Christopher Cedzich
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View article: Twenty dry Martinis for the unitary almost-Mathieu operator
Twenty dry Martinis for the unitary almost-Mathieu operator Open
We solve the dry ten Martini problem for the unitary almost-Mathieu operator with Diophantine frequencies in the non-critical regime.
View article: Observation of Metal-Insulator and Spectral Phase Transitions in Aubry-André-Harper Models
Observation of Metal-Insulator and Spectral Phase Transitions in Aubry-André-Harper Models Open
Non-Hermitian extensions of the Aubry-André-Harper (AAH) model reveal a rich variety of phase transitions arising from the interplay of quasiperiodicity and non-Hermiticity. Despite their theoretical significance, experimental explorations…
View article: Exponential Tail Estimates for Quantum Lattice Dynamics
Exponential Tail Estimates for Quantum Lattice Dynamics Open
We consider the quantum dynamics of a particle on a lattice for large times. Assuming translation invariance, and either discrete or continuous time parameter, the distribution of the ballistically scaled position $$Q(t)/t$$ conver…
View article: Mobility edges in pseudo-unitary quasiperiodic quantum walks
Mobility edges in pseudo-unitary quasiperiodic quantum walks Open
We introduce a Floquet quasicrystal that simulates the motion of Bloch electrons in a homogeneous magnetic field in discrete time steps. We admit the hopping to be non-reciprocal which, via a generalized Aubry duality, leads us to push the…
View article: Absence of bound states for quantum walks and CMV matrices via reflections
Absence of bound states for quantum walks and CMV matrices via reflections Open
We give a criterion based on reflection symmetries in the spirit of Jitomirskaya–Simon to show absence of point spectrum for (split-step) quantum walks and Cantero–Moral–Velázquez (CMV) matrices. To accomplish this, we use some ideas from …
View article: Absolutely continuous edge spectrum of topological insulators with an odd time-reversal symmetry
Absolutely continuous edge spectrum of topological insulators with an odd time-reversal symmetry Open
We show that non-trivial two-dimensional topological insulators protected by an odd time-reversal symmetry have absolutely continuous edge spectrum. To accomplish this, we establish a time-reversal symmetric version of the Wold decompositi…
View article: Absence of Bound States for Quantum Walks and CMV Matrices via Reflections
Absence of Bound States for Quantum Walks and CMV Matrices via Reflections Open
We give a criterion based on reflection symmetries in the spirit of Jitomirskaya--Simon to show absence of point spectrum for (split-step) quantum walks and Cantero--Moral--Velázquez (CMV) matrices. To accomplish this, we use some ideas fr…
View article: Exact mobility edges for almost-periodic CMV matrices via gauge symmetries
Exact mobility edges for almost-periodic CMV matrices via gauge symmetries Open
We investigate the symmetries of so-called generalized extended CMV matrices. It is well-documented that problems involving reflection symmetries of standard extended CMV matrices can be subtle. We show how to deal with this in an elegant …
View article: Synthesis of and compilation with time-optimal multi-qubit gates
Synthesis of and compilation with time-optimal multi-qubit gates Open
We develop a method to synthesize a class of entangling multi-qubit gates for a quantum computing platform with fixed Ising-type interaction with all-to-all connectivity. The only requirement on the flexibility of the interaction is that i…
View article: Addressable Quantum Gates
Addressable Quantum Gates Open
We extend the circuit model of quantum computation so that the wiring between gates is soft-coded within registers inside the gates. The addresses in these registers can be manipulated and put into superpositions. This aims at capturing in…
View article: A single-particle framework for unitary lattice gauge theory in discrete time
A single-particle framework for unitary lattice gauge theory in discrete time Open
We construct a real-time lattice-gauge-theory (LGT)-type action for a spin-1/2 matter field of a single particle on a -dimensional spacetime lattice. The framework is based on a discrete-time quantum walk, and is he…
View article: An algorithm to factorize quantum walks into shift and coin operations
An algorithm to factorize quantum walks into shift and coin operations Open
We provide an algorithm that factorizes one-dimensional quantum walks on an arbitrary but fixed cell structure into a protocol of two basic operations: a fixed conditional shift that transports particles between cells and suitable coin ope…
