arXiv subjects

Hikaru Wakaura

Publications and source records attributed to Hikaru Wakaura.

At least 19 recordsLinked to original sources

arXiv2026

Few-sample regression with an adaptively grown variational quantum Kolmogorov--Arnold network

Kolmogorov-Arnold networks place learnable one-dimensional functions on the edges of a network rather than fixed activations on its nodes, and several quantum realisations have been proposed. Whether any of them offers a practical benefit is unclear, because the reported comparisons rest on single training runs, untuned baselines, and test sets that were also used for model selection. Here we evaluate a variational quantum Kolmogorov-Arnold network whose ansatz is grown one Pauli operator at a time, under a protocol with seed-paired comparisons, a stopping rule that never sees the test set, and a confirmatory study whose hypotheses, seeds, and analysis were committed before the runs. On four-qubit benchmarks the model is indistinguishable from a quantum neural network of the same parameter count and is outperformed by classical regressors. On a difficulty-controlled family of 12- and 16-dimensional targets learned from ten training points, the 32-parameter quantum model beats the best of four unregularised classical regressors and a tuned quantum neural network with Holm-corrected p <= 0.017; the result is unchanged with 256 measurement shots per circuit, and the trained models run on a 156-qubit IBM processor with test errors within 0.3 of the exact values. A kernel ridge regressor with hyperparameters chosen by leave-one-out cross-validation on the same ten points matches the quantum model, and a sample-size sweep shows that the quantum model's error is nearly flat in the training-set size while the classical models keep improving. The benefit of the quantum model is therefore an implicit regularisation of a low-capacity model, present only in the few-sample regime and absent at 18 dimensions, not an expressivity advantage. These results give a reproducible reference point for the resources and limits of variational quantum Kolmogorov-Arnold networks.

quant-ph↗

arXiv2026

Evaluation artifacts in reversible quantum reservoir protocols: a withdrawal of our own claims, and an entangled channel that survives the controls

This replaces v1, which reported a ten-order shot-noise suppression from a quantum reservoir autoencoder and a two-phase protocol reconstructing unseen inputs at MSE ~ 10^-4. We withdraw both claims: under one consistent evaluation the suppression reverses sign (reset channels degrade reconstruction 144x), the two-phase target is invertible in closed form without training, and a polynomial using no quantum features matches the full model. We trace these to four evaluation artifacts; the fourth also invalidates the companion latent code, which never leaves its initialization. What survives the same controls is a joint scrambling channel: injected on one reservoir half, read out on the other, decoded by a readout calibrated once on training messages. Over 32 realizations the held-out error is below chance in 31-32 (permutation p<10^-4) with a shuffled control at chance. Scrambler T-doping is necessary for one-shot injection, while interleaved injection supplies its own non-Cliffordness; a matched classical scrambler decodes the task better, so the transport is not evidence of a quantum mechanism. The access threshold, recomputed on nested subsystems with right-censoring, gives interleaved medians f* = 0.25-0.33; one-shot injection reaches full detectability in only half the realizations at the largest settings. A trained variational ansatz loses to the fixed untrained circuit by 2.6-4.4x. Three extensions pass the same discipline: streaming requires dissipative reset of the accessible half; the decoder does not transfer across the eight keys tested; a receiver holding the key matches the supervised ceiling from self-simulated pairs. A first hardware run decodes at 0.23 with the shuffled control at chance, while coherent device errors partially open the t=0 control. We close with the controls that separate transport from interpolation.

