Tootfinder

Quantum Fourier Transform Based Denoising: Unitary Filtering for Enhanced Speech Clarity
Rajeshwar Tripathi, Sahil Tomar, Sandeep Kumar, Monika Aggarwal
https://arxiv.org/abs/2509.04851

Quantum Fourier Transform Based Denoising: Unitary Filtering for Enhanced Speech Clarity
This paper introduces a quantum-inspired denoising framework that integrates the Quantum Fourier Transform (QFT) into classical audio enhancement pipelines. Unlike conventional Fast Fourier Transform (FFT) based methods, QFT provides a unitary transformation with global phase coherence and energy preservation, enabling improved discrimination between speech and noise. The proposed approach replaces FFT in Wiener and spectral subtraction filters with a QFT operator, ensuring consistent hyperpara…

Projective representations on operator algebras
Sergio Gir\'on Pacheco
https://arxiv.org/abs/2510.02924 https://arxiv.org/pdf/2510.02924

Projective representations on operator algebras
We establish new restrictions on the values of the lifting obstruction for projective unitary representations of second countable, locally compact Hausdorff groups on operator algebras. Using these, we show that every projective representation on the Jiang--Su algebra lifts to a genuine group representation. We also characterise the possible values of lifting obstructions for finite group projective representations on UHF-algebras of infinite type and Cuntz algebras. Finally we show that certai…

Dynamics of Loschmidt echoes from operator growth in noisy quantum many-body systems
Takato Yoshimura, Lucas S\'a
https://arxiv.org/abs/2509.01585 https://

Dynamics of Loschmidt echoes from operator growth in noisy quantum many-body systems
We study the dynamics of Loschmidt echoes in noisy quantum many-body systems without conservation laws. We first show that the operator Loschmidt echo in noisy unitary dynamics is equivalent to the operator norm of the corresponding dissipative dynamics upon noise averaging. We then analyze this quantity in two complementary ways, revealing universal dynamical behavior. First, we develop a heuristic picture for generic Floquet systems that connects Loschmidt echoes, out-of-time-order correlator…

Non-positive measurements aren't beneficial in quantum metrology for unitary encoding, but can be for open schemes
Paranjoy Chaki, Debarupa Saha, Kornikar Sen, Ujjwal Sen
https://arxiv.org/abs/2509.24585

Non-positive measurements aren't beneficial in quantum metrology for unitary encoding, but can be for open schemes
We investigate whether non-positive operator-valued measurements can be beneficial for quantum metrology. For unitary encoding, we show that non-positive measurements offer no advantage over positive ones. Going over to open encoding, we find, however, that non-positive measurements can be advantageous for certain cases, while it may mirror the unitary case - no advantage over positive measurements - for others. For arbitrary open-system encoding, we identify a sufficient condition under which …

Asymptotically optimal unitary estimation in $\mathrm{SU}(3)$ by the analysis of graph Laplacian
Satoshi Yoshida, Hironobu Yoshida, Mio Murao
https://arxiv.org/abs/2509.20608 ht…

Asymptotically optimal unitary estimation in $\mathrm{SU}(3)$ by the analysis of graph Laplacian
Unitary estimation is the task to estimate an unknown unitary operator $U\in\mathrm{SU}(d)$ with $n$ queries to the corresponding unitary operation, and its accuracy is evaluated by an estimation fidelity. We show that the optimal asymptotic fidelity of $3$-dimensional unitary estimation is given by $F_\mathrm{est}(n,d=3) = 1-\frac{56π^2}{9n^2} + O(n^{-3})$ by the analysis of the graph Laplacian based on the finite element method. We also show the lower bound on the fidelity of $d$-dimensional…

Operator algebra of the information-disturbance tradeoff in quantum measurements
Hollis Williams, Holger F. Hofmann
https://arxiv.org/abs/2510.00064 https://

Operator algebra of the information-disturbance tradeoff in quantum measurements
Quantum measurements can be described by operators that assign conditional probabilities to different outcomes while also describing unavoidable physical changes to the system. Here, we point out that operators describing information gain at minimal disturbance can be expanded into a set of unitary operators representing experimentally distinguishable patterns of disturbance. The observable statistics of disturbance defines a tight upper bound on the information gain of the measurement.

