arXiv subjects

Leon Bollmann

Publications and source records attributed to Leon Bollmann.

4 recordsLinked to original sources

arXiv2026

Benchmarking Techniques for Decoded Quantum Interferometry

We develop a new benchmarking scheme for the Decoded Quantum Interferometry (DQI) algorithm quantifying the number of quantum gates required to obtain an optimal solution to a problem amenable to DQI. We apply the benchmarking scheme to the Binary Paint Shop Problem (BPSP) in order to benchmark the performance of DQI against a state of the art classical solver. To do so, we provide an explicit construction of a quantum circuit implementation of a greedy decoder for low-density parity check codes arising from max-2-XORSAT problems.

quant-ph↗

arXiv2025

An enhanced term in the Szeg\H{o}-type asymptotics for the free massless Dirac operator

We consider a regularised Fermi projection of the Hamiltonian of the massless Dirac equation at Fermi energy zero. The matrix-valued symbol of the resulting operator is discontinuous in the origin. For this operator, we prove Szeg\H{o}-type asymptotics with the spatial cut-off domains given by $d$-dimensional cubes. For analytic test functions, we obtain a $d$-term asymptotic expansion and provide an upper bound of logarithmic order for the remaining terms. This bound does not depend on the regularisation. In the special case that the test function is given by a polynomial of degree less or equal than three, we prove a $(d+1)$-term asymptotic expansion with an error term of constant order. The additional term is of logarithmic order and its coefficient is independent of the regularisation.

math.SP↗

arXiv2024

Enhanced area law in the Widom-Sobolev formula for the free Dirac operator in arbitrary dimension

We prove a logarithmically enhanced area law for all R\'enyi entanglement entropies of the ground state of a free gas of relativistic Dirac fermions. Such asymptotics occur in any dimension if the modulus of the Fermi energy is larger than the mass of the particles and in the massless case at Fermi energy zero in one space dimension. In all other cases of mass, Fermi energy and dimension, the entanglement entropy grows no faster than the area of the involved spatial region. The result is established for a general class of test functions which includes the ones corresponding to R\'enyi entropies and relies on a recently proved extension of the Widom-Sobolev formula to matrix-valued symbols by the authors.

math-ph↗

arXiv2023

The Widom-Sobolev formula for discontinuous matrix-valued symbols

We prove the Widom-Sobolev formula for the asymptotic behaviour of truncated Wiener-Hopf operators with discontinuous matrix-valued symbols for three different classes of test functions. The symbols may depend on both position and momentum except when closing the asymptotics for twice differentiable test functions with H\"older singularities. The cut-off domains are allowed to have piecewise differentiable boundaries. In contrast to the case where the symbol is smooth in one variable, the resulting coefficient in the enhanced area law we obtain here remains as explicit for matrix-valued symbols as it is for scalar-valued symbols.

math.SP↗