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Deniz E. Stiegemann

Publications and source records attributed to Deniz E. Stiegemann.

7 recordsLinked to original sources
arXiv2026

Electronically-controlled one- and two-qubit gates for transmon quasicharge qubits

Superconducting protected qubits aim to achieve sufficiently low error rates so as to allow realization of error-corrected, utility-scale quantum computers. A recent proposal encodes a protected qubit in the quasicharge degree of freedom of the conventional transmon device. Operating such a protected `quasicharge qubit' requires implementing new strategies. Here we show that an electronically-controllable tunnel junction formed by two topological superconductors can be used to implement single- and two-qubit gates on quasicharge qubits. Schemes for both these gates are based on the same dynamical $4π$-periodic Josephson effect and therefore have the same gate times and error characteristics. We simulate the dynamics of a topological Josephson junction in a parameter regime with non-negligible charging energy, and characterize the robustness of such gate operations against charge noise. Our results point to a compelling strategy for implementation of quasicharge qubit gates based on junctions of minimal Kitaev chains of quantum dots.

quant-ph↗
arXiv2020

Quantum fields for unitary representations of Thompson's groups F and T

We describe how to define observables analogous to quantum fields for the semicontinuous limit recently introduced by Jones in the study of unitary representations of Thompson's groups $F$ and $T$. We find that, in terms of correlation functions of these fields, one can deduce quantities resembling the conformal data, i.e., primary fields, scaling dimensions, and the operator product expansion. Examples coming from quantum spin systems and anyon chains built on the trivalent category $\mathit{SO}(3)_q$ are studied.

math-ph↗
arXiv2020

Dynamics for holographic codes

We describe how to introduce dynamics for the holographic states and codes introduced by Pastawski, Yoshida, Harlow and Preskill. This task requires the definition of a continuous limit of the kinematical Hilbert space which we argue may be achieved via the semicontinuous limit of Jones. Dynamics is then introduced by building a unitary representation of a group known as Thompson's group T, which is closely related to the conformal group in 1+1 dimensions. The bulk Hilbert space is realised as a special subspace of the semicontinuous limit Hilbert space spanned by a class of distinguished states which can be assigned a discrete bulk geometry. The analogue of the group of large bulk diffeomorphisms is given by a unitary representation of the Ptolemy group Pt, on the bulk Hilbert space thus realising a toy model of the AdS/CFT correspondence which we call the Pt/T correspondence.

quant-ph↗
arXiv2019

Thompson Field Theory

We introduce Thompson field theory, a class of toy models of conformal field theory in which Thompson's group T takes the role of a discrete analogue of the chiral conformal group. T and the related group F are discrete transformations of dyadic partitions of the circle and the unit interval, respectively. When vectors or tensors are associated with partitions, one can construct a direct limit Hilbert space, here called the semicontinuous limit, and F and T have unitary representations on this space. We give an abstract description of these representations following the work of Jones. We also show that T can be thought of as acting on the boundary of an equal-time Poincaré disk in AdS3. This defines a representation of T on the Hilbert space that contains all tree-like holographic states, as introduced by Pastawski, Yoshida, Harlow, and Preskill. It also establishes a bulk-boundary correspondence through Imbert's isomorphism between T and Penner's Ptolemy group. We further propose definitions of field operators and correlation functions for the discrete theory. Finally, we sketch new developments like particle creation and annihilation, as well as black holes and possible connections with topological quantum field theory.

math-ph↗
arXiv2019

The F-Symbols for the H3 Fusion Category

We present a solution for the F-symbols of the H3 fusion category, which is Morita equivalent to the even parts of the Haagerup subfactor. This solution has been computed by solving the pentagon equations and using several properties of trivalent categories.

math.CT↗
arXiv2018

From categories to anyons: a travelogue

In this paper we provide an overview of category theory, focussing on applications in physics. The route we follow is motivated by the final goal of understanding anyons and topological QFTs using category theory. This entails introducing modular tensor categories and fusion rings. Rather than providing an in-depth mathematical development we concentrate instead on presenting the "highlights for a physicist".

quant-ph↗