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arXiv2026

Markovian dephasing has no entanglement-breaking threshold, and a fixed tolerance will report one anyway

When modelling decoherence in a biological spin system it is tempting to seek a critical rate beyond which the channel is entanglement-breaking (EB) and quantum resources are gone. We show that for the two channel families in which such a model would be posed, no critical rate exists. For uniform dephasing at rate $γ$ the partial transpose of the Choi state has eigenvalue $-e^{-γ}/d$, so the channel is non-PPT -- hence not EB -- at every finite $γ$. Adding amplitude damping changes nothing: the qubit map's partial transpose stays negative at all finite rates. What does vanish at a finite rate is the coherent information, exactly where the qubit map turns antidegradable: the root of $c^{2}=p$, $γ_{\Ic}=0.668$ at $κ=0.1$. Antidegradability survives tensor products, so the single-letter and regularised thresholds coincide: of the three properties usually conflated here, two share one finite boundary and the third has none. Our main object is the numerical mechanism that manufactures a threshold where there is none. A quantity that decays exponentially to zero without reaching it, tested against a fixed absolute cutoff, yields a "threshold" set by the cutoff: the PPT test gives $γ=5.49$ at $ε=10^{-10}$ and $6.58$ at $10^{-12}$, sliding by $0.55$ per decade. We reported the first number in three now-retracted preprints. Preparing this paper we made the same error three more times -- most seriously in $γ_{\Ic}$ itself, which a bisection against a $10^{-7}$ cutoff placed at $0.62$ -- and we document all four instances, with the closed forms and code that avoid them.

q-bio.NC↗

arXiv2026

The $γ_c$-Peak: Covariant Recovery on Four Organic Qubit Platforms

We characterize where, in the noise parameter space of the uniform dephasing--depolarizing channel $\mathcal N_γ^δ=\mathcal E_δ\!\circ\!\mathcal D_γ$, a deterministic, \emph{nonlinear, target-informed} denoising heuristic yields its largest fidelity gain. The procedure pulls the off-diagonal magnitudes of the noisy state toward those of a known target, with efficiency set by a SWAP-test-purified catalyst; it is not a quantum channel, and target access is an explicit classical resource, so the results describe a benchmark procedure, not blind error correction. Our main tool is the covariant purification map $\mathcal P_\mathrm{cov}(ρ)=(ρ+ρ^2)/(1+\mathrm{Tr}\,ρ^2)$, an exact closed form for one SWAP-test purification round (a rederivation of symmetrization purification: Barenco \emph{et al.}, Cirac--Ekert--Macchiavello) that reduces the catalyst to a scalar eigenvalue iteration. With it we derive the $d\to\infty$ fidelity-gain peak location on Haar-random pure states (Theorem~3): $γ_{\rm peak}(d)\toγ^\star(r,δ)$, with $γ^\star(2,0.1)=0.4725$ and limiting magnitude $0.2262$. Bootstrap-quantified sweeps to $d=256$ are consistent with both limits. The peak is resource- and protocol-dependent: a catalyst-only reference moves it from $\approx0.50$ to $\approx0.34$, and one purification round instead of two to $\approx0.39$. Bell and uniform $d=4$ states admit unique-peak theorems for the $r=0$, $δ=0$ protocol member. All results are reproducible from the open-source \texttt{organic-qc-bench} package with seed~42.

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arXiv2026

Catalytic Quantum Error Correction: Theory, Efficient Catalyst Preparation, and Numerical Benchmarks

Quantum computers promise transformative speedups, but environmental noise destroys their fragile states. Conventional quantum error correction (QEC) encodes information redundantly across physical qubits, yet fails above a threshold of about 1% and incurs polynomial qubit overhead. A recent theorem from the resource theory of coherence shows that catalytic covariant operations amplify coherence at an unbounded rate, but this result has never been cast as an operational protocol. The challenge is to turn an asymptotic theorem into a recovery scheme that works at any noise strength with realistic resources. Here we show that catalytic coherence amplification can be cast as an error-correction primitive, Catalytic Quantum Error Correction (CQEC), which recovers a known target state from noisy copies without any error magnitude threshold whenever the target's coherent modes are preserved. In an effective model of the recovery map, fidelity exceeds 0.99 across 200 noise configurations spanning d = 4-64; the catalyst cost drops from the constructive bound n* ~ d^4 e^(2 gamma) to 32 copies at matched fidelity (10^4- to 10^9-fold) via a pipeline of dynamical decoupling, Clifford twirling, and recursive swap-test purification. A first explicitly CPTP, exactly covariant joint-channel implementation validates genuine recovery under dephasing at small dimension (0.54 -> 0.77) while showing that shallow circuits consume the catalyst, quantifying the model-vs-channel gap. These results turn an abstract resource-theoretic statement into a concrete protocol candidate complementary to stabilizer- and purification-based QEC; an open-source package reproducing the benchmarks accompanies this work (arXiv:2603.25774, https://github.com/deeptell-inc/cqec).

