks, which has led both to sampling hardness results and to a variety of applications. The same matrix functions also appear in Ising models, since Ising models naturally encode graphs, and the matrix functions emerge from quantum interference. However, previous results have been restricted to balanced bipartite graphs, and hence to the permanent. In this paper, we extend the graph structure of the Ising model so that all three matrix functions can be obtained. In particular, self-loops can be encoded by introducing additional spins, and the loop-hafnian is obtained from a superposition of spin states, which we call the loop-hafnian state. We show how to recover the hafnian and permanent cases as the number of self-loops decreases. Moreover, we show that the Ising dynamics we consider can be simulated on a quantum circuit with $O(n^2)$ gates for a $2n \times 2n$ real symmetric matrix. Specifically, we propose a quantum circuit that maps the loop-hafnian state to a basis state with $O(n^2)$ gates, and show that, by an adaptive measurement, the loop-hafnian states for all subsets of vertices can be measured simultaneously.

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arXiv2026

QUBO-Based Conformer Selection with Quantum-Classical Hybrid Optimization for Multiconformer Ligand Modeling

A ligand can adopt multiple conformations within the same binding site, and these conformations can interact differently with the surrounding protein. Multiconformer modeling must therefore determine which candidate conformations to retain and what occupancies to assign to them. An established automated approach uses mixed-integer quadratic programming (MIQP) with hard occupancy and conformer-count limits for this selection. Here, we reformulated conformer selection as a quadratic unconstrained binary optimization (QUBO) problem with finite penalties and discrete occupancies. We solved the QUBO using a quantum-classical hybrid solver. We compared this workflow with the MIQP-based qFit-ligand workflow across 83 paired X-ray ligand entries using the same experimental inputs and the same qFit-ligand processing protocol. For each entry, both final models were evaluated against the same composite-omit map generated from the common input structure before the two workflows diverged. Quantum-qFit produced higher ligand-region real-space correlation coefficients (RSCC) in 62 entries 74.7% and lower occupancy-weighted torsional strain in 66 entries 79.5%. Similar directional trends remained in the 28 entries with matched final conformer counts. The molecular Electron Density for Individual Atoms score (EDIAm) decreased in most entries. This result shows that higher regional map agreement did not necessarily correspond to stronger atom-level density support. Overall, the results show that the conformer-selection formulation can change which ligand states are represented from the same experimental data and provide a QUBO framework for studying multiconformer ligand selection.

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arXiv2026

Scalability and performance metrics for boson sampling devices

Linear-optical platforms provide a promising route to demonstrate quantum computational advantage, particularly through the boson sampling problem. While a boson sampling system should be large enough to show the quantum advantage, the size of the boson sampling problem is often restricted by experimental constraints. In particular, as a boson sampling system is scaled up, experimental constraints can limit its effective problem size to permit efficient classical simulation. In this paper, we investigate the theoretical scalability bounds for boson sampling systems under practical experimental conditions, including photon loss, mode mismatch, and input state error. We employ non-negativity conditions for phase-space quasiprobability distribution functions to analyze these effects. In addition, we introduce two device-level metrics, the boson sampling score which measures the usable capacity of a given device and the boson sampling volume which provides a common hardware-level benchmark for comparing different platforms and assessing their access to an advantage-relevant problem size regime. Our results provide fundamental insights into the performance of boson sampling systems under realistic experimental conditions and offer practical guidelines for scaling up boson sampling systems.

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arXiv2026

Oscillator-Qubit Primitives for a Molecular Quantum Dynamics Simulator

Molecular quantum dynamics simulations that treat both electrons and nuclei quantum mechanically are crucial for predicting chemical reactions. With classical computation, a full wave-function representation of both types of particles requires resources that grow exponentially with their number. Oscillator-qubit processors, including trapped-ion and circuit QED devices, represent electronic states with qubits and nuclear vibrations with oscillators. Their native operations produce linear vibronic interactions, from which programmable anharmonic interactions can be built. Product-formula approaches build the corresponding phase gates by repeating small noncommuting phase steps, and quantum signal processing (QSP) approaches approximate each gate directly with a Fourier series. Simulations apply many such gates in sequence, so accumulated cost and error limit how long the dynamics can be followed. We propose near-optimal quantum primitives for molecular quantum dynamics simulation, covering the representations of both types of particles and their interactions. We synthesize nonlinear and multimode bosonic phase gates using generalized Jacobi-Anger (GJA) expansions within QSP, with a cost that grows near-optimally in both interaction strength and precision. Our interaction model and gate synthesis each have their own accuracy setting. Chosen together, these settings make our multimode benchmark circuits about one-third shorter than those of the previous direct QSP approach. We then simulate energy exchange between the stretching and bending vibrations of a simplified carbon dioxide model. With circuit-QED noise, a short simulation narrowly misses our accuracy criteria at qubit and oscillator lifetimes near 2 ms and 5 ms. These lifetimes mark a concrete checkpoint on the way to simulating anharmonic multimode molecular quantum dynamics on near-term oscillator-qubit processors.

