91 research outputs found
Unifying (Quantum) Statistical and Parametrized (Quantum) Algorithms
Kearns' statistical query (SQ) oracle (STOC'93) lends a unifying perspective
for most classical machine learning algorithms. This ceases to be true in
quantum learning, where many settings do not admit, neither an SQ analog nor a
quantum statistical query (QSQ) analog. In this work, we take inspiration from
Kearns' SQ oracle and Valiant's weak evaluation oracle (TOCT'14) and establish
a unified perspective bridging the statistical and parametrized learning
paradigms in a novel way. We explore the problem of learning from an evaluation
oracle, which provides an estimate of function values, and introduce an
extensive yet intuitive framework that yields unconditional lower bounds for
learning from evaluation queries and characterizes the query complexity for
learning linear function classes. The framework is directly applicable to the
QSQ setting and virtually all algorithms based on loss function optimization.
Our first application is to extend prior results on the learnability of
output distributions of quantum circuits and Clifford unitaries from the SQ to
the (multi-copy) QSQ setting, implying exponential separations between learning
stabilizer states from (multi-copy) QSQs versus from quantum samples. Our
second application is to analyze some popular quantum machine learning (QML)
settings. We gain an intuitive picture of the hardness of many QML tasks which
goes beyond existing methods such as barren plateaus and the statistical
dimension, and contains crucial setting-dependent implications. Our framework
not only unifies the perspective of cost concentration with that of the
statistical dimension in a unified language but exposes their connectedness and
similarity.Comment: 97 Page
Composite symmetry protected topological order and effective models
Strongly correlated quantum many-body systems at low dimension exhibit a
wealth of phenomena, ranging from features of geometric frustration to
signatures of symmetry-protected topological order. In suitable descriptions of
such systems, it can be helpful to resort to effective models which focus on
the essential degrees of freedom of the given model. In this work, we analyze
how to determine the validity of an effective model by demanding it to be in
the same phase as the original model. We focus our study on one-dimensional
spin-1/2 systems and explain how non-trivial symmetry protected topologically
ordered (SPT) phases of an effective spin 1 model can arise depending on the
couplings in the original Hamiltonian. In this analysis, tensor network methods
feature in two ways: On the one hand, we make use of recent techniques for the
classification of SPT phases using matrix product states in order to identify
the phases in the effective model with those in the underlying physical system,
employing Kuenneth's theorem for cohomology. As an intuitive paradigmatic model
we exemplify the developed methodology by investigating the bi-layered
delta-chain. For strong ferromagnetic inter-layer couplings, we find the system
to transit into exactly the same phase as an effective spin 1 model. However,
for weak but finite coupling strength, we identify a symmetry broken phase
differing from this effective spin-1 description. On the other hand, we
underpin our argument with a numerical analysis making use of matrix product
states.Comment: 13 pages, 6 figure
Tensor types and their use in physics
The content of this paper can be roughly organized into a three-level
hierarchy of generality. At the first, most general level, we introduce a new
language which allows us to express various categorical structures in a
systematic and explicit manner in terms of so-called 2-schemes. Although
2-schemes can formalize categorical structures such as symmetric monoidal
categories, they are not limited to this, and can be used to define structures
with no categorical analogue. Most categorical structures come with an
effective graphical calculus such as string diagrams for symmetric monoidal
categories, and the same is true more generally for interesting 2-schemes. In
this work, we focus on one particular non-categorical 2-scheme, whose instances
we refer to as tensor types. At the second level of the hierarchy, we work out
different flavors of this 2-scheme in detail. The effective graphical calculus
of tensor types is that of tensor networks or Penrose diagrams, that is, string
diagrams without a flow of time. As such, tensor types are similar to compact
closed categories, though there are various small but potentially important
differences. Also, the two definitions use completely different mechanisms
despite both being examples of 2-schemes. At the third level of the hierarchy,
we provide a long list of different families of concrete tensor types, in a way
which makes them accessible to concrete computations, motivated by their
potential use in physics. Different tensor types describe different types of
physical models, such as classical or quantum physics, deterministic or
statistical physics, many-body or single-body physics, or matter with or
without symmetries or fermions
Direct-Write Photolithography for Cylindrical Tooling Fabrication in Roll-to-Roll Microcontact Printing
The scale-up of microcontact printing (μCP) to a roll-to-roll technique for large-scale surface patterning requires scalable tooling for continuous pattern printing with μm-scale features (e.g., 1–50 μm). Here, we examine the process of creating such a tool using an optical direct-write or “maskless” method working on a rotating cylindrical substrate. A predictive model of pattern formation is presented along with experimental results to examine the key control factors for this process. It is shown that factors can be modulated to vary the cross-sectional shape in addition to feature height and width. This feature can then be exploited to improve the robustness of the final printing process.Center for Clean Water and Clean Energy at MIT and KFUP
Dynamics of interacting transport qubits
We investigate the electronic transport through two parallel double quantum
dots coupled both capacitively and via a perpendicularly aligned charge qubit.