quant-ph↗

arXiv2026

Enhanced Variational Quantum Kolmogorov-Arnold Network

The Kolmogorov-Arnold Network (KAN) places the trainable functions on the synapses rather than on the neurons. Existing quantum implementations either lack accuracy (Variational Quantum KAN, VQKAN) or rely on block encoding and Quantum Signal Processing, which demand many control gates and ancillae. We propose the Enhanced Variational Quantum Kolmogorov-Arnold Network (EVQKAN), a variational ansatz that emulates a $2^{N_q}$-dimensional KAN layer matrix by tiling controlled rotations through a sum-operator construction, using only $2^{N_q-1}$ trainable spline functions per layer. On the fitting of an elementary function, EVQKAN attains a significantly lower test error than Quantum Neural Networks (QNN), VQKAN and Adaptive VQKAN (Mann-Whitney $p<0.002$, Cliff's $δ\leq-0.86$ over ten attempts; EVQKAN beats VQKAN on every attempt), though classical KAN is more accurate still. On a two-dimensional classification task the ordering reverses: under a leak-free protocol introduced here, EVQKAN classifies above chance (accuracy $0.620$, $p=0.0005$) but is significantly less accurate than a QNN carrying one fifth as many parameters ($Δ$accuracy $-0.134$, $p=0.0014$; $Δ$AUC $-0.252$, $p=0.0002$). We withdraw the classification results of an earlier version of this work: their encoding placed the target label into the circuit as a feature for EVQKAN but not for the methods it was compared against. The dominant error source is overfitting from an under-determined training set; enlarging that set closes the train-test gap by $58\%$ (Spearman $p<10^{-3}$). We also report the circuit cost in full --- three layers emit $1017$ operations, or $4110$ two-qubit gates once the multi-controlled gates are decomposed --- so the construction is simulator-scale and fault-tolerant-era rather than NISQ-ready, with block encoding and qubitization the route to reducing it.

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arXiv2026

Merged amplitude encoding for Chebyshev quantum Kolmogorov--Arnold networks: trading qubits for circuit executions

Quantum Kolmogorov--Arnold networks based on Chebyshev polynomials (CCQKAN) evaluate each edge activation function as a quantum inner product, creating a trade-off between qubit count and the number of circuit executions per forward pass. We introduce merged amplitude encoding, a technique that packs the element-wise products of all $n$ input-edge vectors for a given output node into a single amplitude state, reducing circuit executions by a factor of $n$ at a cost of only 1--2 additional qubits relative to the sequential baseline. The merged and original circuits compute the same mathematical quantity exactly; the open question is whether they remain equally trainable within a gradient-based optimization loop. We address this question through numerical experiments on 10 network configurations under ideal, finite-shot, and noisy simulation conditions, comparing original, parameter-transferred, and independently initialized merged circuits over 16 random seeds. Wilcoxon signed-rank tests show no significant difference between the independently initialized merged circuit and the original ($p > 0.05$ in 28 of 30 comparisons), while parameter transfer yields significantly lower loss under ideal conditions ($p < 0.001$ in 9 of 10 configurations). On 10-class digit classification with the $8\times8$ MNIST dataset using a one-vs-all strategy, original and merged circuits achieve comparable test accuracies of 53--78\% with no significant difference in any configuration. These results provide empirical evidence that merged amplitude encoding preserves trainability under the simulation conditions tested.

