arXiv subjects

Yudai Suzuki

Publications and source records attributed to Yudai Suzuki.

At least 19 recordsLinked to original sources

arXiv2026

On some generalizations of Gödel's second incompleteness theorem

In this note, we give some generalizations of Gödel's second incompleteness theorem and study their surroundings. We revisit it from two perspectives. One perspective is the relationship between the definable complexity of a theory and unprovability of its soundness. We clarify the relationship between this perspective and induction axioms. We also determine the logical strength of Craig's trick, which is important for studying the definability of a theory, from the point of view of reverse mathematics. The other perspective is semantic incompleteness. The second incompleteness theorem may be seen as the unprovability of the existence of a model. It is known that `model' is replaced with `$ω$-model' or `$β_n$-model'. We give a new and unified proof of the $ω$-model and $β_n$-model versions of the incompleteness theorem.

math.LO↗

arXiv2026

Double-bracket quantum algorithms for thermal state preparation

We propose quantum algorithms for preparing thermal states via the simulation of the thermofield double states. The key idea is to leverage double-bracket quantum algorithms to implement imaginary-time evolution on thermofield double states, whose reduced state realizes the Gibbs state. Our method, termed double-bracket thermofield double (DB-TFD), introduces two variants. The first, the vanilla DB-TFD algorithm, directly implements imaginary-time evolution using double-bracket quantum imaginary-time evolution. The second, poly DB-TFD, employs double-bracket quantum signal processing to approximate the imaginary-time evolution operator via a polynomial transformation. We demonstrate that the complexity of the poly DB-TFD algorithm scales exponentially with the inverse temperature in a broad practical regime. This scaling is consistent with existing methods, and numerical simulations support the corresponding theoretical bound. We further demonstrate the utility of DB-TFD in quantum Boltzmann machines for generative modeling, achieving improved performance compared with variational imaginary-time evolution approaches. These results establish DB-TFD as a promising route for thermal state preparation in the near-term and early-fault-tolerant regimes.

quant-ph↗

arXiv2026

Learning from imperfect quantum data via unsupervised domain adaptation with classical shadows

Learning from quantum data using classical machine learning models has emerged as a promising paradigm toward realizing quantum advantages. Despite extensive analyses on their performance, clean and fully labeled quantum data from the target domain are often unavailable in practical scenarios, forcing models to be trained on data collected under conditions that differ from those encountered at deployment. This mismatch highlights the need for new approaches beyond the common assumptions of prior work. In this work, we address this issue by employing an unsupervised domain adaptation framework for learning from imperfect quantum data. Specifically, by leveraging classical representations of quantum states obtained via classical shadows, we perform unsupervised domain adaptation entirely within a classical computational pipeline once measurements on the quantum states are executed. We numerically evaluate the framework on quantum phases of matter and entanglement classification tasks under realistic domain shifts. Across both tasks, our method outperforms source-only non-adaptive baselines and target-only unsupervised learning approaches, demonstrating the practical applicability of domain adaptation to realistic quantum data learning.

quant-ph↗

arXiv2026

Grover's algorithm is an approximation of imaginary-time evolution

We reveal the power of Grover's algorithm from thermodynamic and geometric perspectives by showing that it is a product formula approximation of imaginary-time evolution (ITE), a Riemannian gradient flow on the special unitary group. This ITE formulation provides a unified perspective on Grover's algorithm, its variants and extensions to widely used quantum subroutines including amplitude amplification and oblivious amplitude amplification. Specifically, the framework explains the choice of angles in the original Grover's algorithm and $π/3$-algorithm. It also motivates a new $π/2$-algorithm, for cases a modest failure probability is acceptable, that converges faster than the $π/3$-algorithm without overshooting. Our analysis further provides a link between ITE and quantum signal processing, which yields a new implementation of the fixed-point quantum search algorithm. Moreover, the ITE formulation can systematically reproduce widely-used subroutines in modern quantum algorithms, such as (oblivious) amplitude amplification. These results collectively establish a deeper understanding of Grover's algorithm and suggest a potential role for thermodynamics and geometry in quantum algorithm design.

quant-ph↗

arXiv2025

On Dequantization of Supervised Quantum Machine Learning via Random Fourier Features

