225 research outputs found
Tightening Quantum Speed Limits for Almost All States
Conventional quantum speed limits perform poorly for mixed quantum states:
They are generally not tight and often significantly underestimate the fastest
possible evolution speed. To remedy this, for unitary driving, we derive two
quantum speed limits that outperform the traditional bounds for almost all
quantum states. Moreover, our bounds are significantly simpler to compute as
well as experimentally more accessible. Our bounds have a clear geometric
interpretation; they arise from the evaluation of the angle between generalized
Bloch vectors.Comment: Updated and revised version; 5 pages, 2 figures, 1 page appendi
A practical, unitary simulator for non-Markovian complex processes
Stochastic processes are as ubiquitous throughout the quantitative sciences
as they are notorious for being difficult to simulate and predict. In this
letter we propose a unitary quantum simulator for discrete-time stochastic
processes which requires less internal memory than any classical analogue
throughout the simulation. The simulator's internal memory requirements equal
those of the best previous quantum models. However, in contrast to previous
models it only requires a (small) finite-dimensional Hilbert space. Moreover,
since the simulator operates unitarily throughout, it avoids any unnecessary
information loss. We provide a stepwise construction for simulators for a large
class of stochastic processes hence directly opening the possibility for
experimental implementations with current platforms for quantum computation.
The results are illustrated for an example process.Comment: 12 pages, 5 figure
Speeding up Thermalisation via Open Quantum System Variational Optimisation
Optimizing open quantum system evolution is an important step on the way to
achieving quantum computing and quantum thermodynamic tasks. In this article,
we approach optimisation via variational principles and derive an open quantum
system variational algorithm explicitly for Lindblad evolution in Liouville
space. As an example of such control over open system evolution, we control the
thermalisation of a qubit attached to a thermal Lindbladian bath with a damping
rate . Since thermalisation is an asymptotic process and the
variational algorithm we consider is for fixed time, we present a way to
discuss the potential speedup of thermalisation that can be expected from such
variational algorithms.Comment: 10 pages, 4 figures, comments welcom
Quantacell: Powerful charging of quantum batteries
We study the problem of charging a quantum battery in finite time. We
demonstrate an analytical optimal protocol for the case of a single qubit.
Extending this analysis to an array of N qubits, we demonstrate that an N-fold
advantage in power per qubit can be achieved when global operations are
permitted. The exemplary analytic argument for this quantum advantage in the
charging power is backed up by numerical analysis using optimal control
techniques. It is demonstrated that the quantum advantage for power holds when,
with cyclic operation in mind, initial and final states are required to be
separable.Comment: 11 pages, 3 figures, comments welcom
Enhancing the charging power of quantum batteries
Can collective quantum effects make a difference in a meaningful
thermodynamic operation? Focusing on energy storage and batteries, we
demonstrate that quantum mechanics can lead to an enhancement in the amount of
work deposited per unit time, i.e., the charging power, when batteries are
charged collectively. We first derive analytic upper bounds for the collective
\emph{quantum advantage} in charging power for two choices of constraints on
the charging Hamiltonian. We then highlight the importance of entanglement by
proving that the quantum advantage vanishes when the collective state of the
batteries is restricted to be in the separable ball. Finally, we provide an
upper bound to the achievable quantum advantage when the interaction order is
restricted, i.e., at most batteries are interacting. Our result is a
fundamental limit on the advantage offered by quantum technologies over their
classical counterparts as far as energy deposition is concerned.Comment: In this new updated version Theorem 1 has been changed with
Proposition 1. The paper has been published on PRL, and DOI included
accordingl
Optimal stochastic modelling with unitary quantum dynamics
Identifying and extracting the past information relevant to the future
behaviour of stochastic processes is a central task in the quantitative
sciences. Quantum models offer a promising approach to this, allowing for
accurate simulation of future trajectories whilst using less past information
than any classical counterpart. Here we introduce a class of phase-enhanced
quantum models, representing the most general means of causal simulation with a
unitary quantum circuit. We show that the resulting constructions can display
advantages over previous state-of-art methods - both in the amount of
information they need to store about the past, and in the minimal memory
dimension they require to store this information. Moreover, we find that these
two features are generally competing factors in optimisation - leading to an
ambiguity in what constitutes the optimal model - a phenomenon that does not
manifest classically. Our results thus simultaneously offer new quantum
advantages for stochastic simulation, and illustrate further qualitative
differences in behaviour between classical and quantum notions of complexity.Comment: 9 pages, 5 figure
A Gillespie algorithm for efficient simulation of quantum jump trajectories
The jump unravelling of a quantum master equation decomposes the dynamics of
an open quantum system into abrupt jumps, interspersed by periods of coherent
dynamics where no jumps occur. Simulating these jump trajectories is
computationally expensive, as it requires very small time steps to ensure
convergence. This computational challenge is aggravated in regimes where the
coherent, Hamiltonian dynamics are fast compared to the dissipative dynamics
responsible for the jumps. Here, we present a quantum version of the Gillespie
algorithm that bypasses this issue by directly constructing the waiting time
distribution for the next jump to occur. In effect, this avoids the need for
timestep discretisation altogether, instead evolving the system continuously
from one jump to the next. We describe the algorithm in detail and discuss
relevant limiting cases. To illustrate it we include four example applications
of increasing physical complexity. These additionally serve to compare the
performance of the algorithm to alternative approaches -- namely, the
widely-used routines contained in the powerful Python library QuTip. We find
significant gains in efficiency for our algorithm and discuss in which regimes
these are most pronounced. Publicly available implementations of our code are
provided in Julia and Mathematica.Comment: 13 pages, 4 figures. Comments welcom
Stabilizing open quantum batteries by sequential measurements
A quantum battery is a work reservoir that stores energy in quantum degrees
of freedom. When immersed in an environment an open quantum battery needs to be
stabilized against free energy leakage into the environment. For this purpose
we here propose a simple protocol that relies on projective measurement and
obeys a second-law like inequality for the battery entropy production rate.Comment: 5+5 pages, 3+2 figure
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