arXiv subjects

Andrew Connelly

Publications and source records attributed to Andrew Connelly.

4 recordsLinked to original sources

arXiv2025

Affine Equivalence in the Clifford Hierarchy

In this paper we prove a collection of results on the structure of permutations in the Clifford Hierarchy. First, we leverage results from the cryptography literature on affine equivalence classes of 4-bit permutations which we use to find all 4-qubit permutations in the Clifford Hierarchy. We then use the classification of 4-qubit permutations and previous results on the structure of diagonal gates in the Clifford Hierarchy to prove that all 4-qubit gates in the third level of the Clifford Hierarchy are semi-Clifford. Finally, we introduce the formalism of cycle structures to permutations in the Clifford Hierarchy and prove a general structure theorem about them. We also classify many small cycle structures up to affine equivalence. Interestingly, this classification is independent of the number of qubits.

quant-ph↗

arXiv2023

Quantum computation of dynamical quantum phase transitions and entanglement tomography in a lattice gauge theory

Strongly-coupled gauge theories far from equilibrium may exhibit unique features that could illuminate the physics of the early universe and of hadron and ion colliders. Studying real-time phenomena has proven challenging with classical-simulation methods, but is a natural application of quantum simulation. To demonstrate this prospect, we quantum compute non-equal time correlation functions and perform entanglement tomography of non-equilibrium states of a simple lattice gauge theory, the Schwinger model, using a trapped-ion quantum computer by IonQ Inc. As an ideal target for near-term devices, a recently-predicted [Zache et al., Phys. Rev. Lett. 122, 050403 (2019)] dynamical quantum phase transition in this model is studied by preparing, quenching, and tracking the subsequent non-equilibrium dynamics in three ways: i) overlap echos signaling dynamical transitions, ii) non-equal time correlation functions with an underlying topological nature, and iii) the entanglement structure of non-equilibrium states, including entanglement Hamiltonians. These results constitute the first observation of a dynamical quantum phase transition in a lattice gauge theory on a quantum computer, and are a first step toward investigating topological phenomena in nuclear and high-energy physics using quantum technologies.

quant-ph↗

arXiv2020

Universal location of the Yang-Lee edge singularity in O(N) theories

We determine a previously unknown universal quantity, the location of the Yang-Lee edge singularity for the O($N$) theories in a wide range of $N$ and various dimensions. At large $N$, we reproduce the $N\to\infty$ analytical result on the location of the singularity and, additionally, we obtain the mean-field result for the location in $d=4$ dimensions. In order to capture the nonperturbative physics for arbitrary $N$, $d$ and complex-valued external fields, we use the functional renormalization group approach.

cond-mat.stat-mech↗

arXiv2020

Universality driven analytic structure of QCD crossover: radius of convergence and QCD critical point

Recent lattice QCD calculations show strong indications that the crossover of QCD at zero baryon chemical potential ($μ_B$) is a remnant of the second order chiral phase transition. The non-universal parameters needed to map temperature $T$ and $μ_B$ to the universal properties of the second order chiral phase transition were determined by lattice QCD calculations. Motivated by these advances, first, we discuss the analytic structure of the partition function -- the so-called Yang-Lee edge singularity -- in the QCD crossover regime, solely based on universal properties. Then, utilizing the lattice calculated non-universal parameters, we map this singularity to the real $T$ and complex $μ_B$ plane, in order to find the radius of convergence for a Taylor series expansion of QCD partition function around $μ_B=0$ in the QCD crossover regime. Our most important findings are: (i) An universality-based estimate of the radius of convergence around $μ_B=0$; (ii) Universality and lattice QCD based constraints on the location of the QCD critical point in the $T-μ_B$ plane.

hep-ph↗