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Howard J. Schnitzer

Publications and source records attributed to Howard J. Schnitzer.

At least 19 recordsLinked to original sources
arXiv2026

Topological Preparation of Non-Stabilizer States and Clifford Evolution in $SU(2)_1$ Chern-Simons Theory

We develop a topological framework for preparing families of non-stabilizer states, and computing their entanglement entropies, in $SU(2)_1$ Chern-Simons theory. Using the Kac-Moody algebra, we construct Pauli and Clifford operators as path integrals over 3-manifolds with Wilson loop insertions, enabling an explicit topological realization of $W_n$ and Dicke states, as well as their entanglement properties. We further establish a correspondence between Clifford group action and modular transformations generated by Dehn twists on genus-$g$ surfaces, linking the mapping class group to quantum operations. Our results extend existing topological constructions for stabilizer states to include families of non-stabilizer states, improving the geometric interpretation of entanglement and quantum resources in topological quantum field theory.

hep-th↗
arXiv2026

Magic and Non-Clifford Gates in Topological Quantum Field Theory

Non-Clifford gates, used to generate quantum magic, are essential for universal quantum computation. We show that non-Clifford gates arise naturally from path integrals in topological quantum field theories, where their magic-generating properties are determined by the algebraic data of the theory. In Chern-Simons theory, we construct the Ising interaction gate, whose generator is prepared by path integration over simple three-boundary manifolds, and show that it produces non-local magic away from discrete Clifford points. We show that the Toffoli gate is obstructed in $SU(2)_1$ by the $\mathbb{Z}_2$ fusion structure, while $SU(2)_3$ is the minimal theory supporting the required conditional logic, given the density of the mapping class group in the projective unitary group on the manifold boundary. Finally, we demonstrate that the T gate arises as a path integral in Dijkgraaf-Witten theory, with gauge group $\mathbb{Z}_4$, where a single Dehn twist on the boundary torus produces the gate without approximation. These results show that topological path integrals construct gates in multiple levels of the Clifford hierarchy, and across distinct classes of field theories, with implications for topological quantum computing.

hep-th↗
arXiv2023

Entropy Cones and Entanglement Evolution for Dicke States

The $N$-qubit Dicke states $|D^N_k\rangle$, of Hamming-weight $k$, are a class of entangled states which play an important role in quantum algorithm optimization. We present a general calculation of entanglement entropy in Dicke states, which we use to describe the $|D^N_k\rangle$ entropy cone. We demonstrate that all $|D^N_k\rangle$ entropy vectors emerge symmetrized, and use this to define a min-cut protocol on star graphs which realizes $|D^N_k\rangle$ entropy vectors. We identify the stabilizer group for all $|D^N_k\rangle$, under the action of the $N$-qubit Pauli group and two-qubit Clifford group, which we use to construct $|D^N_k\rangle$ reachability graphs. We use these reachability graphs to analyze and bound the evolution of $|D^N_k\rangle$ entropy vectors in Clifford circuits.

quant-ph↗
arXiv2022

The entropy cones of $W_N$ and $W_N^d$ states

The quantum entropy cones (QEC) for $W_N$ states of qubits and $W_N^d$ states of qudits are computed. These cones emerge as symmetrized quantum entropy cones (SQEC) for arbitrary $N$ and $d$. Directed graph models are presented which describe the SQEC for $W_N$ states and $W_N^d$ states. Monogamous mutual information (MMI) is violated for all $N>3$.

hep-th↗
arXiv2021

Level-rank duality of knot and link invariants

A number of results for the level-rank duality of $G(N)_K$ $\leftrightarrow$ $G(K)_N$ Chern-Simons theory are summarized, with emphasis on the applications to knot and link invariants. Explicit examples for $SU(2)_K$ $\leftrightarrow$ $SU(K)_2$ illustrate general results. A criterion to distinguish torus knots and links from hyperbolic knots and links, based on tables constructed by Kaul for one and two strand invariants, is presented. Possible symmetries of hyperbolic knot and link invariants are discussed. The level-rank duality of torus knot and link invariants of minimal models is examined

math.GT↗
arXiv2021

Hypergraph States in SU(N)1, N odd prime, Chern-Simons Theory

Graph states and hypergraph states can be constructed from products of basic operations that appear in SU(N)1. The level-rank dual of a theorem of Salton, Swingle, and Walter implies that these operations can be prepared topologically in the n-torus Hilbert space of Chern-Simons theory for N neq 5 mod 4. For SU(N)1, N = 5 mod 4, only stabilizer states can be prepared on the n-torus Hilbert space, which restricts the construction to graph states.

