arXiv subjects

Sergey V. Tarasov

Publications and source records attributed to Sergey V. Tarasov.

5 recordsLinked to original sources

arXiv2025

Derivation of the Loop Hafnian Generating Function for Arbitrary Symmetric Matrices via Gaussian Integration

This short note shows that the recently proposed generating function for loop hafnians -- originally derived using quantum-optical methods for a restricted class of matrices -- is in fact valid for arbitrary symmetric matrices. The proof relies solely on Gaussian integration and does not assume any additional properties inherited from the covariance matrices of quantum Gaussian states.

quant-ph↗

arXiv2024

Boson sampling with self-generation of squeezing via interaction of photons and atoms

We suggest a novel scheme for generating multimode squeezed states for the boson sampling implementation. The idea is to replace a commonly used linear interferometer by a multimode resonator containing a passive optical element consisting of two-level atoms dispersively interacting with photons and self-generating a squeezed compound state of both bosons -- photons and atoms. The suggested scheme does not need (a) on-demand external sources of photons in squeezed or Fock quantum states and (b) numerous interchannel couplers which introduce phase noise and losses that prevent scaling up the system and achieving quantum advantage. The idea is illustrated by a setup based on a Bose-Einstein-condensed gas confined in a multimode resonator, one of whose optical modes is in the classical coherent regime. The joint probability distribution of photon and/or noncondensed atom numbers is calculated via a matrix hafnian that, for certain parameters of the system, is hardly to be effectively calculated by classical computers. Such experiments are at reach via existing cavity-QED and cold-gas technology.

quant-ph↗

arXiv2022

Quantum supremacy of the many-body fluctuations in the occupations of the excited particle states in a Bose-Einstein-condensed gas

We find a universal analytic formula for a characteristic function (Fourier transform) of a joint probability distribution for the particle occupation numbers in a BEC gas and the Hafnian Master Theorem generalizing the famous Permanent Master Theorem of MacMahon. We suggest an appealing model, a multi-qubit BEC trap formed by a set of qubit potential wells, and discuss specifics of such an atomic boson-sampling system vs a photonic one. Finally, the process of many-body fluctuations in a BEC trap is #P-hard for computing. It could serve as a basis for demonstrating quantum supremacy of the many-body interacting systems over classical simulators.

cond-mat.stat-mech↗

arXiv2021

Exact recursive calculation of circulant permanents: A band of different diagonals inside a uniform matrix

We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence relations which is based on the permanents of the matrices with defects. The proposed system of linear recurrence equations with variable coefficients provides a powerful tool for the analysis of the circulant permanents, their fast, linear time computing and finding their asymptotics in a large-matrix-size limit. The latter problem is an open fundamental problem. Its solution would be tremendously important for a unified analysis of a wide range of the nature's #P-hard problems, including problems in the physics of many-body systems, critical phenomena, quantum computing, quantum field theory, theory of chaos, fractals, theory of graphs, number theory, combinatorics, cryptography, etc.

cond-mat.stat-mech↗

arXiv2021

Bose-Einstein condensate fluctuations versus an interparticle interaction

We calculate the Bose-Einstein condensate (BEC) occupation statistics vs. the interparticle interaction in a dilute gas with a nonuniform condensate in a box trap within the Bogoliubov approach. The results are compared against the previously found BEC-occupation statistics in (i) an ideal gas and (ii) a weakly interacting gas with a uniform condensate. In particular, we reveal and explicitly describe an appearance of a nontrivial transition from the ideal gas to the Thomas-Fermi regime. The results include finding the main regimes of the BEC statistics - the anomalous non-Gaussian thermally-dominated fluctuations and the Gaussian quantum-dominated fluctuations - as well as a crossover between them and their manifestations in a mesoscopic system. Remarkably, we show that the effect of the boundary conditions, imposed at the box trap, on the BEC fluctuations does not vanish in the thermodynamic limit of a macroscopic system even in the presence of the interparticle interactions. Finally, we discuss a challenging problem of an experimental verification of the theory of the BEC fluctuations addressing a much deeper level of the many-body statistical physics than usually studied quantities related to the mean condensate occupation.

cond-mat.quant-gas↗