In the quest for quantum advantage, a central question is under what conditions can classical algorithms achieve a performance comparable to quantum algorithms--a concept known as dequantization. Random Fourier features (RFFs) have demonstrated potential for dequantizing certain quantum neural networks (QNNs) applied to regression tasks, but their applicability to other learning problems and architectures remained unexplored. In this work, we derive bounds on the true risk gap between classical RFF models and quantum models for regression and classification tasks with both QNN and quantum kernel architectures. Furthermore, we provide sufficient conditions under which this gap is small and thus the quantum system can be dequantized via the RFF method. We support our findings with numerical experiments that illustrate the practical dequantization of existing quantum kernel-based methods. Our findings not only broaden the applicability of RFF-dequantization but also enhance the understanding of potential quantum advantages in practical machine-learning tasks.

quant-ph↗

arXiv2025

Double-bracket algorithm for quantum signal processing without post-selection

Quantum signal processing (QSP), a framework for implementing matrix-valued polynomials, is a fundamental primitive in various quantum algorithms. Despite its versatility, a potentially underappreciated challenge is that all systematic protocols for implementing QSP rely on post-selection. This can impose prohibitive costs for tasks when amplitude amplification cannot sufficiently improve the success probability. For example, in the context of ground-state preparation, this occurs when using a too poor initial state. In this work, we introduce a new formula for implementing QSP transformations of Hermitian matrices, which requires neither auxiliary qubits nor post-selection. Rather, using approximation to the exact unitary synthesis, we leverage the theory of the double-bracket quantum algorithms to provide a new quantum algorithm for QSP, termed Double-Bracket QSP (DB-QSP). The algorithm requires the energy and energetic variance of the state to be measured at each step and has a recursive structure, which leads to circuit depths that can grow super exponentially with the degree of the polynomial. With these strengths and caveats in mind, DB-QSP should be viewed as complementing the established QSP toolkit. In particular, DB-QSP can deterministically implement low-degree polynomials to "warm start" QSP methods involving post-selection.

quant-ph↗

arXiv2025

Role of scrambling and noise in temporal information processing with quantum systems

Scrambling quantum systems have attracted attention as effective substrates for temporal information processing. Here we consider a quantum reservoir processing framework that captures a broad range of physical computing models with quantum systems. We examine the scalability and memory retention of the model with scrambling reservoirs modelled by high-order unitary designs in both noiseless and noisy settings. In the former regime, we show that measurement readouts become exponentially concentrated with increasing reservoir size, yet strikingly do not worsen with the reservoir iterations. Thus, while repeatedly reusing a small scrambling reservoir with quantum data might be viable, scaling up the problem size deteriorates generalization unless one can afford an exponential shot overhead. In contrast, the memory of early inputs and initial states decays exponentially in both reservoir size and reservoir iterations. In the noisy regime, we also prove that memory decays exponentially in time for local noisy channels. These results required us to introduce new proof techniques for bounding concentration in temporal quantum models.

quant-ph↗

arXiv2025

Double-bracket quantum algorithms for quantum imaginary-time evolution

Efficiently preparing approximate ground-states of large, strongly correlated systems on quantum hardware is challenging and yet nature is innately adept at this. This has motivated the study of thermodynamically inspired approaches to ground-state preparation that aim to replicate cooling processes via imaginary-time evolution. However, synthesizing quantum circuits that efficiently implement imaginary-time evolution is itself difficult, with prior proposals generally adopting heuristic variational approaches or using deep block encodings. Here, we use the insight that quantum imaginary-time evolution is a solution of Brockett's double-bracket flow and synthesize circuits that implement double-bracket flows coherently on the quantum computer. We prove that our Double-Bracket Quantum Imaginary-Time Evolution (DB-QITE) algorithm inherits the cooling guarantees of imaginary-time evolution. Concretely, each step is guaranteed to i) decrease the energy of an initial approximate ground-state by an amount proportion to the energy fluctuations of the initial state and ii) increase the fidelity with the ground-state. We provide gate counts for DB-QITE through numerical simulations in Qrisp which demonstrate scenarios where DB-QITE outperforms quantum phase estimation. Thus DB-QITE provides a means to systematically improve the approximation of a ground-state using shallow circuits.

quant-ph↗

arXiv2024

On some subtheories of strong dependent choice

In this paper, we give characterizations of the set of $Π^1_{e}$-consequences, $Σ^1_{e}$-consequences and $\mathsf{B}(Π^1_{e})$-consequences of the axiomatic system of the strong dependent choice for $Σ^1_i$ formulas $Σ^1_i$-$\mathsf{SDC}_0$ for $i > 0$ and $e < i+2$. Here, $\mathsf{B}(Γ)$ denotes the set generated by $\land,\lor,\lnot$ starting from $Γ$.

