42 research outputs found
Measuring correlations of cold atom systems using multiple quantum probes
We present a non-destructive method to probe a complex quantum system using
multiple impurity atoms as quantum probes. Our protocol provides access to
different equilibrium properties of the system by changing its coupling to the
probes. In particular, we show that measurements with two probes reveal the
system's non-local two-point density correlations, for probe-system contact
interactions. We illustrate our findings with analytic and numerical
calculations for the Bose-Hubbard model in the weakly and strongly-interacting
regimes, under conditions relevant to ongoing experiments in cold atom systems.Comment: 11 pages, 6 figures. v2: enhanced discussion in light of other
correlation measurement methods available; matches published versio
A map-based model predictive control approach for train operation
Trains are a corner stone of public transport and play an important role in
daily life. A challenging task in train operation is to avoid skidding and
sliding during fast changes of traction conditions, which can, for example,
occur due to changing weather conditions, crossings, tunnels or forest entries.
The latter depends on local track conditions and can be recorded in a map
together with other location-dependent information like speed limits and
inclination. In this paper, a model predictive control (MPC) approach is
developed. Thanks to the knowledge of future changes of traction conditions,
the approach is able to avoid short-term skidding and sliding even under fast
changes of traction conditions. In a first step, an optimal reference
trajectory is determined by a multiple-shooting approach. In a second step, the
reference trajectory is tracked by an MPC setup. The developed method is
simulated along a track with fast-changing traction conditions for different
scenarios, like changing weather conditions and unexpected delays. In all
cases, skidding and sliding is avoided.Comment: 6 pages, 7 figures, accepted at ECC 202
Improved precision scaling for simulating coupled quantum-classical dynamics
We present a super-polynomial improvement in the precision scaling of quantum
simulations for coupled classical-quantum systems in this paper. Such systems
are found, for example, in molecular dynamics simulations within the
Born-Oppenheimer approximation. By employing a framework based on the
Koopman-von Neumann formalism, we express the Liouville equation of motion as
unitary dynamics and utilize phase kickback from a dynamical quantum simulation
to calculate the quantum forces acting on classical particles. This approach
allows us to simulate the dynamics of these particles without the overheads
associated with measuring gradients and solving the equations of motion on a
classical computer, resulting in a super-polynomial advantage at the price of
increased space complexity. We demonstrate that these simulations can be
performed in both microcanonical and canonical ensembles, enabling the
estimation of thermodynamic properties from the prepared probability density.Comment: 19 + 51 page
Fault-tolerant quantum computation of molecular observables
Over the past three decades significant reductions have been made to the cost of estimating ground-state energies of molecular Hamiltonians with quantum computers. However, comparatively little attention has been paid to estimating the expectation values of other observables with respect to said ground states, which is important for many industrial applications. In this work we present a novel expectation value estimation (EVE) quantum algorithm which can be applied to estimate the expectation values of arbitrary observables with respect to any of the system's eigenstates. In particular, we consider two variants of EVE: std-EVE, based on standard quantum phase estimation, and QSP-EVE, which utilizes quantum signal processing (QSP) techniques. We provide rigorous error analysis for both both variants and minimize the number of individual phase factors for QSPEVE. These error analyses enable us to produce constant-factor quantum resource estimates for both std-EVE and QSP-EVE across a variety of molecular systems and observables. For the systems considered, we show that QSP-EVE reduces (Toffoli) gate counts by up to three orders of magnitude and reduces qubit width by up to 25% compared to std-EVE. While estimated resource counts remain far too high for the first generations of fault-tolerant quantum computers, our estimates mark a first of their kind for both the application of expectation value estimation and modern QSP-based techniques