18 research outputs found
Measuring Chern numbers in Hofstadter strips
Topologically non-trivial Hamiltonians with periodic boundary conditions are
characterized by strictly quantized invariants. Open questions and fundamental
challenges concern their existence, and the possibility of measuring them in
systems with open boundary conditions and limited spatial extension. Here, we
consider transport in Hofstadter strips, that is, two-dimensional lattices
pierced by a uniform magnetic flux which extend over few sites in one of the
spatial dimensions. As we show, an atomic wavepacket exhibits a transverse
displacement under the action of a weak constant force. After one Bloch
oscillation, this displacement approaches the quantized Chern number of the
periodic system in the limit of vanishing tunneling along the transverse
direction. We further demonstrate that this scheme is able to map out the Chern
number of ground and excited bands, and we investigate the robustness of the
method in presence of both disorder and harmonic trapping. Our results prove
that topological invariants can be measured in Hofstadter strips with open
boundary conditions and as few as three sites along one direction.Comment: v1: 17 pages, 10 figures; v2: minor changes, reference added, SciPost
style, 26 pages, 10 figures; v3: published versio
Topological bound states of a quantum walk with cold atoms
We suggest a method for engineering a quantum walk, with cold atoms as
walkers, which presents topologically non-trivial properties. We derive the
phase diagram, and show that we are able to produce a boundary between
topologically distinct phases using the finite beam width of the applied
lasers. A topologically protected bound state can then be observed, which is
pinned to the interface and is robust to perturbations. We show that it is
possible to identify this bound state by averaging over spin sensitive measures
of the atom's position, based on the spin distribution that these states
display. Interestingly, there exists a parameter regime in which our system
maps on to the Creutz ladder.Comment: 17 pages, 16 figure
Towards Prediction of Financial Crashes with a D-Wave Quantum Computer
Prediction of financial crashes in a complex financial network is known to be
an NP-hard problem, i.e., a problem which cannot be solved efficiently with a
classical computer. We experimentally explore a novel approach to this problem
by using a D-Wave quantum computer to obtain financial equilibrium more
efficiently. To be specific, the equilibrium condition of a nonlinear financial
model is embedded into a higher-order unconstrained binary optimization (HUBO)
problem, which is then transformed to a spin- Hamiltonian with at most
two-qubit interactions. The problem is thus equivalent to finding the ground
state of an interacting spin Hamiltonian, which can be approximated with a
quantum annealer. Our experiment paves the way to study quantitative
macroeconomics, enlarging the number of problems that can be handled by current
quantum computers
Quantum artificial vision for defect detection in manufacturing
In this paper we consider several algorithms for quantum computer vision
using Noisy Intermediate-Scale Quantum (NISQ) devices, and benchmark them for a
real problem against their classical counterparts. Specifically, we consider
two approaches: a quantum Support Vector Machine (QSVM) on a universal
gate-based quantum computer, and QBoost on a quantum annealer. The quantum
vision systems are benchmarked for an unbalanced dataset of images where the
aim is to detect defects in manufactured car pieces. We see that the quantum
algorithms outperform their classical counterparts in several ways, with QBoost
allowing for larger problems to be analyzed with present-day quantum annealers.
Data preprocessing, including dimensionality reduction and contrast
enhancement, is also discussed, as well as hyperparameter tuning in QBoost. To
the best of our knowledge, this is the first implementation of quantum computer
vision systems for a problem of industrial relevance in a manufacturing
production line.Comment: 11 pages, 7 figures, 16 tables, revised versio
Application of Tensor Neural Networks to Pricing Bermudan Swaptions
The Cheyette model is a quasi-Gaussian volatility interest rate model widely
used to price interest rate derivatives such as European and Bermudan Swaptions
for which Monte Carlo simulation has become the industry standard. In low
dimensions, these approaches provide accurate and robust prices for European
Swaptions but, even in this computationally simple setting, they are known to
underestimate the value of Bermudan Swaptions when using the state variables as
regressors. This is mainly due to the use of a finite number of predetermined
basis functions in the regression. Moreover, in high-dimensional settings,
these approaches succumb to the Curse of Dimensionality. To address these
issues, Deep-learning techniques have been used to solve the backward
Stochastic Differential Equation associated with the value process for European
and Bermudan Swaptions; however, these methods are constrained by training time
and memory. To overcome these limitations, we propose leveraging Tensor Neural
Networks as they can provide significant parameter savings while attaining the
same accuracy as classical Dense Neural Networks. In this paper we rigorously
benchmark the performance of Tensor Neural Networks and Dense Neural Networks
for pricing European and Bermudan Swaptions, and we show that Tensor Neural
Networks can be trained faster than Dense Neural Networks and provide more
accurate and robust prices than their Dense counterparts.Comment: 15 pages, 9 figures, 2 table