arXiv subjects

Kyunghyun Baek

Publications and source records attributed to Kyunghyun Baek.

At least 19 recordsLinked to original sources

arXiv2026

Phase-Flag Access and No-Go Constraints on Quotient-Space Real Quantum Mechanics

Barrios Hita et al. [Phys. Rev. Lett. 136, 240202 (2026)] proposed a quotient-space formulation of quantum mechanics over the real numbers and concluded that complex numbers are only a convenience. A preceding analysis [arXiv:2607.05865] showed that, when the construction is empirically equivalent to complex quantum mechanics, its real flag is protected by a hidden complex structure $\hat{J}$ and its composition rule is the balanced tensor product over that structure. Here we ask what would follow from the stronger operational reading that the flag is an accessible real degree of freedom. The answer is a direct clash with overlap-determinability (OD), introduced in [arXiv:2601.14638], and with standard no-go theorems. A readable or coherently controllable flag fixes a representative of each ray, and hence supplies precisely the phase convention that OD identifies as the missing resource for universal superposition of unknown states. Once promoted to a generic phase-access primitive, this resource enables probabilistic cloning of a linearly dependent set, steering-based signaling, and logarithmic-query unstructured search. Thus the quotient construction has a sharp follow-up interpretation: as a protected gauge representation it is standard complex quantum mechanics in real notation; as an accessible real theory it leaves the quantum operational framework.

quant-ph↗

arXiv2026

Maximal coherence of quantum measurement and the resource theory of sharpness

A resource theory of quantum measurement can be addressed in terms of quantum coherence and measurement sharpness, respectively. The former analyzes the off-diagonal structure of POVM elements in a predetermined basis while the latter analyzes the deviation from trivial, state-independent, measurements. We establish a direct connection between the two resource theories by identifying measurement sharpness as the maximal coherence that is achievable under all possible unitary changes of the reference basis. For a broad class of POVMs whose elements share a common eigenbasis, we show that the maximal distance-based coherence of measurement coincides exactly with the corresponding distance-based sharpness monotone. We further extend this equivalence, with element-additive distances, to POVMs whose elements admit a common mutually unbiased basis structure. These results provide a measurement-theoretic analogue of the maximal-coherence \& purity correspondence for quantum states. We also show that the maximal coherence of measurement is faithful with respect to trivial measurements and is monotonic under fuzzifying operations for dichotomic measurements, as well as under mixed-unitary and unitarily covariant preprocessing channels. Finally, we illustrate the operational meaning and limitations of the equivalence through qubit POVMs, single-photon phase sensing, and noisy photon-number resolving detection. In particular, the maximal Fisher information in a Mach-Zehnder interferometer is shown to be determined by the squared maximal coherence of the measurement, while in an imperfect photon-number resolving detector the maximal coherence behaves as a proper sharpness monotone, unlike conventional PVM-based unsharpness measures.

quant-ph↗

arXiv2026

Hidden Complex Structure in Quotient-Space Real Quantum Mechanics

Barrios Hita et al. [Phys. Rev. Lett. $\bf{136}$, 240202 (2026)] argued that quantum mechanics can be formulated over the real numbers by replacing the tensor-product postulate with a quotient-space construction, and concluded that complex numbers are therefore a matter of convenience. We show that the operational content of this construction is not that of a generic real Hilbert-space theory. Empirical equivalence requires a distinguished real linear operator $J$ with $J^2 = -\mathbb{1}$, and all physical effects, instruments, and dynamics must preserve the corresponding $SO(2)$ gauge. Moreover, the composite-system rule is a balanced tensor product over this hidden complex structure, not the ordinary tensor product over $\mathbb{R}$. In multipartite network scenarios, this changes the meaning of source independence: canonical real representatives are not source-factorizable in the usual tensor-product sense. Thus, the construction is best understood as standard complex quantum mechanics written in real notation, not as an independent real-amplitude theory. This clarifies what is, and is not, excluded by experiments testing the necessity of complex numbers.

quant-ph↗

arXiv2026

First-Quantized Relativistic Quantum Simulation with Periodic and Dirichlet Boundary Conditions

In this work, we present a methodology for first-quantized relativistic quantum simulation on one-dimensional finite domains under the two boundary conditions most commonly used in lattice models: periodic boundary conditions (PBC) and Dirichlet boundary conditions (DBC). Starting from the positive-energy relativistic kinetic operator, we construct weakly relativistic lattice Hamiltonians whose leading correction requires the boundary-consistent discretized momentum moments $\langle \hat{P}^{2}\rangle$ and $\langle \hat{P}^{4}\rangle$. These moments are reconstructed in the PBC Hamiltonian from moments of a unitary cyclic translation while the DBC Hamiltonian uses the open-chain finite-difference. In a qubit-register implementation, it can be evaluated as the corresponding cyclic translation estimator plus boundary-local terms that remove the unphysical wrap-around link. The resulting energy-estimation workflow uses translation measurements for the kinetic terms, a small number of endpoints and near-endpoints overlap probabilities for DBC, and position-basis sampling for diagonal potentials. We valdate the framework of the relativistic quantum simulation in various benchmark potentials such as no potential and a cosine potential for PBC as well as an infinite square well and a harmonic potential for DBC, with finite-shot sampling tests. These benchmarks show good agreement between the estimator reconstruction and direct matrix evaluation while separating the finite-grid discretization, weak-relativistic truncation, and measurement errors.