View article: Synthesis of and compilation with time-optimal multi-qubit gates
Synthesis of and compilation with time-optimal multi-qubit gates Open
We develop a method to synthesize a class of entangling multi-qubit gates for a quantum computing platform with fixed Ising-type interaction with all-to-all connectivity. The only requirement on the flexibility of the interaction is that i…
View article: Absolutely continuous edge spectrum of topological insulators with an odd time-reversal symmetry
Absolutely continuous edge spectrum of topological insulators with an odd time-reversal symmetry Open
We show that non-trivial two-dimensional topological insulators protected by an odd time-reversal symmetry have absolutely continuous edge spectrum. The proof employs a time-reversal symmetric version of the Wold decomposition that singles…
View article: Quantum Walks: Schur Functions Meet Symmetry Protected Topological Phases
Quantum Walks: Schur Functions Meet Symmetry Protected Topological Phases Open
View article: Almost Everything About the Unitary Almost Mathieu Operator
Almost Everything About the Unitary Almost Mathieu Operator Open
We introduce a unitary almost-Mathieu operator, which is obtained from a two-dimensional quantum walk in a uniform magnetic field. We exhibit a version of Aubry--André duality for this model, which partitions the parameter space into three…
View article: Anderson Localization for Electric Quantum Walks and Skew-Shift CMV Matrices
Anderson Localization for Electric Quantum Walks and Skew-Shift CMV Matrices Open
View article: Addressable quantum gates
Addressable quantum gates Open
We extend the circuit model of quantum computation so that the wiring between gates is soft-coded within registers inside the gates. The addresses in these registers can be manipulated and put into superpositions. This aims at capturing in…
View article: An algorithm to factorize quantum walks into shift and coin operations
An algorithm to factorize quantum walks into shift and coin operations Open
We provide an algorithm that factorizes one-dimensional quantum walks into a protocol of two basic operations: A fixed conditional shift that transports particles between cells and suitable coin operators that act locally in each cell. Thi…
View article: Anderson localization for electric quantum walks and skew-shift CMV\n matrices
Anderson localization for electric quantum walks and skew-shift CMV\n matrices Open
We consider the spectral and dynamical properties of one-dimensional quantum\nwalks placed into homogenous electric fields according to a discrete version of\nthe minimal coupling principle. We show that for all irrational fields the\nabso…
View article: Eigenvalue measurement of topologically protected edge states in split-step quantum walks
Eigenvalue measurement of topologically protected edge states in split-step quantum walks Open
We study topological phenomena of quantum walks by implementing a novel protocol that extends the range of accessible properties to the eigenvalues of the walk operator. To this end, we experimentally realise for the first time a split-ste…
View article: Quantum walks in external gauge fields
Quantum walks in external gauge fields Open
Describing a particle in an external electromagnetic field is a basic task of quantum mechanics. The standard scheme for this is known as “minimal coupling” and consists of replacing the momentum operators in the Hamiltonian by the modifie…
View article: Complete homotopy invariants for translation invariant symmetric quantum walks on a chain
Complete homotopy invariants for translation invariant symmetric quantum walks on a chain Open
We provide a classification of translation invariant one-dimensional quantum walks with respect to continuous deformations preserving unitarity, locality, translation invariance, a gap condition, and some symmetry of the tenfold way. The c…
View article: The Topological Classification of One-Dimensional Symmetric Quantum Walks
The Topological Classification of One-Dimensional Symmetric Quantum Walks Open
View article: Revivals in quantum walks with a quasiperiodically-time-dependent coin
Revivals in quantum walks with a quasiperiodically-time-dependent coin Open
We provide an explanation of recent experimental results of Xue et al., where\nfull revivals in a time-dependent quantum walk model with a periodically\nchanging coin are found. Using methods originally developed for "electric"\nwalks with…