142 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Disorder-free localisation in permutation symmetric fermionic quantum walks
We investigate the phenomenon of disorder-free localisation in a quantum
system with a global permutation symmetry and the exchange symmetry for
identical particles. We start with a systematic construction of many-fermion
Hamiltonians with a global permutation symmetry using the conjugacy classes of
the permutation group , with being the total number of fermions. The
resulting Hamiltonians are interpreted as generators of continuous-time quantum
walk of indistinguishable fermions. In this setup we analytically solve the
simplest example and show that for large all the states are localised
without the introduction of any disorder coefficients. The localisation is also
time-independent and is not the result of any emergent disorder. This seems to
be an important distinction from other mechanisms of disorder-free
localisation. Furthermore, we show that the localisation is stable to
interactions that preserve the global symmetry making these systems
potential candidates for a quantum memory. By marking sites and reducing the
symmetry to subgroups of , the localisation can be obtained for any by
tuning the symmetry-reducing parameters in the Hamiltonian. Finally we show
that similar localisation also occurs for spin systems governed by a
-symmetric Heisenberg chain and we make a few comments about
-symmetric bosonic systems. The models we propose feature all-to-all
connectivity and can be realised on superconducting quantum circuits and
trapped ion systems.Comment: 24 pages, 2 figures ; v2- 27 pages, 2 figures, slight modifications
in the abstract and introductio
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
A Riemannian Optimization Approach to Clustering Problems
This paper considers the optimization problem in the form of where is smooth, , and
is a given positive vector. The clustering models including but not limited
to the models used by -means, community detection, and normalized cut can be
reformulated as such optimization problems. It is proven that the domain
forms a compact embedded submanifold of and optimization-related tools including a family of computationally
efficient retractions and an orthonormal basis of any normal space of
are derived. An inexact accelerated Riemannian proximal
gradient method that allows adaptive step size is proposed and its global
convergence is established. Numerical experiments on community detection in
networks and normalized cut for image segmentation are used to demonstrate the
performance of the proposed method
Methods of free probability
This is a joint introduction to classical and free probability, which are
twin sisters. We first review the foundations of classical probability, notably
with the main limiting theorems (CLT, CCLT, PLT, CPLT), and with a look into
examples coming from Lie groups and random matrices. Then we present the
foundations and main results of free probability, notably with free limiting
theorems, and with a look into examples coming from quantum groups and random
matrices. We discuss then a number of more advanced aspects, in relation on one
hand with free geometry, and on the other hand with questions in operator
algebras coming from subfactor theory.Comment: 400 pages. arXiv admin note: text overlap with arXiv:2208.0360
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum
Processes and diagrams: an integrated and multidisciplinary approach for the education of quantum information science
The background to this thesis is the παιδέια , the education. To educate is a dialecti- cal process that moves from an abstract line of thought, through scientifically designed techniques, into concrete action; and vice versa. We believe that educating today means enabling teachers first and their students second, to be able to read and interpret the complexity of phenomena, to teach them a model for observing this complexity, describing it, analyzing it and, finally, making it their own. In this thesis, we attempt to make sense of these needs by describing an integrated and multidisciplinary pathway, whose diagram- matic language pushes towards the search for a universal approach to science.
An initial educational contribution is thus made to the understanding of the dialectic between disciplines: theoretical physics, experimental physics, computer science, mathe- matics and mathematical logic are presented in their mutual influence, in an attempt to clarify the informational viewpoint on modern physics. The search for this dialectic for educational purposes is, in our opinion, the most significant contribution of the present work.
To address this issue, we sought to build a community of practice on the topics of the second quantum revolution. Guided by the Model of Educational Reconstruction (MER), we built a first course for teacher professional development that would enable teachers to be introduced to quantum computation and quantum communication. The emergence and development of quantum technologies provides the impetus for a deep conceptual change: “a paradigm shift from quantum theory as a theory of microscopic matter to quantum theory as a framework for technological applications and information processing”. This shift is supported, theoretically, by the informational interpretation of the postulates of quantum mechanics: preparation, transformation and measurement are reinterpreted com- putationally as the encoding, processing and decoding of information; and vice versa. In this interpretation, what changes between classical and quantum theory? From a logical point of view, the transition from bit to qubit, from a physical point of view, the laws of composition of systems. We therefore present monoidal categories as a natural theoretical framework for the description of physical systems and processes for quantum and non- quantum computation and communication, demonstrating how this language is suitable for an integrated and multidisciplinary approach.