math.LO↗

arXiv2024

On the $Π^1_2$ consequences of $Π^1_1$-$\mathsf{CA}_0$

In this paper, we introduce a hierarchy dividing the set $\{σ\in Π^1_2 : Π^1_1$-$\mathsf{CA}_0 \vdash σ\}$. Then, we give some characterizations of this set using weaker variants of some principles equivalent to $Π^1_1$-$\mathsf{CA}_0$: leftmost path principle, Ramsey's theorem for $Σ^0_n$ classes of $[\mathbb{N}]^{\mathbb{N}}$ and determinacy for $(Σ^0_1)_n$ classes of $\mathbb{N}^{\mathbb{N}}$.

math.LO↗

arXiv2024

An Ising Machine Formulation for Design Updates in Topology Optimization of Flow Channels

Topology optimization is an essential tool in computational engineering, for example, to improve the design and efficiency of flow channels. At the same time, Ising machines, including digital or quantum annealers, have been used as efficient solvers for combinatorial optimization problems. Beyond combinatorial optimization, recent works have demonstrated applicability to other engineering tasks by tailoring corresponding problem formulations. In this study, we present a novel Ising machine formulation for computing design updates during topology optimization with the goal of minimizing dissipation energy in flow channels. We explore the potential of this approach to improve the efficiency and performance of the optimization process. To this end, we conduct experiments to study the impact of various factors within the novel formulation. Additionally, we compare it to a classical method using the number of optimization steps and the final values of the objective function as indicators of the time intensity of the optimization and the performance of the resulting designs, respectively. Our findings show that the proposed update strategy can accelerate the topology optimization process while producing comparable designs. However, it tends to be less exploratory, which may lead to lower performance of the designs. These results highlight the potential of incorporating Ising formulations for optimization tasks but also show their limitations when used to compute design updates in an iterative optimization process. In conclusion, this work provides an efficient alternative for design updates in topology optimization and enhances the understanding of integrating Ising machine formulations in engineering optimization.

cs.CE↗

arXiv2024

Relative leftmost path principles and omega-model reflections of transfinite inductions

In this paper, we give characterizations of Towsner's relative leftmost path principles in terms of omega-model reflections of transfinite inductions. In particular, we show that the omega-model reflection of $Π^1_{n+1}$ transfinite induction is equivalent to the $Σ^0_n$ relative leftmost path principle over $\mathsf{RCA}_0$ for $n > 1$. As a consequence, we have that $Σ^0_{n+1}\mathsf{LPP}$ is strictly stronger than $Σ^0_{n}\mathsf{LPP}$.

math.LO↗

arXiv2024

A Study on Quantum Car-Parrinello Molecular Dynamics with Classical Shadows for Resource Efficient Molecular Simulation

Ab-initio molecular dynamics (AIMD) is a powerful tool to simulate physical movements of molecules for investigating properties of materials. While AIMD is successful in some applications, circumventing its high computational costs is imperative to perform large-scale and long-time simulations. In recent days, near-term quantum computers have attracted much attentions as a possible solution to alleviate the challenge. Specifically, Kuroiwa et al. proposed a new AIMD method called quantum Car-Parrinello molecular dynamics (QCPMD), which exploits the Car-Parrinello method and Langevin formulation to realize cost-efficient simulations at the equilibrium state, using near-term quantum devices. In this work, we build on the proposed QCPMD method and introduce the classical shadow technique to further improve resource efficiency of the simulations. More precisely, classical shadows are used to estimate the forces of all nuclei simultaneously, implying this approach is more effective as the number of molecules increases. We numerically study the performance of our scheme on the $\text{H}_2$ molecule and show that QCPMD with classical shadows can simulate the equilibrium state. Our results will give some insights into efficient AIMD simulations on currently-available quantum computers.