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arXiv2026

Algorithmic Design of Heralded Linear Optical Circuits for Multipartite Entanglement

Heralded multipartite entanglement is a key resource for various quantum information tasks. However, designing linear optical circuits that generate specific target states is generally challenging due to the complexity of the required optical structures. Here we formulate the design of heralded photonic circuits as an algorithmic graph-search problem. Our framework enables the automated construction and optimization of heralded photonic circuits by substantially reducing the search space using the linear quantum graph (LQG) picture. Our strategy reconstructs circuit structures as graphs in the picture and identifies suitable graphs automatically. As a result, we design efficient schemes for a broad range of useful multipartite resource states, including hypergraph magic states, quantum error correcting codes, general three-qubit states and length-1 caterpillar graph states. Our work establishes an algorithmic framework for the systematic discovery of heralded resource states, laying the foundation for the automated design of increasingly complex multipartite entangled resources.

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arXiv2026

Filtered Quantum Phase Estimation

Accurate state preparation is a critical bottleneck in many quantum algorithms, particularly those for ground-state energy estimation. Even in fault-tolerant quantum computing, preparing a quantum state with sufficient overlap with the desired eigenstate remains a major challenge. To address this, we develop a unified cost-aware framework for filtered-state preparation that enhances the overlap of a given input state through spectral filtering. The framework covers polynomial and trigonometric realizations of filters and makes explicit the trade-off among overlap amplification, preparation success probability, and filter-implementation cost. As representative examples, we analyze Gaussian filters and introduce a modified Krylov-subspace-based filter that improves the success-probability/overlap trade-off relevant to filtered state preparation. Within this framework, we study a filtered variant of quantum phase estimation (FQPE) that mitigates the unfavorable dependence on the initial overlap present in standard QPE. Numerical experiments on Fermi-Hubbard models show that FQPE reduces the total runtime by more than two orders of magnitude in the high-precision regime, with overlap amplification exceeding a factor of one hundred.

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arXiv2026

Analog Circuit-QED Simulator of Quantum Spin Dynamics Through the Extended Bose-Hubbard Model

We propose and validate a framework for analog simulation of the Heisenberg spin model using a circuit quantum electrodynamics (circuit-QED) platform. To this end, we develop a continuous family of deformed boson representations of the SU(2) algebra, which includes the Holstein-Primakoff and Dyson-Maleev transformations as special cases. For spin-1/2 systems, we introduce a procedure to circumvent the inherent non-Hermiticity of the representation, showing that this entire family yields the extended Bose-Hubbard (EBH) Hamiltonian. For the experimental realization of this EBH model, we design a scalable circuit-QED architecture based on an engineered Josephson junction array. Numerical simulations confirm that the microwave photon dynamics in this simulator accurately reproduces the original spin dynamics. Our work establishes an experimentally accessible method for investigating complex quantum spin dynamics in a highly controllable bosonic setting.

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arXiv2026

Finite Imaginary-Time Evolution for Polynomial Unconstrained Binary Optimization

Imaginary-time evolution is a standard primitive for ground-state preparation but is nonunitary, precluding direct quantum implementation. We develop Finite Imaginary-Time Evolution (FinITE), a finite-beta construction for diagonal Pauli-Z cost Hamiltonians arising from polynomial unconstrained binary optimization (PUBO) instances, including QUBO and HUBO cases. FinITE uses the linear-combination-of-unitaries (LCU) framework to implement a scaled imaginary-time propagator. The commuting Pauli-Z structure makes termwise block-encodings compose without product-formula error, and higher-order Pauli-Z terms are handled directly without quadratization. The structure yields an exact finite-beta identity between the LCU success probability and the ground-subspace fidelity. Combined with a gap-based fidelity lower bound, the identity yields a closed-form sufficient imaginary-time threshold beta-star for a chosen target fidelity. The threshold depends on estimates of the spectral gap and the initial ground-subspace overlap. Because the LCU success event is flagged by a known ancilla outcome, we integrate fixed-point amplitude amplification with an explicit query-complexity bound. Statevector simulations verify the identity on a five-vertex MaxCut (QUBO) and an eight-qubit cubic HUBO instance, and shot-based simulations on the MaxCut instance illustrate the predicted finite-beta threshold and amplification procedure.

