arXiv subjects

Michael Kastoryano

Publications and source records attributed to Michael Kastoryano.

11 recordsLinked to original sources

arXiv2026

Subsystem self-correction of the GKP qubit

Passive quantum error correction, also known as self-correction, is a holy grail in quantum information science. Recent theoretical advances suggest that the Gottesman-Kitaev-Preskill (GKP) code can exhibit self-correction properties, positioning it as a candidate for the realization of self-correcting quantum memories. In this article, we provide a self-contained derivation of the self-correcting behavior of the ideal GKP Hamiltonian, manifested in the Arrhenius type scaling of the logical lifetime, from a quantum-information perspective based on the subsystem code decomposition. When coupling through the physical quadrature $q$ and $p$, the detailed-balance jump operators decompose into a dominant part acting only on the gauge subsystem and a boundary term that acts non-trivially on the logical qubit. The boundary term is then exponentially suppressed by the Gibbs weights near the edge of the modular cells. In contrast to spin-based quantum memories such as the two-dimensional surface code, the GKP Hamiltonian realizes an effective string tension in modular phase space, whereby the energy cost increases as an error approaches the boundary of a logical sector.

quant-ph↗

arXiv2026

COS-TT-CHF: A Tensor-Train Characteristic-Function COS Method for Multi-Asset Option Pricing

This paper considers European multi-asset option pricing under L\'evy and affine characteristic-function models. The main obstruction is the curse of dimensionality: direct multidimensional COS pricing forms tensor-product coefficient arrays whose size grows exponentially with the number of assets. We study and extend COS-TT-CHF, a low-rank construction that uses TT-cross to compress sampled characteristic-function tensors into tensor-train COS coefficients for arithmetic basket and min/max option pricing. Once built, the compressed representation gives fast post-setup strike-grid and selected component Delta/Vega calculations. The numerical study compares with adaptive-quadrature Fourier benchmarks, direct COS, a tensor-Fourier min-option benchmark, and quasi-Monte Carlo (QMC) references based on randomized Sobol points. The reported timings show a low-dimensional crossover against direct COS as the benchmark moves from $d=2$ to $d=4$, favorable timings against the tensor-Fourier min-option benchmark from $d=3$ onward, and favorable timings against the QMC common-Heston reference already at $d=2$. The reported tests reach $d=30$ for GBM and $d=20$ for VG, NIG, and common-Heston benchmark families, with accuracy, rank, runtime, control-sensitivity, and component Delta/Vega diagnostics reported throughout.

q-fin.CP↗

arXiv2026

(MPO)$^2$: Multivariate Polynomial Optimization based on Matrix Product Operators

Central to machine learning and signal processing is the ability to perform universal function approximation and learn complex input-output relationships from limited numbers of observations. Multivariate polynomial models offer a natural way to express such relationships through multiplicative feature interactions, but their coefficient tensors grow exponentially in size with the polynomial degree. Existing tensorized polynomial models reduce this cost, yet canonical polyadic decompositions have rank-limited expressivity, and tensor train formulations are feature order dependent. We introduce Multivariate Polynomial Optimization based on Matrix Product Operators (MPO)$^2$, a framework that combines learned MPO feature embeddings with compact polynomial weight tensors. This yields feature order independent polynomial representations that can incorporate structured operators such as projections, convolutions, and masks for weight tensor symmetries. Across regression and classification benchmarks, (MPO)$^2$ improves over existing tensor decomposition based polynomial models and provides a flexible alternative for efficient polynomial function approximation.

cs.LG↗

arXiv2026

A tensor-train multidimensional inverse Laplace transform

Laplace transforms and their numerical inverses arise throughout applied mathematics, physics, finance, and probability theory. Numerical inversion, however, quickly becomes intractable in high dimensions because the number of quadrature evaluations grows exponentially with dimension. We develop a tensor train (TT) formulation of the multidimensional inverse Laplace transform. The method constructs a TT approximation of the transformed function on the complex quadrature grid and then performs the inversion through a sequence of tensor contractions. Under suitable low-rank assumptions, this reduces the computational cost from exponential to polynomial in the dimension, provided that the relevant bond dimensions remain bounded. The method has only a small number of tunable parameters and admits error estimations. We demonstrate its performance in numerical experiments, benchmarked against Monte Carlo estimates and exact references, for multivariate normal-inverse Gaussian, Wishart, and correlated Gamma-type distributions.

math.NA↗

arXiv2025

Full grid solution for multi-asset options pricing with tensor networks

Pricing multi-asset options via the Black-Scholes PDE is limited by the curse of dimensionality: classical full-grid solvers scale exponentially in the number of underlyings and are effectively restricted to three assets. Practitioners typically rely on Monte Carlo methods for computing complex instrument involving multiple correlated underlyings. We show that quantized tensor trains (QTT) turn the d-asset Black-Scholes PDE into a tractable high-dimensional problem on a personal computer. We construct QTT representations of the operator, payoffs, and boundary conditions with ranks that scale polynomially in d and polylogarithmically in the grid size, and build two solvers: a time-stepping algorithm for European and American options and a space-time algorithm for European options. We compute full-grid prices and Greeks for correlated basket and max-min options in three to five dimensions with high accuracy. The methods introduced can comfortably be pushed to full-grid solutions on 10-15 underlyings, with further algorithmic optimization and more compute power.

