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The Born-Fock theorem is one of the most fundamental theorems of quantum mechanics and forms the basis for reliable and efficient navigation in the Hilbert space of a quantum system with a time-dependent Hamiltonian by adiabatic evolution.…
Theoretical research suggests a emergence of the Majorana bound states at the ends of the nanowires. Experimental verifications of said concept has already been executed, e.g., in superconductor/semiconductor nanowire devices where…
Counterdiabatic driving, which enforces adiabatic evolution in arbitrary timescales, can be realised by engineering a Floquet Hamiltonian which oscillates between the Hamiltonian and its derivative requiring no additional control terms.…
We introduce a theoretical framework for computing transport coefficients for complex materials. As a first example, we resolve long-standing inconsistencies between experiment and theory pertaining to the conductivity and Hall mobility for…
We show how to perform scalable fault-tolerant non-Clifford gates in two dimensions by introducing domain walls between the surface code and a non-Abelian topological code whose codespace is stabilized by Clifford operators. We formulate a…
We study translation-invariant quantum spin Hamiltonians on general graphs with non-commuting interactions either given by (i) a random rank-$1$ projection or (ii) Haar projectors. For (i), we prove that the Hamiltonian is gapped on any…
Adiabatic quantum computing and optimization have garnered much attention recently as possible models for achieving a quantum advantage over classical approaches to optimization and other special purpose computations. Both techniques are…
Higher-order topological superconductors host Majorana zero modes localized at corners or hinges, providing a promising route toward scalable and controllable Majorana networks without vortices or magnetic flux. Here we propose a…
In space-adiabatic approaches one can approximate Hamiltonians that are modulated slowly in space by phase-space functions that depend on position and momentum. In this paper, we establish a rigorous relation between this approach and the…
We present a topological mechanism for superconductivity emerging from Chern-2 insulators. While, naively, time-reversal symmetry breaking is expected to prevent superconductivity, it turns out that the opposite is the case: An explicit…
Understanding and predicting thermal transport in disordered materials remains a significant challenge due to the absence of periodicity and the complex nature of medium-range structural motifs. In this work, we investigate amorphous…
We propose a family of explicit geometrically local circuits on a 2-dimensional planar grid of qudits, realizing any abelian non-chiral topological phase as an actively error-corrected fault-tolerant memory. These circuits are constructed…
We study the transport properties of a tight-binding model of non-interacting fermions with random hopping on the honeycomb lattice. At the particle-hole symmetric chemical potential, the absence of diagonal disorder (random onsite…
One promising application of near-term quantum devices is to prepare trial wavefunctions using short circuits for solving different problems via variational algorithms. For this purpose, we introduce a new circuit design that combines…
Topological color codes are among the stabilizer codes with remarkable properties from quantum information perspective. In this paper we construct a four-valent lattice, the so called ruby lattice, governed by a 2-body Hamiltonian. In a…
We present a new scheme to perform noise resilient universal adiabatic quantum computation using two-body interactions. To achieve this, we introduce a new family of error detecting subsystem codes whose gauge generators and a set of their…
We define a range of new coarse geometric invariants based on various graph-theoretic measures of complexity for finite graphs, including: treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these…
The transmission across a graphene bilayer region is calculated for two different types of connections to monolayer leads. A transfer matrix algorithm based on a tight binding model is developed to obtain the ballistic transmission beyond…
The presence and character of local integrals of motion -- quasi-local operators that commute with the Hamiltonian -- encode valuable information about the dynamics of a quantum system. In particular, strongly disordered many-body systems…
A numerical study of Anderson transition on random regular graphs (RRG) with diagonal disorder is performed. The problem can be described as a tight-binding model on a lattice with N sites that is locally a tree with constant connectivity.…