hep-th↗
arXiv2020

The Crucial Calculation as a Motivating Force In Particle Physics

Crucial experiments have a long history of contributions to progress in physics. Similarly, we claim that in the period roughly from 1955 to 1985 crucial calculations played a significant role in setting the agenda for elementary particle physics. The highlights of the contributions of theoretical physics to the achievement of the standard model is emphasized

physics.hist-ph↗
arXiv2020

Clifford operators in SU(N)1; N not odd prime

Farinholt gives a characterization of Clifford operators for qudits; d both odd and even. In this comment it is shown that the necessary gates for the construction of Clifford operators; N both odd and even, are obtained directly from operations that appear in SU(N)1. A witness for W3 states in SU(2)1 is discussed. See e.g. [1-4].

hep-th↗
arXiv2020

SU(N)1 Chern-Simons theory, the Clifford group, and Entropy Cone

Entropy cones for SU(N)1 Chern-Simons theory are discussed. It is shown that stabilizer states can be constructed from topological operators in SU(N)1 for N odd prime, but not for SU(N)K; K >= 2. This implies that the topological entropy cone is properly contained in the stabilizer entropy cone for SU(N)K; K >= 2.

hep-th↗
arXiv2018

Level-rank duality for a Universal Topological Quantum Computer

It is shown, using level-rank duality that a universal topological quantum computer based on Chern-Simons theory for SU(2)$_3$ also implies an analogous universal quantum computer based on SU(3)$_2$. Suggestions are made for the possible role of level-rank duality in entanglement from topology.

hep-th↗
arXiv2016

Rényi Entropy for a $\bf 2d$ CFT with a gauge field: $\bf \widehat{\rm SU}(N)_1$ WZW theory on a branched torus

The Rényi entropy for the $\widehat{\rm SU}(N)_1$ WZW model as described by $N$ free fermions coupled to a $U(1)$ constraint field is computed on an $n$-sheeted branched torus. The boundary condition of the harmonic component of the gauge field on the homology cycles of the genus $g$ Riemann surface is central to the final result. This calculation is complementary to that of arXiv:$1510.05993$, which presents the bose side of the bose-fermi equivalence.

hep-th↗
arXiv2016

Large distance expansion of Mutual Information for disjoint disks in a free scalar theory

We compute the next-to-leading order term in the long-distance expansion of the mutual information for free scalars in three space-time dimensions. The geometry considered is two disjoint disks separated by a distance $r$ between their centers. No evidence for non-analyticity in the Rényi parameter $n$ for the continuation $n \rightarrow 1$ in the next-to-leading order term is found.

hep-th↗
arXiv2016

Holographic Mutual Information at small separations

The holographic mutual information for the small separation of two circles and two strips in 2+1 dimensional space-time is considered based on the known exact minimal surfaces spanning the boundaries on AdS4. The results suggest a universality for the leading term in the short-distance expansion of holographic mutual information. A conjecture for a similar result for d > 2 is also presented, as well as comments about the analogous expansion in conformal field theory.

hep-th↗
arXiv2016

Topological Rényi and Entanglement Entropy for a 2d q-deformed $U(N)$ Yang-Mills theory and its Chern-Simons dual

Rényi and entanglement entropies are constructed for 2d q-deformed topological Yang-Mills theories with gauge group $U(N)$, as well as the dual 3d Chern-Simons (CS) theory on Seifert manifolds. When $q=\exp[2πi/(N+K)]$, and $K$ is odd, the topological Rényi entropy and Wilson line observables of the CS theory can be expressed in terms of the modular transformation matrices of the WZW theory, $\rm{\hat{U}(N)}_{K,N(K+N)}$. If both $K$ and $N$ are odd, there is a level-rank duality of the 2d qYM theory and of the associated CS theory, as well as that of the Rényi and entanglement entropies, and Wilson line observables.

hep-th↗
arXiv2016

Rényi Entropy for the $\sun1$ WZW model on the torus

The $\sun1$ WZW model is constructed on a n-sheeted branched torus, which allows the investigation of the Rényi entropy for a single interval at finite temperature. The small and large interval limits, as well as the low temperature expansion are presented for this theory.

hep-th↗