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arXiv2026

Blind Catalytic Quantum Error Correction: Target-State Estimation and Fidelity Recovery Without A Priori Knowledge

Near-term quantum computers must protect fragile coherence against decoherence to deliver useful results. Catalytic quantum error correction (CQEC) addresses this challenge by amplifying residual coherence with a reusable catalyst, achieving threshold-free recovery whenever the target coherent modes survive in the noisy state. However, the original protocol requires complete knowledge of the ideal target -- an assumption that fails for variational and iterative algorithms whose output is unknown to the correction module. Here we show that this requirement can be removed by estimating the target from the noisy output alone, in a two-stage protocol we call \emph{blind CQEC}. We benchmark five estimation strategies across three noise channels, four quantum algorithms ($d = 4$--$64$), Haar-random states up to $d = 256$, and mixed targets, and find that estimation and recovery fidelities are linearly correlated ($r > 0.99$); we prove an analytical Lipschitz bound $F_\mathrm{rec} \geq 1 - 2\|\hatρ_\mathrm{est} - ρ_\mathrm{target}\|_1$ that explains the correlation, derive a crossover dimension $d^* \approx 25$--$40$, and show that a tunable hybrid bridges the two regimes. Unlike error-mitigation methods (zero-noise extrapolation, probabilistic error cancellation, virtual distillation), blind CQEC returns the state itself rather than corrected expectation values, with single-copy overhead. A noisy-VQE demonstration for H$_2$ yields $3.4\times$ energy-error reduction, and a \texttt{qiskit-aer} circuit-level check confirms transfer to small circuits. These results identify the bottleneck of blind error correction as a classical estimation problem, opening a route to autonomous, threshold-free recovery in algorithms where pre-encoding is unavailable.

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arXiv2026

Quantum Reservoir Autoencoder: Conditions, Protocol, and Noise Resilience

Quantum reservoir computing exploits fixed quantum dynamics and a trainable linear readout to process temporal data, yet reversing the transformation -- reconstructing the input from the reservoir output -- has been considered intractable due to the recursive nonlinearity of sequential quantum state evolution. We introduce the quantum reservoir autoencoder, a four-equation encode--decode protocol with cross-key pairing, and constructively empirically demonstrate that satisfying reservoir--key combinations can be found using a full XYZ Hamiltonian reservoir (10~data qubits, feature dimension~76, 16~random Hamiltonian realizations). Under ideal conditions the mean-squared error (MSE) reaches ${\sim}10^{-17}$ for data lengths up to 30; under shot noise (1\,000~shots) and depolarizing noise ($p = 0.005$), the MSE degrades to $10^{-3}$--$10^{-1}$. Asymmetric resource allocation -- 10~shots for encoding, $10^5$ for decoding -- yields a 102-fold MSE improvement (16~seeds $\times$ 3~trials). Comparison of single-body features (dimension~31) with the full feature set and six baselines identifies the iterative protocol structure -- not the feature dimension -- as the dominant noise bottleneck: baselines solving the linear system in a single step retain machine precision under identical noise, whereas per-iteration noise inconsistency in the coupled solver limits the MSE to ${\sim}10^{-1}$. The current protocol requires plaintext access during decoder training, restricting practical deployment. These results establish a proof-of-concept for bidirectional information transformation within quantum reservoir computing and identify iterative noise mismatch and blind decryption as the principal open challenges.

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arXiv2025

Generative Adversarial Variational Quantum Kolmogorov-Arnold Network

Kolmogorov Arnold Networks is a novel multilayer neuromorphic network that can exhibit higher accuracy than a neural network. It can learn and predict more accurately than neural networks with a smaller number of parameters, and many research groups worldwide have adopted it. As a result, many types of applications have been proposed. This network can be used as a generator solely or with a Generative Adversarial Network; however, KAN has a slower speed of learning than neural networks for the number of parameters. Hence,it has not been researched as a generator. Therefore, we propose a novel Generative Adversarial Network called Generative Adversarial Variational Quantum KAN that uses Variational Quantum KAN as a generator. This method enables efficient learning with significantly fewer parameters by leveraging the computational advantages of quantum circuits and their output distributions. We performed the training and generation task on MNIST and CIFAR10, and revealed that our method can achieve higher accuracy than neural networks and Quantum Generative Adversarial Network with less data.