The presence of the qubit leads to a modification of the coherent tunnel
amplitudes of each double quantum dot. We study the influence of the qubit on
the electronic steady state currents through the system, the entanglement
between the transport double quantum dots, and the back action on the charge
qubit. We use a Born-Markov-Secular quantum master equation for the system. The
obtained currents show signatures of the qubit. The stationary qubit state may
be tuned and even rendered pure by applying suitable voltages. In the Coulomb
diamonds it is also possible to stabilize pure entangled states of the
transport double quantum dots
A route towards engineering many-body localization in real materials
The interplay of interactions and disorder in a quantum many body system may
lead to the elusive phenomenon of many body localization (MBL). It has been
observed under precisely controlled conditions in synthetic quantum many-body
systems, but to detect it in actual quantum materials seems challenging. In
this work, we present a path to synthesize real materials that show signatures
of many body localization by mixing different species of materials in the
laboratory. To provide evidence for the functioning of our approach, we perform
a detailed tensor-network based numerical analysis to study the effects of
various doping ratios of the constituting materials. Moreover, in order to
provide guidance to experiments, we investigate different choices of actual
candidate materials. To address the challenge of how to achieve stability under
heating, we study the effect of the electron-phonon coupling, focusing on
effectively one dimensional materials embedded in one, two and three
dimensional lattices. We analyze how this coupling affects the MBL and provide
an intuitive microscopic description of the interplay between the electronic
degrees of freedom and the lattice vibrations. Our work provides a guideline
for the necessary conditions on the properties of the ingredient materials and,
as such, serves as a road map to experimentally synthesizing real quantum
materials exhibiting signatures of MBL.Comment: 12 pages, 7 figure
Relaxation dynamics of meso-reservoirs
We study the phenomenology of maximum-entropy meso-reservoirs, where we assume that their local thermal equilibrium state changes consistently with the heat transferred between the meso-reservoirs. Depending on heat and matter carrying capacities, the chemical potentials and temperatures are allowed to vary in time, and using global conservation relations we solve their evolution equations. We compare two-terminal transport between bosonic and fermionic meso-reservoirs via systems that tightly couple energy and matter currents and systems that do not. For bosonic reservoirs, we observe the temporary formation of a Bose–Einstein condensate in one of the meso-reservoirs from an initial nonequilibrium setup.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und AnwendungskonzepteDFG, 87159868, GRK 1558: Kollektive Dynamik im Nichtgleichgewicht: in kondensierter Materie und biologischen Systeme
Ginzburg-Landau Theory for the Jaynes-Cummings-Hubbard Model
We develop a Ginzburg-Landau theory for the Jaynes-Cummings-Hubbard model
which effectively describes both static and dynamic properties of photons
evolving in a cubic lattice of cavities, each filled with a two-level atom. To
this end we calculate the effective action to first-order in the hopping
parameter. Within a Landau description of a spatially and temporally constant
order parameter we calculate the finite-temperature mean-field quantum phase
boundary between a Mott insulating and a superfluid phase of polaritons.
Furthermore, within the Ginzburg-Landau description of a spatio-temporal
varying order parameter we determine the excitation spectra in both phases and,
in particular, the sound velocity of light in the superfluid phase
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