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arXiv2026

Simultaneous Fragment Docking for Geometrically Linkable Pose Pairs

Computational molecular design requires binding arrangements that are not only energetically favorable but also chemically realizable. However, computational methods remain limited in directly recovering fragment pose pairs that can later be connected into a single molecule. To address this problem, we formulated the simultaneous placement of two fragments as a quadratic unconstrained binary optimization problem, Q-SFD, and introduced an explicit inter-fragment distance term to favor reconstruction-feasible arrangements. Relative to the formulation without this term, Q-SFD approximately doubled top-1 recovery of reconstruction-feasible pairs, and the top-5 solutions contained at least one feasible pair for more than 90% of benchmark cases without loss of fragment-level pose accuracy.

q-bio.BM↗

arXiv2026

Heralded Linear Optical Generation of Dicke States

Entanglement is a fundamental feature of quantum mechanics and a key resource for quantum information processing. Among multipartite entangled states, Dicke states $|D_n^k\rangle$ are distinguished by their permutation symmetry, which provides robustness against particle loss and enables applications for quantum communication and computation. Although Dicke states have been realized in various platforms, most optical implementations rely on postselection, which destroys the state upon detection and prevents its further use. A heralded optical scheme is therefore highly desirable. Here, we present a linear-optical heralded scheme for generating arbitrary Dicke states $|D_n^k\rangle$ with $3n+k$ photons through the framework of the linear quantum graph (LQG) picture. By mapping the scheme design into the graph-finding problem, and exploiting the permutation symmetry of Dicke states, we overcome the structural complexity that has hindered previous approaches. Our results provide a resource-efficient pathway toward practical heralded preparation of Dicke states for quantum technologies.

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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

Quantum Amplitude-Amplification Eigensolver: A State-Learning-Assisted Approach beyond Energy-Gradient-Based Heuristics

Ground-state estimation lies at the heart of a broad range of quantum simulations. Most near-term approaches are cast as variational energy minimization and thus inherit the challenges of problem-specific energy landscapes. We develop the quantum amplitude-amplification eigensolver (QAAE), which departs from the variational paradigm and instead coherently drives a trial state toward the ground state via quantum amplitude amplification. Each amplitude-amplification round interleaves a reflection about the learned trial state with a controlled short-time evolution under a normalized Hamiltonian; an ancilla readout yields an amplitude-amplified pure target state that a state-learning step then re-encodes into an ansatz circuit for the next round -- without evaluating the energy gradients. Under standard assumptions (normalized $\hat{H}$, a nondegenerate ground-state, and a learning update), the ground-state overlap increases monotonically per round and the procedure converges; here, a per-round depth bound in terms of the ansatz depth and Hamiltonian-simulation cost establishes hardware compatibility. Cloud experiments on IBMQ processor verify our amplification mechanism on a two-level Hamiltonian and a two-qubit Ising model, and numerical benchmarks on $\mathrm{H}_2$, $\mathrm{LiH}$, and a $10$-qubit longitudinal-and-transverse-field Ising model show that QAAE integrates with chemistry-inspired and hardware-efficient circuits and can surpass gradient-based VQE in accuracy and stability. These results position QAAE as a variational-free and hardware-compatible route to ground-state estimation for near-term quantum simulation.

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arXiv2025

Jacobi-Anger Density Estimation for Energy Distribution of Quantum States

The energy distribution of a quantum state is essential for accurately estimating a molecule's ground state energy in quantum computing. Directly obtaining this distribution requires full Hamiltonian diagonalization, which is computationally prohibitive for large-scale systems. A more practical strategy is to approximate the distribution from a finite set of Hamiltonian moments. However, reconstructing an accurate distribution from only a limited number of moments remains a significant challenge. In this work, we introduce Jacobi-Anger Density Estimation (JADE), a non-parametric, quantum-inspired method designed to overcome this difficulty. JADE reconstructs the characteristic function from a finite set of moments using the Jacobi-Anger expansion and then estimates the underlying distribution via an inverse Fourier transform. We demonstrate that JADE can accurately recover the energy distribution of a quantum state for a molecular system. Beyond quantum chemistry, we also show that JADE is broadly applicable to the estimation of complicated probability density functions in various other scientific and engineering fields. Our results highlight JADE as a powerful and versatile tool for practical quantum systems, with the potential to significantly enhance ground state energy estimation and related applications.