The matched projection and geodesics of the Grassmann manifold
Esteban Andruchow
https://arxiv.org/abs/2508.14870 https://arxiv.org/pdf/2508.14870

The matched projection and geodesics of the Grassmann manifold
Given an idempotent operator $E$ in a complex Hilbert space ${\mathcal H}$, one can associate to it two orthogonal projections: - The polar decomposition $2E-1=(2P-1)|2E-1|$ provides an orthogonal projection $P$. That the unitary part in the decomposition of $2E-1$ is of this form, i.e., a selfadjoint unitary operator, is a remarkable observation done by G. Corach, H. Porta and L. Recht (see references below). - The question of which, among all orthogonal projections, is the one c…

A class of vertex operator algebras generated by Virasoro vectors
Runkang Feng
https://arxiv.org/abs/2510.09397 https://arxiv.org/pdf/2510.09397

A class of vertex operator algebras generated by Virasoro vectors
In this paper, we study a class of simple OZ-type vertex operator algebras $V$ generated by simple Virasoro vectors $ω^{ij}=ω^{ji}$, $1\leq i

Optimal quantum simulation of linear non-unitary dynamics
Guang Hao Low, Rolando D. Somma
https://arxiv.org/abs/2508.19238 https://arxiv.org/pdf/2508.19238…

Optimal quantum simulation of linear non-unitary dynamics
We present a quantum algorithm for simulating the time evolution generated by any bounded, time-dependent operator $-A$ with non-positive logarithmic norm, thereby serving as a natural generalization of the Hamiltonian simulation problem. Our method generalizes the recent Linear-Combination-of-Hamiltonian-Simulation (LCHS) framework. In instances where $A$ is time-independent, we provide a block-encoding of the evolution operator $e^{-At}$ with $\mathcal{O}\big(t\log\frac{1}ε)$ queries to the …

Exact Solvability and Integrability Signatures in a Periodically Driven Infinite-Range Spin Chain: The Case of Floquet interval $\pi/2$
Harshit Sharma, Sashmita Rout, Avadhut V. Purohit, Udaysinh T. Bhosale
https://arxiv.org/abs/2509.19991

Exact Solvability and Integrability Signatures in a Periodically Driven Infinite-Range Spin Chain: The Case of Floquet interval $π/2$
We study the signatures of quantum integrability (QI) in a spin chain model, having infinite-range Ising interaction and subjected to a periodic pulse of an external magnetic field. We analyze the unitary operator, its eigensystem, the single-qubit reduced density matrix, and the entanglement dynamics for arbitrary initial state for any $N$. The QI in our model can be identified through key signatures such as the periodicity of entanglement dynamics and the time-evolved unitary operator, and hi…

Zeros of Holomorphic Functions in Commuting and Non-commuting Variables as Spectral Data
Poornendu Kumar, Jeet Sampat
https://arxiv.org/abs/2510.12718 https://

Zeros of Holomorphic Functions in Commuting and Non-commuting Variables as Spectral Data
We characterize the zero sets of functions in the Schur--Agler class over the unit polydisk as well as functions in the unit ball of the multiplier algebra of the Drury--Arveson space via operators associated with a unitary realization formula for these functions. To this end, new notions of `eigenvalues' for tuples of operators are introduced, where the eigenvalues depend on the operator space structure of the ambient domain. Several examples showcasing the properties of these eigenvalues and …

The unitary group of a $\mathrm{II}_1$ factor is SOT-contractible
David Jekel
https://arxiv.org/abs/2508.05834 https://arxiv.org/pdf/2508.05834

The unitary group of a $\mathrm{II}_1$ factor is SOT-contractible
We show that the unitary group of any SOT-separable $\mathrm{II}_1$ factor $M$, with the strong operator topology, is contractible. Combined with several old results, this implies that the same is true for any SOT-separable von Neumann algebra with no type $\mathrm{I}_n$ direct summands ($n < \infty$). The proof for the $\mathrm{II}_1$-factor case uses regularization via free convolution and Popa's theorem on the existence of approximately free Haar unitaries in $\mathrm{II}_1$ factors.