quant-ph↗

arXiv2024

Searching problems above arithmetical transfinite recursion

We investigate some Weihrauch problems between $\mathsf{ATR}_2$ and $\mathsf{C}_{ω^ω}$ . We show that the fixed point theorem for monotone operators on the Cantor space (a weaker version of the Knaster-Tarski theorem) is not Weihrauch reducible to $\mathsf{ATR}_2$. Furthermore, we introduce the $ω$-model reflection $\mathsf{ATR}_2^{\mathrm{rfn}}$ of $\mathsf{ATR} $ and show that it is an upper bound for problems provable from the axiomatic system $\mathrm{ATR}_0$ which are of the form $\forall X(θ(X) \to \exists Y η(X, Y ))$ with arithmetical formulas $θ, η$. We also show that Weihrauch degrees of relativized least fixed point theorem for monotone operators on the Cantor space forms a linear hierarchy between $\mathsf{ATR}^{\mathrm{rfn}}$ and $\mathsf{C}_{ω^ω} $.

math.LO↗

arXiv2024

Light-cone feature selection for quantum machine learning

Feature selection plays an essential role in improving the predictive performance and interpretability of trained models in classical machine learning. On the other hand, the usability of conventional feature selection could be limited for quantum machine learning tasks; the technique might not provide a clear interpretation on embedding quantum circuits for classical data tasks and, more importantly, is not applicable to quantum data tasks. In this work, we propose a feature selection method with a specific focus on quantum machine learning. Our scheme treats the light-cones (i.e., subspace) of quantum models as features and then select relevant ones through training of the corresponding local quantum kernels. We numerically demonstrate its versatility for four different applications using toy tasks: (1) feature selection of classical inputs, (2) circuit architecture search for data embedding, (3) compression of quantum machine learning models and (4) subspace selection for quantum data. The proposed framework paves the way towards applications of quantum machine learning to practical tasks. Also, this technique could be used to practically test if the quantum machine learning tasks really need quantumness, while it is beyond the scope of this work.

quant-ph↗

arXiv2023

Enhancing VQE Convergence for Optimization Problems with Problem-specific Parameterized Quantum Circuits

The Variational Quantum Eigensolver (VQE) algorithm is gaining interest for its potential use in near-term quantum devices. In the VQE algorithm, parameterized quantum circuits (PQCs) are employed to prepare quantum states, which are then utilized to compute the expectation value of a given Hamiltonian. Designing efficient PQCs is crucial for improving convergence speed. In this study, we introduce problem-specific PQCs tailored for optimization problems by dynamically generating PQCs that incorporate problem constraints. This approach reduces a search space by focusing on unitary transformations that benefit the VQE algorithm, and accelerate convergence. Our experimental results demonstrate that the convergence speed of our proposed PQCs outperforms state-of-the-art PQCs, highlighting the potential of problem-specific PQCs in optimization problems.

quant-ph↗

arXiv2023

Quantum reservoir computing with repeated measurements on superconducting devices

Reservoir computing is a machine learning framework that uses artificial or physical dissipative dynamics to predict time-series data using nonlinearity and memory properties of dynamical systems. Quantum systems are considered as promising reservoirs, but the conventional quantum reservoir computing (QRC) models have problems in the execution time. In this paper, we develop a quantum reservoir (QR) system that exploits repeated measurement to generate a time-series, which can effectively reduce the execution time. We experimentally implement the proposed QRC on the IBM's quantum superconducting device and show that it achieves higher accuracy as well as shorter execution time than the conventional QRC method. Furthermore, we study the temporal information processing capacity to quantify the computational capability of the proposed QRC; in particular, we use this quantity to identify the measurement strength that best tradeoffs the amount of available information and the strength of dissipation. An experimental demonstration with soft robot is also provided, where the repeated measurement over 1000 timesteps was effectively applied. Finally, a preliminary result with 120 qubits device is discussed.

quant-ph↗

arXiv2023

Effect of alternating layered ansatzes on trainability of projected quantum kernel

Quantum kernel methods have been actively examined from both theoretical and practical perspectives due to the potential of quantum advantage in machine learning tasks. Despite a provable advantage of fine-tuned quantum kernels for specific problems, widespread practical usage of quantum kernel methods requires resolving the so-called vanishing similarity issue, where exponentially vanishing variance of the quantum kernels causes implementation infeasibility and trainability problems. In this work, we analytically and numerically investigate the vanishing similarity issue in projected quantum kernels with alternating layered ansatzes. We find that variance depends on circuit depth, size of local unitary blocks and initial state, indicating the issue is avoidable if shallow alternating layered ansatzes are used and initial state is not highly entangled. Our work provides some insights into design principles of projected quantum kernels and implies the need for caution when using highly entangled states as input to quantum kernel-based learning models.

quant-ph↗