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arXiv2025

Oscillator-qubit generalized quantum signal processing for vibronic models: a case study of uracil cation

Hybrid oscillator-qubit processors have recently demonstrated high-fidelity control of both continuous- and discrete-variable information processing. However, most of the quantum algorithms remain limited to homogeneous quantum architectures. Here, we present a compiler for hybrid oscillator-qubit processors, implementing state preparation and time evolution. In hybrid oscillator-qubit processors, this compiler invokes generalized quantum signal processing (GQSP) to constructively synthesize arbitrary bosonic phase gates with moderate circuit depth O(log(1/{\varepsilon})). The approximation cost is scaled by the Fourier bandwidth of the target bosonic phase, rather than by the degree of nonlinearity. Armed with GQSP, nonadiabatic molecular dynamics can be decomposed with arbitrary-phase potential propagators. Compared to fully discrete encodings, our approach avoids the overhead of truncating continuous variables, showing linear dependence on the number of vibration modes while trading success probability for circuit depth. We validate our method on the uracil cation, a canonical system whose accurate modeling requires anharmonic vibronic models, estimating the cost for state preparation and time evolution.

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arXiv2025

Doubling Qubits in a Trapped-Ion System via Vibrational Dual-Rail Encoding

Vibrational modes of trapped ions have traditionally served as quantum buses to mediate internal qubits. However, with recent advances in quantum control, it has become possible to use these vibrational modes directly as quantum computational resources, such as bosonic qubits. Here, we propose a dual-rail encoding scheme in which a dual-rail qubit is encoded by two vibrational modes that share a single phonon. We present the preparation, measurement, and implementation of single- and two-qubit gates, enabling universal quantum computation. The dual-rail qubit system offers scalability and all-to-all connectivity. Moreover, we extend the dual-rail qubit system to a logical internal qubit--dual-rail qubit hybrid system by incorporating internal qubits into the dual-rail qubit system as another type of logical qubit. The hybrid system nearly doubles the number of available logical qubits compared to conventional trapped-ion quantum computers while maintaining all-to-all connectivity. Additionally, we propose a method for implementing multi-qubit controlled gates and discuss potential applications that can leverage the advantages of the hybrid system. Our scheme provides a practical framework for an internal qubit-boson qubit hybrid system.

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arXiv2025

Efficient Strategies for Reducing Sampling Error in Quantum Krylov Subspace Diagonalization

Within the realm of early fault-tolerant quantum computing (EFTQC), quantum Krylov subspace diagonalization (QKSD) has emerged as a promising quantum algorithm for the approximate Hamiltonian diagonalization via projection onto the quantum Krylov subspace. However, the algorithm often requires solving an ill-conditioned generalized eigenvalue problem (GEVP) involving erroneous matrix pairs, which can significantly distort the solution. Since EFTQC assumes limited-scale error correction, finite sampling error becomes a dominant source of error in these matrices. This work focuses on quantifying sampling errors during the measurement of matrix element in the projected Hamiltonian examining two measurement approaches based on the Hamiltonian decompositions: the linear combination of unitaries and diagonalizable fragments. To reduce sampling error within a fixed budget of quantum circuit repetitions, we propose two measurement strategies: the shifting technique and coefficient splitting. The shifting technique eliminates redundant Hamiltonian components that annihilate either the bra or ket states, while coefficient splitting optimizes the measurement of common terms across different circuits. Numerical experiments with electronic structures of small molecules demonstrate the effectiveness of these strategies, reducing sampling costs by a factor of 20-500.

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arXiv2024

Quantum superposing algorithm for quantum encoding

Efficient encoding of classical data into quantum state -- currently referred to as quantum encoding -- holds crucial significance in quantum computation. For finite-size databases and qubit registers, a common strategy of the quantum encoding entails establishing a classical mapping that correlates machine-recognizable data addresses with qubit indices that are subsequently superposed. Herein, the most imperative lies in casting an algorithm for generating the superposition of any given number of qubit indices. This algorithm is formally known as quantum superposing algorithm. In this work, we present an efficient quantum superposing algorithm, affirming its effectiveness and superior computational performance in a practical quantum encoding scenario. Our theoretical and numerical analyses demonstrate a substantial enhancement in computational efficiency compared to existing algorithms. Notably, our algorithm has a maximum of 2n-3 controlled-not (CNOT) counts, representing the most optimized result to date.

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