Ryan L. Mann
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View article: A graph-theoretic framework for free-parafermion solvability
A graph-theoretic framework for free-parafermion solvability Open
We present a graph-theoretic characterization of when a quantum spin model admits an exact solution via a mapping to free parafermions. Our characterization is based on the concept of a frustration graph, which represents the commutation r…
View article: A Graph-Theoretic Framework for Free-Parafermion Solvability
A Graph-Theoretic Framework for Free-Parafermion Solvability Open
We present a graph-theoretic characterisation of when a quantum spin model admits an exact solution via a mapping to free parafermions. Our characterisation is based on the concept of a frustration graph, which represents the commutation r…
Optimal Scheduling of Graph States via Path Decompositions Open
We study the optimal scheduling of graph states in measurement-based quantum computation, establishing an equivalence between measurement schedules and path decompositions of graphs. We define the spatial cost of a measurement schedule bas…
Algorithmic Cluster Expansions for Quantum Problems Open
We establish a general framework for developing approximation algorithms for a class of counting problems. Our framework is based on the cluster expansion of the abstract polymer model formalism of Kotecký and Preiss. We apply our framewor…
View article: Efficient Algorithms for Approximating Quantum Partition Functions at Low Temperature
Efficient Algorithms for Approximating Quantum Partition Functions at Low Temperature Open
We establish an efficient approximation algorithm for the partition functions of a class of quantum spin systems at low temperature, which can be viewed as stable quantum perturbations of classical spin systems. Our algorithm is based on c…
Algorithmic Cluster Expansions for Quantum Problems Open
We establish a general framework for developing approximation algorithms for a class of counting problems. Our framework is based on the cluster expansion of abstract polymer models formalism of Kotecký and Preiss. We apply our framework t…
View article: A Unified Graph-Theoretic Framework for Free-Fermion Solvability
A Unified Graph-Theoretic Framework for Free-Fermion Solvability Open
We show that a quantum spin system has an exact description by non-interacting fermions if its frustration graph is claw-free and contains a simplicial clique. The frustration graph of a spin model captures the pairwise anticommutation rel…
Quantum Parameterized Complexity Open
Parameterized complexity theory was developed in the 1990s to enrich the complexity-theoretic analysis of problems that depend on a range of parameters. In this paper we establish a quantum equivalent of classical parameterized complexity …
View article: Efficient algorithms for approximating quantum partition functions
Efficient algorithms for approximating quantum partition functions Open
We establish a polynomial-time approximation algorithm for partition functions of quantum spin models at high temperature. Our algorithm is based on the quantum cluster expansion of Netočný and Redig and the cluster expansion approach to d…
Data from "Simulating Quantum Computations with Tutte Polynomials" Open
Source code and experimental data for the paper "Simulating Quantum Computations with Tutte Polynomials" by Ryan L. Mann.
View article: On the Parameterised Complexity of Induced Multipartite Graph Parameters
On the Parameterised Complexity of Induced Multipartite Graph Parameters Open
We introduce a family of graph parameters, called induced multipartite graph parameters, and study their computational complexity. First, we consider the following decision problem: an instance is an induced multipartite graph parameter $p…
Quantum computation and combinatorial structures Open
This thesis explores the relationship between quantum computation and combinatorial structures, with the goal of improving our understanding of the complexity of quantum computation. We begin by studying the case when the complexity of com…
On the Complexity of Random Quantum Computations and the Jones Polynomial Open
There is a natural relationship between Jones polynomials and quantum computation. We use this relationship to show that the complexity of evaluating relative-error approximations of Jones polynomials can be used to bound the classical com…
Efficient recycling strategies for preparing large Fock states from single-photon sources: Applications to quantum metrology Open
Fock states are a fundamental resource for many quantum technologies such as\nquantum metrology. While much progress has been made in single-photon source\ntechnologies, preparing Fock states with large photon number remains\nchallenging. …