Related papers: Symmetry and Topology of Successive Quantum Feedba…
A general framework for analyzing the topology of quantum channels of single-particle systems is developed to find a class of genuinely dynamical topological phases that can be realized by means of discrete quantum feedback control. We…
The interplay between unitary dynamics and quantum measurements induces diverse phenomena in open quantum systems with no counterparts in closed quantum systems at equilibrium. Here, we generally classify Kraus operators and their effective…
We introduce a general framework, based on collision models and discrete CP-maps, to describe on an equal footing coherent and measurement-based feedback control of quantum mechanical systems. We apply our framework to prominent tasks in…
We discuss control of the quantum-transport properties of a mesoscopic device by connecting it in a coherent feedback loop with a quantum-mechanical controller. We work in a scattering approach and derive results for the combined scattering…
Topology concepts have significantly deepened of our understanding in recent years of the electronic properties of one-dimensional (1D) nano structures such as the graphene nanoribbons. Controlling topological electronic properties of GNRs…
We derive quantum geometric bounds in spinful systems with spin topology characterized by a single $\mathbb{Z}$ index protected by a spin gap. Our bounds provide geometric conditions on the spin topology, distinct from the known quantum…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
The interplay between symmetry and topology in electronic band structures has been one of the central subjects in condensed-matter physics. Recently, it has been getting clear that a wide variety of useful information about the band…
Topological metamaterials have invaded the mechanical world, demonstrating acoustic cloaking and waveguiding at finite frequencies and variable, tunable elastic response at zero frequency. Zero frequency topological states have previously…
In this article, we study quantum critical phenomena in surfaces of symmetry-protected topological matter, i.e. surface topological quantum criticality. A generic phase boundary of gapless surfaces in a symmetry-protected state shall be a…
The quantization of the continous cat maps on the torus has led to rather pathological quantum objects [6]. The non-generic behaviour of this model has led some to conclude that the Correspondence Principle fails in this case [2]. In this…
We exhibit nontrivial transversal logical multi-controlled-$Z$ gates on $[\![N,\Theta(N),\tilde\Theta(N)]\!]$ quantum low-density parity-check codes and $[\![N,\Theta(N),\tilde\Theta(N)]\!]$ quantum locally testable codes with soundness…
In this paper we consider $Z_3$-graded topological symmetries (TSs) in one dimensional quantum mechanics. We give a classification of one dimensional quantum systems possessing these symmetries and show that different classes correspond to…
In this review paper, we survey the main concepts and some of the recent developments in quantum feedback control. For consistency and clarity, essential ideas and notations in the theory of open quantum systems and quantum stochastic…
Feedback control of open quantum systems is of fundamental importance for practical applications in various contexts, ranging from quantum computation to quantum error correction and quantum metrology. Its use in the context of…
The limits of quantum feedback control have immediate consequences for quantum information science at large, yet remain largely unexplored. Here, we combine quantum filtering theory and moment-sum-of-squares techniques to construct a…
Protecting quantum information from decoherence due to environmental noise is vital for fault-tolerant quantum computation. To this end, standard quantum error correction employs parallel projective measurements of individual particles,…
We introduce the coherent algebra of a compact metric measure space by analogy with the corresponding concept for a finite graph. As an application we show that upon topologizing the collection of isomorphism classes of compact metric…
Conventional quantum trajectory theory developed in quantum optics is largely based on the physical unravelling of Lindbald-type master equation, which constitutes the theoretical basis of continuous quantum measurement and feedback…
This paper addresses the equivalence problem of conic submanifolds in the tangent bundle of a smooth 2-dimensional manifold. Those are given by a quadratic relation between the velocities and are treated as nonholonomic constraints whose…