95 citations · 528 across the 27 of their papers we have counts for
28 papers
Absence of ballistic motion and presence of almost-ballistic motion for unitary operators with pure point spectrum
Christopher Cedzich, Jake Fillman, Luis Velázquez
We adapt two results of Simon and collaborators to the setting of discrete-time unitary dynamics. We show that pure point spectrum precludes ballistic motion, and exhibit a family…
Exponential Suppression of Transport in Electric Quantum Walks
Houssam Abdul-Rahman, Christopher Cedzich, Günter Stolz +1
We establish exact scalings for the maximal group velocity of translation-invariant quantum walks in periodic electric fields. Our main result shows that the maximal group velocity…
Observation of Metal-Insulator and Spectral Phase Transitions in Aubry-André-Harper Models
Quan Lin, Christopher Cedzich, Qi Zhou +1
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. Despit…
Twenty dry Martinis for the Unitary Almost Mathieu Operator
Christopher Cedzich, Long Li
We solve the Dry Ten Martini Problem for the unitary almost Mathieu operator with Diophantine frequencies in the non-critical regime.
Mobility edges in pseudo-unitary quasiperiodic quantum walks
Christopher Cedzich, Jake Fillman
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 w…
Exponential tail estimates for quantum lattice dynamics
Christopher Cedzich, Alain Joye, Albert H. Werner +1
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…
Absence of Bound States for Quantum Walks and CMV Matrices via Reflections
Christopher Cedzich, Jake Fillman
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--Velázqu…
Exact mobility edges for almost-periodic CMV matrices via gauge symmetries
Christopher Cedzich, Jake Fillman, Long Li +2
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…
A single-particle framework for unitary lattice gauge theory in discrete time
Pablo Arnault, Christopher Cedzich
We construct a real-time lattice-gauge-theory-type action for a spin-1/2 matter field of a single particle on a (1+1)-dimensional spacetime lattice. The framework is based on a dis…
Synthesis of and compilation with time-optimal multi-qubit gates
Pascal Baßler, Matthias Zipper, Christopher Cedzich +4
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…
Absolutely continuous edge spectrum of topological insulators with an odd time-reversal symmetry
Alex Bols, Christopher Cedzich
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-revers…
Almost Everything About the Unitary Almost Mathieu Operator
Christopher Cedzich, Jake Fillman, Darren C. Ong
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…
Addressable quantum gates
Pablo Arrighi, Christopher Cedzich, Marin Costes +2
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 manipul…
An algorithm to factorize quantum walks into shift and coin operations
C. Cedzich, T. Geib, R. F. Werner
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…
Chiral Floquet systems and quantum walks at half period
C. Cedzich, T. Geib, A. H. Werner +1
We classify chiral symmetric periodically driven quantum systems on a one-dimensional lattice. The driving process is local, can be continuous or discrete in time, and we assume a…
Singular continuous Cantor spectrum for magnetic quantum walks
C. Cedzich, J. Fillman, T. Geib +1
In this note, we consider a physical system given by a two-dimensional quantum walk in an external magnetic field. In this setup, we show that both the topological structure as wel…
Anderson localization for electric quantum walks and skew-shift CMV matrices
C. Cedzich, A. H. Werner
We consider the spectral and dynamical properties of one-dimensional quantum walks placed into homogenous electric fields according to a discrete version of the minimal coupling pr…
Quantum walks: Schur functions meet symmetry protected topological phases
C. Cedzich, T. Geib, F. A. Grünbaum +3
This paper uncovers and exploits a link between a central object in harmonic analysis, the so-called Schur functions, and the very hot topic of symmetry protected topological phase…
Eigenvalue Measurement of Topologically Protected Edge states in Split-Step Quantum Walks
Thomas Nitsche, Tobias Geib, Christoph Stahl +5
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 en…
Quantum walks in external gauge fields
C. Cedzich, T. Geib, A. H. Werner +1
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 replac…
Complete homotopy invariants for translation invariant symmetric quantum walks on a chain
C. Cedzich, T. Geib, C. Stahl +3
We provide a classification of translation invariant one-dimensional quantum walks with respect to continuous deformations preserving unitarity, locality, translation invariance, a…
The topological classification of one-dimensional symmetric quantum walks
C. Cedzich, T. Geib, F. A. Grünbaum +4
We give a topological classification of quantum walks on an infinite 1D lattice, which obey one of the discrete symmetry groups of the tenfold way, have a gap around some eigenvalu…
Revivals in Quantum Walks with quasi-periodically time-dependent coin
C. Cedzich, R. F. Werner
We provide an explanation of recent experimental results of Xue et al., where full revivals in a time-dependent quantum walk model with a periodically changing coin are found. Usin…
Bulk-edge correspondence of one-dimensional quantum walks
C. Cedzich, F. A. Grünbaum, C. Stahl +3
We outline a theory of symmetry protected topological phases of one-dimensional quantum walks. We assume spectral gaps around the symmetry-distinguished points +1 and -1, in which…