Symmetric quantum walks on Hamming graphs and their limit distributions
Robert C. Griffiths, Shuhei Mano
https://arxiv.org/abs/2509.26243 https://arxiv.org…

Symmetric quantum walks on Hamming graphs and their limit distributions
We study a class of symmetric quantum walks on Hamming graphs, where the distance between vertices specifies the transition probability. A special model is the simple quantum walk on the hypercube, which has been discussed in the literature. Eigenvalues of the unitary operator of the quantum walks are zeros of certain self-reciprocal polynomials. We obtain a spectral representation of the wave vector, where our systematic treatment relies on the coin space isomorphic to the state space and the …

Weak relative Dixmier property and Popa's intertwining technique for type III subfactors
Yusuke Isono
https://arxiv.org/abs/2508.17592 https://arxiv.or…

Weak relative Dixmier property and Popa's intertwining technique for type III subfactors
Let \( A \subset M \) be an inclusion of von Neumann algebras equipped with a faithful normal semifinite operator valued weight \( E \colon M \to A \). We prove that every positive element \( x \in M \) with \( E(x) < \infty \) satisfies the weak Dixmier property relative to \( A \): the \( σ\)-weak closure of the convex hull of its unitary orbit under \( \mathcal{U}(A) \) intersects the relative commutant \( A' \cap M \). This extends Marrakchi's result for the case of conditional expectation…

Efficient block-encodings require structure
Parker Kuklinski, Benjamin Rempfer, Justin Elenewski, Kevin Obenland
https://arxiv.org/abs/2509.19667 https://a…

Efficient block-encodings require structure
Block-encodings are ubiquitous in quantum computing as a way to represent data within a unitary operator. While several unstructured methods are applicable to arbitrary data, these techniques are burdened by hidden costs and poor accuracy. In this paper, we demonstrate that, even for a small 6-qubit encoding, these structure-agnostic techniques require wildly intractable resources. We compare these resources with an encoding method which respects a mathematical representation of the block, lead…

Quasi-Monte Carlo Method for Linear Combination Unitaries via Classical Post-Processing
Yuya Kawamata, Kosuke Mitarai, Keisuke Fujii
https://arxiv.org/abs/2509.14451 https://

Quasi-Monte Carlo Method for Linear Combination Unitaries via Classical Post-Processing
We propose the quasi-Monte Carlo method for linear combination of unitaries via classical post-processing (LCU-CPP) on quantum applications. The LCU-CPP framework has been proposed as an approach to reduce hardware resources, expressing a general target operator $F(A)$ as $F(A) = \int_V f(t) G(A, t)dt$, where each $G(A, t)$ is proportional to a unitary operator. On a quantum device, $Re[Tr(G(A, t)ρ)]$ can be estimated using the Hadamard test and then combined through classical integration, all…

Replaced article(s) found for math.OA. https://arxiv.org/list/math.OA/new
[1/1]:
- Every conformal net has an associated unitary VOA
Andr\'e G. Henriques, James E. Tener

Quantum kernel and HHL-based support vector machines for multi-class classification
Gabriela Pinheiro, Donovan Slabbert, Luis Kowada, Francesco Petruccione
https://arxiv.org/abs/2509.10190

Quantum kernel and HHL-based support vector machines for multi-class classification
We compare two quantum approaches that use support vector machines for multi-class classification on a reduced Sloan Digital Sky Survey (SDSS) dataset: the quantum kernel-based QSVM and the Harrow-Hassidim-Lloyd least-squares SVM (HHL LS-SVM). Both one-vs-rest and two-step hierarchical classification schemes were implemented. The QSVM involves angle encoding of ten features, two unitary operator blocks consisting of rotational operator gates, and a projective measurement that projects the final…

Observation of Metal-Insulator and Spectral Phase Transitions in Aubry-Andr\'e-Harper Models
Quan Lin, Christopher Cedzich, Qi Zhou, Peng Xue
https://arxiv.org/abs/2508.08255

Observation of Metal-Insulator and Spectral Phase Transitions in Aubry-André-Harper Models
Non-Hermitian extensions of the Aubry-André-Harper (AAH) model reveal a rich variety of phase transitions arising from the interplay of quasiperiodicity and non-Hermiticity. Despite their theoretical significance, experimental explorations remain challenging due to complexities in realizing controlled non-Hermiticity. Here, we present the first experimental realization of the unitary almost-Mathieu operator (UAMO) which simulates the AAH model by employing single-photon quantum walks. Through …