quant-ph↗

arXiv2025

Proposal of method to solve a Traveling Salesman Problem using Variational Quantum Kolmogorov-Arnold Network

Traveling salesman problems (TSP) are one of the well-known combinatorial optimization problems that many groups tackle to solve. This problem appears in many types of combinational optimization, such as scheduling, route optimization, and circuit optimization. However, this problem is NP-hard, as the number of combinations increases exponentially as the number of sites increases. Quantum Annealers and Adiabatic Quantum Computers are good at solving it, and universal quantum computers are limited by the number of qubits they have. Therefore, we propose a novel approach that solves it using a Variational Quantum Kolmogorov-Arnold network (VQKAN). Our approach requires a smaller number of qubits than the former approaches on quantum computers. We confirmed that our approach can optimize the paths on the graphs whose length of each path is time-dependent, partial.

quant-ph↗

arXiv2025

Quantum Reservoir GAN

Quantum machine learning is known as one of the promising applications of quantum computers. Many types of quantum machine learning methods have been released, such as Quantum Annealer, Quantum Neural Network, Variational Quantum Algorithms, and Quantum Reservoir Computers. They can work, consuming far less energy for networks of equivalent size. Quantum Reservoir Computers, in particular, have no limit on the size of input data. However, their accuracy is not enough for practical use, and the effort to improve accuracy is mainly focused on hardware improvements. Therefore, we propose the approach from software called Quantum Reservoir Generative Adversarial Network (GAN), which uses Quantum Reservoir Computers as a generator of GAN. We performed the generation of handwritten single digits and monochrome pictures on the CIFAR-10 and Fashion-MNIST datasets. As a result, Quantum Reservoir GAN is confirmed to be more accurate than Quantum GAN, Classical Neural Network, and ordinary Quantum Reservoir Computers.

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arXiv2025

Optimization by VarQITE on Adaptive Variational Quantum Kolmogorov-Arnold Network

Quantum imaginary time evolution (QITE) is a powerful method to derive the ground states of the systems. Only the damping of quantum states leads it; hence, reaching the ground state is guaranteed by nature without any external manipulation. Numerous QITE methods by many groups are used to improve speed and accuracy, derive excited states, and solve combined optimization problems. However, the QITE methods have not been used for quantum machine learning to predict the ideal values for multiple input values. Therefore, we propose a method for applying QITE methods for quantum machine learning and demonstrate fitting problems of elementary functions and classification problems on a 2-D plane. As a result, we confirmed that our method was more accurate than a quantum neural network in solving some problems. Our method can be used for other quantum machine learning algorithms; hence, it may be the milestone for applying QITE to quantum machine learning.

quant-ph↗

arXiv2025

The effect of Quantum Time Crystal Computing to Quantum Machine Learning methods

Many body localization shows the robustness for external perturbations and time reversal symmetry on Time Crystal. This Time Crystal prolongs the coherence time, hence, it is used for quantum computers as qubits. Therefore, we established the method to exploit Time Crystals for quantum computing by controlling external noise called Quantum Time Crystal Computing and demonstrated solving the problem of generating correct waves using Quantum Reservoir Computing, and fitting of given function using Quantum Neural Network and Variational Quantum Kolmogorov-Arnold Network. As a consequence, we revealed that Quantum Time Crystal Computing lower the accuracy of Quantum Reservoir Computing and improved the accuracy of Quantum Neural Network and Variational Quantum Kolmogorov-Arnold Network. This result may be the one of milestones of Quantum Error Mitigation as the case that noise improves the accuracy of Quantum Machine Learning.