The cultural impact of the proposal, the fruitful interaction between researchers in physics education and those in the area of theoretical research, and the passion of some teachers made it possible to start a collaboration to build an educational sequence for students. The result of this collaboration is a teaching leaning sequence on quantum technologies for students, led by the MER and based on inquiry-based learning and the modelling- based teaching. Supported by these methodological frameworks, we produced lessons and worksheets all along the way that had the dual task of supporting teachers’ work and students’ learning. They also made it possible to experimentally verify the positive and critical effects of the proposal. The instructional materials constructed, the data analysis and the constant monitoring with the teachers involved, determined the development of a second course for teacher professional development, inspired by the first, based entirely on research. We hope that this attempt at integrated and multidisciplinary approach for the education of quantum information science, based on the concept of compositionality and the diagrammatic model, can be increased and provide inspiration for future educational paths in other disciplines as well
Understanding Quantum Technologies 2022
Understanding Quantum Technologies 2022 is a creative-commons ebook that
provides a unique 360 degrees overview of quantum technologies from science and
technology to geopolitical and societal issues. It covers quantum physics
history, quantum physics 101, gate-based quantum computing, quantum computing
engineering (including quantum error corrections and quantum computing
energetics), quantum computing hardware (all qubit types, including quantum
annealing and quantum simulation paradigms, history, science, research,
implementation and vendors), quantum enabling technologies (cryogenics, control
electronics, photonics, components fabs, raw materials), quantum computing
algorithms, software development tools and use cases, unconventional computing
(potential alternatives to quantum and classical computing), quantum
telecommunications and cryptography, quantum sensing, quantum technologies
around the world, quantum technologies societal impact and even quantum fake
sciences. The main audience are computer science engineers, developers and IT
specialists as well as quantum scientists and students who want to acquire a
global view of how quantum technologies work, and particularly quantum
computing. This version is an extensive update to the 2021 edition published in
October 2021.Comment: 1132 pages, 920 figures, Letter forma
Topological classification of symmetric quantum walks. Discrete symmetry types and chiral symmetric protocols
In this thesis, we study the topological classification of symmetric quantum walks. These describe the discrete time evolution of single quantum particles on the lattice with additional locally acting symmetries. The thesis consists of three parts:
In the first part, we discuss discrete symmetry types for self-adjoint and unitary operators from an abstract point of view, i.e. without assuming an underlying physical model. We reduce any abstract finite group of involutive symmetries and their projective representations to a smaller set of symmetry types, eliminating elements that are redundant for topological classifications. This reduction process leads to the well-known tenfold way for self-adjoint operators, and for unitary operators, we identify 38 non-redundant symmetry types. For these, we define a symmetry index, which labels equivalence classes of finite-dimensional representations up to trivial direct summands. We show that these equivalence classes naturally carry a group structure and finish the discussion by explicitly computing the corresponding index groups for all non-trivial symmetry types.
Second, we develop a topological classification for symmetric quantum walks based on the symmetry index derived in the first part. We begin without a locality condition on the unitary time evolution operator but only assume an underlying discrete spatial structure. Unlike continuous-time systems, quantum walks exhibit non-gentle perturbations, i.e. local or compact perturbations that cannot be undone continuously. Using the symmetry index, we provide a complete topological classification of such perturbations of unitary operators on any lattice or graph. We add a locality condition on the one-dimensional lattice and detail the implications of such assumption on the classification. The spatial structure of the one-dimensional lattice allows us to define the left- and right symmetry index, which characterise a walks topological properties on the two half-chains.
The sum of these two indices equals the overall symmetry index, which provides a lower bound on the number of symmetry protected eigenstates of the walk. For the symmetry types of the tenfold way, a subset of three different symmetry indices is complete with respect to norm-continuous deformations and compact perturbations.
In the third part, we consider quantum walk protocols instead of single time-step unitaries. We show that any unitary operator with finite jump length on a one-dimensional lattice can be factorised into a sequence of shift and coin operations. We then provide a complete topological classification of such protocols under the influence of chiral symmetry. The classification is in terms of the half-step operator, i.e. the time evolution operator at half of the driving period, which is singled out by the chiral symmetry. We also show that a half-step operator can be constructed for every chiral symmetric single time-step unitary without a pre-defined underlying protocol. This renders the classification via the half-step operator valid for periodically driven continuous-time (Floquet systems), discretely driven protocols, and single time-step quantum walks
- …