quant-ph↗

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.

quant-ph↗

arXiv2026

Subspace Variational Quantum Simulation: Fidelity Lower Bounds as Measures of Training Success

We propose an iterative variational quantum algorithm to simulate the time evolution of arbitrary initial states within a given subspace. The algorithm compresses the Trotter circuit into a shorter-depth parameterized circuit, which is optimized simultaneously over multiple initial states in a single training process using fidelity-based cost functions. After the whole training procedure, we provide an efficiently computable lower bound on the fidelities for arbitrary states within the subspace, which guarantees the performance of the algorithm in the worst-case training scenario. We also show our cost function exhibits a barren-plateau-free region near the initial parameters at each iteration in the training landscape. The experimental demonstration of the algorithm is presented through the simulation of a 2-qubit Ising model on an IBMQ processor. As a demonstration for a larger system, a simulation of a 10-qubit Ising model is also provided.

quant-ph↗

arXiv2026

Dual channel multi-product formulas

Product-formula (PF) based quantum simulation is a promising approach for simulating quantum systems on near-term quantum computers. Achieving a desired simulation precision typically requires a polynomially increasing number of Trotter steps, which remains challenging due to the limited performance of current quantum hardware. To alleviate this issue, post-processing techniques such as the multi-product formula (MPF) have been introduced to suppress algorithmic errors within restricted hardware resources. In this work, we propose a dual-channel multi-product formula that achieves a two-fold improvement in Trotter error scaling. As a result, our method enables the target simulation precision to be reached with approximately half the circuit depth compared to conventional MPF schemes. Importantly, the reduced circuit depth directly translates into lower physical error mitigation overhead when implemented on real quantum hardware. We demonstrate that, for a fixed CNOT count as a measure of quantum circuit, our proposal yields significantly smaller algorithmic errors, while the sampling error remains essentially unchanged.

quant-ph↗

arXiv2025

Quantum Simulation of Dynamical Transition Rates in Open Quantum Systems

Estimating transition rates in open quantum systems is hampered by computing-resource demands that grow rapidly with system size. We present a quantum-simulation framework that enables efficient estimation by recasting the transition rate, given as the time derivative of an equilibrium correlation function, into a set of independently measurable contributions. Each contribution term is evaluated as the expectation value of a parameter-tuned quantum process, thereby circumventing explicit Lindbladian numerics. We validate our method on a spin-1/2 decoherence model using an IBM quantum processor. Further, we apply the method to the Caldeira-Leggett model of quantum Brownian motion as a realistic and practically relevant setting and reaffirm the theoretical soundness and practical implementability. These results provide evidence that quantum simulation can deliver substantial computational advantages in studying open-system kinetics for quantum chemistry on an intermediate-scale quantum computer.

quant-ph↗

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.

quant-ph↗

arXiv2025

Relativistic Quantum Simulation under Periodic and Dirichlet Boundary Conditions: A First-Quantised Framework for Near-Term Devices

We present a new recipe for relativistic quantum simulation using the first quantisation approach, under periodic (PBC) and Dirichlet (DBC) boundary conditions. The wavefunction is discretised across a finite grid represented by system qubits, and the squared momentum operator is expressed using the finite-difference method based on quantum translation operations. The relativistic kinetic energy is approximated through a perturbative expansion of the total kinetic Hamiltonian, incorporating higher-order momentum terms. The approach would allow variational optimisation of appropriate ansatz states to estimate both non-relativistic and relativistic ground-state energies on a quantum computer. This work offers a practical route to simulating relativistic effects on near-term quantum devices, supporting future developments in quantum physics and chemistry.

quant-ph↗

arXiv2025

Robustness measures for quantifying nonlocality

We suggest generalized robustness for quantifying nonlocality and derive its equivalence to the maximum violation ratio of Bell inequalities defined as vectors with non-negative elements. We investigate its properties by comparing it with white-noise and standard robustness measures. As a result, we show that white-noise robustness does not fulfill monotonicity under local operations and shared randomness, whereas the other measures do. To compare the standard and generalized robustness measures, we introduce the concept of inequivalence, which indicates a reversal in the order relationship depending on the choice of monotones. From an operational perspective, the inequivalence of monotones for resourceful objects implies the absence of free operations that connect them. Applying this concept, we find that standard and generalized robustness measures are inequivalent between even- and odd-dimensional cases up to eight dimensions. This is obtained using randomly performed CGLMP measurement settings in a maximally entangled state. This study contributes to the resource theory of nonlocality and sheds light on comparing monotones by using the concept of inequivalence valid for all resource theories.

quant-ph↗

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.

quant-ph↗

arXiv2024

Global optimization in variational quantum algorithms via dynamic tunneling method