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arXiv2023

Derivation of Hamiltonians from time propagations using Born machines

Recently there are more promising qubit technology such as Majorana fermions Rydberg atoms and Silicon quantum dot have yet to be developed for realizing a quantum computer than Superconductivity and Ion trap into the world The simulation of the quantum hardware of these qubits can only be done numerically However a classical numerical simulation is limited concerning available resources The method for simulation of quantum hardware by quantum hardware may be necessary In this paper we propose a novel method for optimizing time propagation from initial states to aimed given states of systems by the Born machine We call this method the Hamiltonian Engineering Born Machine HEBM We calculated the optimal Hamiltonians for propagation to Bars and Stripes distribution Gaussian distribution and Gibbs state for $H=-\Sum Z_j Z_{j+1}$ and revealed that they can be realized rapidly and accurately

quant-ph↗

arXiv2023

Tangent Vector Variational Quantum Eigensolver: A Robust Variational Quantum Eigensolver against the inaccuracy of derivative

Observing rapid developments of both the number of qubits and quantum volume, especially with recent advances in ion-trap quantum computers, it is no doubt that Fault-Tolerant-Quantum-Computer (FTQC) will be realized in the near future. Since FTQC requires 10,000 physical qubits for every 100 logical ones, it will be used as the first large-scale Noisy-Intermediate-Scale-Quantum (NISQ) . The Variational Quantum Eigensolver (VQE) method will be used until large-scale FTQC with more than 100 logical qubits are realized. Therefore, the VQE method must be improved with respect to both accuracy and time to solution using large resource of the near FTQC . In this paper, we propose Tangent-Vector VQE (TVVQE) method to manage these issues. The method optimizes the norm of tangent vector of trial energy. We demonstrate the calculation of energy levels on Hydrogen molecule, Hubbard model, and Lithium Hydride molecule and reveal that TVVQE has a potential to calculate ground and excited energy levels more accurately than other VQE methods.

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arXiv2021

Splitting of energy levels of Spin-vortex Induced Loop Currents by feeding external currents

The spin-vortex-induced loop current (SVILC) is a nano-sized loop current predicted to exist in the CuO$_2$ plane in the bulk of hole-doped cuprate superconductors. It is a persistent loop current protected by the topological winding number associated with the wave function. It exists around a spin-vortex created by the itinerant electrons with a doped hole at its center. The direction of each SVILC can be either clockwise (winding number is -1) or counterclockwise (winding number is +1) and the winding number with no current (winding number is zero) is forbidden by the singlevalued requirement of the wave function with respect to the electron coordinates. Recently, it has been demonstrated, theoretically, that this degree-of-freedom can be used for qubits. Coupling of neighboring qubits by external current feeding is confirmed to be realizable. This means that nano-sized couplers of SVILC qubits using feeding external currents are realizable. The size of couplers of SVILC qubits can be conparable or smaller than that of trapped ion qubits. Couper size of SVILC qubits is decided by the range of spin vortices in CuO$_2$ plane and current distribution, thus, this is tunable by feeding external current and substituting Cu atoms in barrier atoms. That of trapped ion qubits is limited by the distance that combined vibration occurs or laser range with respect to the coordinates. In the present work, We demonstrated splitting energy levels by external feeding current of three qubit system of SVILC qubits. This means that nano-sized qubit differentiator can be realized, and noise by static magnetic field can be cut off, and this may enable the realizing fully-fault tolerant quantum computers by SVILC qubits. Moreover, the possibility of downscaling of them is shown.

quant-ph↗

arXiv2021

Period and intrinsic noises of permanent spin vortex system centered by small polaron

Some fascinating phenomena have been investigated, hence spin vortex systems are a hot subarea of solid-state physics. However, simulations of these systems require some simplifications. Quantum computers have the potential to simulate these systems without them. Therefore, we simulated the time propagation of spin vortex systems centered by small polarons by the simulator of quantum computers. As a result, we revealed that these systems have much shorter periods than XXZ models and are never be relaxed. Though there is intrinsic persistent noise, this result will affect both fundamental and applied solid-state physics.

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