q-fin.CP↗

arXiv2025

Fast and Flexible Quantum-Inspired Differential Equation Solvers with Data Integration

Accurately solving high-dimensional partial differential equations (PDEs) remains a central challenge in computational mathematics. Traditional numerical methods, while effective in low-dimensional settings or on coarse grids, often struggle to deliver the precision required in practical applications. Recent machine learning-based approaches offer flexibility but frequently fall short in terms of accuracy and reliability, particularly in industrial contexts. In this work, we explore a quantum-inspired method based on quantized tensor trains (QTT), enabling efficient and accurate solutions to PDEs in a variety of challenging scenarios. Through several representative examples, we demonstrate that the QTT approach can achieve logarithmic scaling in both memory and computational cost for linear and nonlinear PDEs. Additionally, we introduce a novel technique for data-driven learning within the quantum-inspired framework, combining the adaptability of neural networks with enhanced accuracy and reduced training time.

math.NA↗

arXiv2025

Functional matrix product state simulation of continuous variable quantum circuits

We introduce a functional matrix product state (FMPS) based method for simulating the real-space representation of continuous-variable (CV) quantum computation. This approach efficiently simulates non-Gaussian CV systems by leveraging their functional form. By addressing scaling bottlenecks, FMPS enables more efficient simulation of shallow, multi-mode CV quantum circuits with non-Gaussian input states. The method is validated by simulating random shallow and cascaded circuits with highly non-Gaussian input states, showing superior performance compared to existing techniques, also in the presence of loss.

quant-ph↗

arXiv2022

Is there evidence for exponential quantum advantage in quantum chemistry?

The idea to use quantum mechanical devices to simulate other quantum systems is commonly ascribed to Feynman. Since the original suggestion, concrete proposals have appeared for simulating molecular and materials chemistry through quantum computation, as a potential ``killer application''. Indications of potential exponential quantum advantage in artificial tasks have increased interest in this application, thus, it is critical to understand the basis for potential exponential quantum advantage in quantum chemistry. Here we gather the evidence for this case in the most common task in quantum chemistry, namely, ground-state energy estimation. We conclude that evidence for such an exponential advantage across chemical space has yet to be found. While quantum computers may still prove useful for quantum chemistry, it may be prudent to assume exponential speedups are not generically available for this problem.

physics.chem-ph↗

arXiv2022

A highly efficient tensor network algorithm for multi-asset Fourier options pricing

Risk assessment and in particular derivatives pricing is one of the core areas in computational finance and accounts for a sizeable fraction of the global computing resources of the financial industry. We outline a quantum-inspired algorithm for multi-asset options pricing. The algorithm is based on tensor networks, which have allowed for major conceptual and numerical breakthroughs in quantum many body physics and quantum computation. In the proof-of-concept example explored, the tensor network approach yields several orders of magnitude speedup over vanilla Monte Carlo simulations. We take this as good evidence that the use of tensor network methods holds great promise for alleviating the computation burden of risk evaluation in the financial and other industries, thus potentially lowering the carbon footprint these simulations incur today.

quant-ph↗

arXiv2020

Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer

We compare the BFGS optimizer, ADAM and Natural Gradient Descent (NatGrad) in the context of Variational Quantum Eigensolvers (VQEs). We systematically analyze their performance on the QAOA ansatz for the Transverse Field Ising Model (TFIM) as well as on overparametrized circuits with the ability to break the symmetry of the Hamiltonian. The BFGS algorithm is frequently unable to find a global minimum for systems beyond about 20 spins and ADAM easily gets trapped in local minima. On the other hand, NatGrad shows stable performance on all considered system sizes, albeit at a significantly higher cost per epoch. In sharp contrast to most classical gradient based learning, the performance of all optimizers is found to decrease upon seemingly benign overparametrization of the ansatz class, with BFGS and ADAM failing more often and more severely than NatGrad. Additional tests for the Heisenberg XXZ model corroborate the accuracy problems of BFGS in high dimensions, but they reveal some shortcomings of NatGrad as well. Our results suggest that great care needs to be taken in the choice of gradient based optimizers and the parametrization for VQEs.

quant-ph↗

arXiv2015

Quantum reverse hypercontractivity

We develop reverse versions of hypercontractive inequalities for quantum channels. By generalizing classical techniques, we prove a reverse hypercontractive inequality for tensor products of qubit depolarizing channels. We apply this to obtain a rapid mixing result for depolarizing noise applied to large subspaces, and to prove bounds on a quantum generalization of non-interactive correlation distillation.

quant-ph↗