We present a global optimization routine for the variational quantum algorithms, which utilizes the dynamic tunneling flow. Originally designed to leverage information gathered by a gradient-based optimizer around local minima, we adapt the conventional dynamic tunneling flow to exploit the distance measure of quantum states, resolving issues of extrinsic degeneracy arising from the parametrization of quantum states. Our global optimization algorithm is applied to the variational quantum eigensolver for the transverse-field Ising model to demonstrate the performance of our routine while comparing it with the conventional dynamic tunneling method, which is based on the Euclidean distance measure on the parameter space.

quant-ph↗

arXiv2024

Resource-compact time-optimal quantum computation

Fault-tolerant quantum computation enables reliable quantum computation but incurs a significant overhead from both time and resource perspectives. To reduce computation time, Austin G. Fowler proposed time-optimal quantum computation by constructing a quantum circuit for a fault-tolerant $T$ gate without probabilistic $S$ gate correction. In this work, we introduce a resource-compact quantum circuit that significantly reduces resource requirements by more than 60% for a fault-tolerant $T$ gate without probabilistic $S$ gate correction. Consequently, we present a quantum circuit that minimizes resource utilization for time-optimal quantum computation, demonstrating efficient time-optimal quantum computation. Additionally, we describe an efficient form involving initialization, CNOTs, and measurements, laying the foundation for the development of an efficient compiler for fault-tolerant quantum computation.

quant-ph↗

arXiv2024

Fundamental limits on concentrating and preserving tensorized quantum resources

Quantum technology offers great advantages in many applications by exploiting quantum resources like nonclassicality, coherence, and entanglement. In practice, an environmental noise unavoidably affects a quantum system and it is thus an important issue to protect quantum resources from noise. In this work, we investigate the manipulation of quantum resources possessing the so-called tensorization property and identify the fundamental limitations on concentrating and preserving those quantum resources. We show that if a resource measure satisfies the tensorization property as well as the monotonicity, it is impossible to concentrate multiple noisy copies into a single better resource by free operations. Furthermore, we show that quantum resources cannot be better protected from channel noises by employing correlated input states on joint channels if the channel output resource exhibits the tensorization property. We address several practical resource measures where our theorems apply and manifest their physical meanings in quantum resource manipulation.

quant-ph↗

arXiv2023

$T$-depth-optimized Quantum Search with Quantum Data-access Machine

Quantum search algorithms offer a remarkable advantage of quadratic reduction in query complexity using quantum superposition principle. However, how an actual architecture may access and handle the database in a quantum superposed state has been largely unexplored so far; the quantum state of data was simply assumed to be prepared and accessed by a black-box operation -- so-called oracle, even though this process, if not appropriately designed, may adversely diminish the quantum query advantage. Here, we introduce an efficient quantum data-access process, dubbed as quantum data-access machine (QDAM), and present a general architecture for quantum search algorithm. We analyze the runtime of our algorithm in view of the fault-tolerant quantum computation (FTQC) consisting of logical qubits within an effective quantum error correction code. Specifically, we introduce a measure involving two computational complexities, i.e. quantum query and $T$-depth complexities, which can be critical to assess performance since the logical non-Clifford gates, such as the $T$ (i.e., $π/8$ rotation) gate, are known to be costliest to implement in FTQC. Our analysis shows that for $N$ searching data, a QDAM model exhibiting a logarithmic, i.e., $O(\log{N})$, growth of the $T$-depth complexity can be constructed. Further analysis reveals that our QDAM-embedded quantum search requires $O(\sqrt{N} \times \log{N})$ runtime cost. Our study thus demonstrates that the quantum data search algorithm can truly speed up over classical approaches with the logarithmic $T$-depth QDAM as a key component.

quant-ph↗

arXiv2023

Generalized Euler angles for a unitary control of the Hamiltonian system

We provide an angular parametrization of the special unitary group $\textrm{SU}(2^{n})$ generalizing Euler angles for $\textrm{SU}(2)$ by successively applying the KAK decomposition. We then determine constraint equations for the parametric curve of generalized Euler angles corresponding to the exponential curve of a given Hamiltonian. The constraint equations are in the form of first-order differential-algebraic equations and resemble Wei-Norman equations of canonical coordinates of the second kind for $\textrm{SU}(2^{n})$.

quant-ph↗

arXiv2023

Variational quantum state discriminator for supervised machine learning

Quantum state discrimination (QSD) is a fundamental task in quantum information processing with numerous applications. We present a variational quantum algorithm that performs the minimum-error QSD, called the variational quantum state discriminator (VQSD). The VQSD uses a parameterized quantum circuit that is trained by minimizing a cost function derived from the QSD, and finds the optimal positive-operator valued measure (POVM) for distinguishing target quantum states. The VQSD is capable of discriminating even unknown states, eliminating the need for expensive quantum state tomography. Our numerical simulations and comparisons with semidefinite programming demonstrate the effectiveness of the VQSD in finding optimal POVMs for minimum-error QSD of both pure and mixed states. In addition, the VQSD can be utilized as a supervised machine learning algorithm for multi-class classification. The area under the receiver operating characteristic curve obtained in numerical simulations with the Iris flower dataset ranges from 0.97 to 1 with an average of 0.985, demonstrating excellent performance of the VQSD classifier.

quant-ph↗