arXiv subjects

Ward L. Vleeshouwers

Publications and source records attributed to Ward L. Vleeshouwers.

3 recordsLinked to original sources

arXiv2023

20-Mode Universal Quantum Photonic Processor

Integrated photonics is an essential technology for optical quantum computing. Universal, phase-stable, reconfigurable multimode interferometers (quantum photonic processors) enable manipulation of photonic quantum states and are one of the main components of photonic quantum computers in various architectures. In this paper, we report the realization of the largest quantum photonic processor to date. The processor enables arbitrary unitary transformations on its 20 input modes with an amplitude fidelity of $F_{\text{Haar}} = 97.4\%$ and $F_{\text{Perm}} = 99.5\%$ for Haar-random and permutation matrices, respectively, an optical loss of 2.9 dB averaged over all modes, and high-visibility quantum interference with $V_{\text{HOM}}=98\%$. The processor is realized in $\mathrm{Si_3N_4}$ waveguides and is actively cooled by a Peltier element.

quant-ph↗

arXiv2023

Unitary matrix integrals, symmetric polynomials, and long-range random walks

Unitary matrix integrals over symmetric polynomials play an important role in a wide variety of applications, including random matrix theory, gauge theory, number theory, and enumerative combinatorics. We derive novel results on such integrals and apply these and other identities to correlation functions of long-range random walks (LRRW) consisting of hard-core bosons. We generalize an identity due to Diaconis and Shahshahani which computes unitary matrix integrals over products of power sum polynomials. This allows us to derive two expressions for unitary matrix integrals over Schur polynomials, which can be directly applied to LRRW correlation functions. We then demonstrate a duality between distinct LRRW models, which we refer to as quasi-local particle-hole duality. We note a relation between the multiplication properties of power sum polynomials of degree $n$ and fermionic particles hopping by $n$ sites. This allows us to compute LRRW correlation functions in terms of auxiliary fermionic rather than hard-core bosonic systems. Inverting this reasoning leads to various results on long-range fermionic models as well. In principle, all results derived in this work can be implemented in experimental setups such as trapped ion systems, where LRRW models appear as an effective description. We further suggest specific correlation functions which may be applied to the benchmarking of such experimental setups.

cond-mat.stat-mech↗

arXiv2021

Topological field theory approach to intermediate statistics

Random matrix models provide a phenomenological description of a vast variety of physical phenomena. Prominent examples include the eigenvalue statistics of quantum (chaotic) systems, which are conveniently characterized using the spectral form factor (SFF). Here, we calculate the SFF of unitary matrix ensembles of infinite order with the weight function satisfying the assumptions of Szegö's limit theorem. We then consider a parameter-dependent critical ensemble which has intermediate statistics characteristic of ergodic-to-nonergodic transitions such as the Anderson localization transition. This same ensemble is the matrix model of $U(N)$ Chern-Simons theory on $S^3$, and the SFF of this ensemble is proportional to the HOMFLY invariant of $(2n,2)$-torus links with one component in the fundamental and one in the antifundamental representation. This is one of a large class of ensembles arising from topological field and string theories which exhibit intermediate statistics. Indeed, the absence of a local order parameter suggests that it is natural to characterize ergodic-to-nonergodic transitions using topological tools, such as we have done here.

cond-mat.str-el↗