19,106 research outputs found
Quantum Strategies Win in a Defector-Dominated Population
Quantum strategies are introduced into evolutionary games. The agents using
quantum strategies are regarded as invaders whose fraction generally is 1% of a
population in contrast to the 50% defectors. In this paper, the evolution of
strategies on networks is investigated in a defector-dominated population, when
three networks (Regular Lattice, Newman-Watts small world network, scale-free
network) are constructed and three games (Prisoners' Dilemma, Snowdrift,
Stag-Hunt) are employed. As far as these three games are concerned, the results
show that quantum strategies can always invade the population successfully.
Comparing the three networks, we find that the regular lattice is most easily
invaded by agents that adopt quantum strategies. However, for a scale-free
network it can be invaded by agents adopting quantum strategies only if a hub
is occupied by an agent with a quantum strategy or if the fraction of agents
with quantum strategies in the population is significant.Comment: 8 pages, 7figure
Quantum Entanglement Percolation
Quantum communication demands efficient distribution of quantum entanglement
across a network of connected partners. The search for efficient strategies for
the entanglement distribution may be based on percolation theory, which
describes evolution of network connectivity with respect to some network
parameters. In this framework, the probability to establish perfect
entanglement between two remote partners decays exponentially with the distance
between them before the percolation transition point, which unambiguously
defines percolation properties of any classical network or lattice. Here we
introduce quantum networks created with local operations and classical
communication, which exhibit non-classical percolation transition points
leading to the striking communication advantages over those offered by the
corresponding classical networks. We show, in particular, how to establish
perfect entanglement between any two nodes in the simplest possible network --
the 1D chain -- using imperfect entangled pairs of qubits.Comment: 5 pages, 2 figure
Ground state energy and magnetization curve of a frustrated magnetic system from real-time evolution on a digital quantum processor
Models of interacting many-body quantum systems that may realize new exotic
phases of matter, notably quantum spin liquids, are challenging to study using
even state-of-the-art classical methods such as tensor network simulations.
Quantum computing provides a promising route for overcoming these difficulties
to find ground states, dynamics, and more. In this paper, we argue that
recently developed hybrid quantum-classical algorithms based on real-time
evolution are promising methods for solving a particularly important model in
the search for spin liquids, the antiferromagnetic Heisenberg model on the
two-dimensional kagome lattice. We show how to construct efficient quantum
circuits to implement time evolution for the model and to evaluate key
observables on the quantum computer, and we argue that the method has favorable
scaling with increasing system size. We then restrict to a 12-spin star
plaquette from the kagome lattice and a related 8-spin system, and we give an
empirical demonstration on these small systems that the hybrid algorithms can
efficiently find the ground state energy and the magnetization curve. For these
demonstrations, we use four levels of approximation: exact state vectors, exact
state vectors with statistical noise from sampling, noisy classical emulators,
and (for the 8-spin system only) real quantum hardware, specifically the
Quantinuum H1-1 processor; for the noisy simulations, we also employ error
mitigation strategies based on the symmetries of the Hamiltonian. Our results
strongly suggest that these hybrid algorithms present a promising direction for
resolving important unsolved problems in condensed matter theory and beyond.Comment: 29 pages, 22 figure
Perfect quantum transport in arbitrary spin networks
Spin chains have been proposed as wires to transport information between
distributed registers in a quantum information processor. Unfortunately, the
challenges in manufacturing linear chains with engineered couplings has
hindered experimental implementations. Here we present strategies to achieve
perfect quantum information transport in arbitrary spin networks. Our proposal
is based on the weak coupling limit for pure state transport, where information
is transferred between two end-spins that are only weakly coupled to the rest
of the network. This regime allows disregarding the complex, internal dynamics
of the bulk network and relying on virtual transitions or on the coupling to a
single bulk eigenmode. We further introduce control methods capable of tuning
the transport process and achieve perfect fidelity with limited resources,
involving only manipulation of the end-qubits. These strategies could be thus
applied not only to engineered systems with relaxed fabrication precision, but
also to naturally occurring networks; specifically, we discuss the practical
implementation of quantum state transfer between two separated nitrogen vacancy
(NV) centers through a network of nitrogen substitutional impurities.Comment: 5+7 page
Lattice gauge theories simulations in the quantum information era
The many-body problem is ubiquitous in the theoretical description of
physical phenomena, ranging from the behavior of elementary particles to the
physics of electrons in solids. Most of our understanding of many-body systems
comes from analyzing the symmetry properties of Hamiltonian and states: the
most striking example are gauge theories such as quantum electrodynamics, where
a local symmetry strongly constrains the microscopic dynamics. The physics of
such gauge theories is relevant for the understanding of a diverse set of
systems, including frustrated quantum magnets and the collective dynamics of
elementary particles within the standard model. In the last few years, several
approaches have been put forward to tackle the complex dynamics of gauge
theories using quantum information concepts. In particular, quantum simulation
platforms have been put forward for the realization of synthetic gauge
theories, and novel classical simulation algorithms based on quantum
information concepts have been formulated. In this review we present an
introduction to these approaches, illustrating the basics concepts and
highlighting the connections between apparently very different fields, and
report the recent developments in this new thriving field of research.Comment: Pedagogical review article. Originally submitted to Contemporary
Physics, the final version will appear soon on the on-line version of the
journal. 34 page
Optimal control technique for Many Body Quantum Systems dynamics
We present an efficient strategy for controlling a vast range of
non-integrable quantum many body one-dimensional systems that can be merged
with state-of-the-art tensor network simulation methods like the density Matrix
Renormalization Group. To demonstrate its potential, we employ it to solve a
major issue in current optical-lattice physics with ultra-cold atoms: we show
how to reduce by about two orders of magnitudes the time needed to bring a
superfluid gas into a Mott insulator state, while suppressing defects by more
than one order of magnitude as compared to current experiments [1]. Finally, we
show that the optimal pulse is robust against atom number fluctuations.Comment: 5 pages, 4 figures, published versio
Evolutionary games on graphs
Game theory is one of the key paradigms behind many scientific disciplines
from biology to behavioral sciences to economics. In its evolutionary form and
especially when the interacting agents are linked in a specific social network
the underlying solution concepts and methods are very similar to those applied
in non-equilibrium statistical physics. This review gives a tutorial-type
overview of the field for physicists. The first three sections introduce the
necessary background in classical and evolutionary game theory from the basic
definitions to the most important results. The fourth section surveys the
topological complications implied by non-mean-field-type social network
structures in general. The last three sections discuss in detail the dynamic
behavior of three prominent classes of models: the Prisoner's Dilemma, the
Rock-Scissors-Paper game, and Competing Associations. The major theme of the
review is in what sense and how the graph structure of interactions can modify
and enrich the picture of long term behavioral patterns emerging in
evolutionary games.Comment: Review, final version, 133 pages, 65 figure
Learning and innovative elements of strategy adoption rules expand cooperative network topologies
Cooperation plays a key role in the evolution of complex systems. However,
the level of cooperation extensively varies with the topology of agent networks
in the widely used models of repeated games. Here we show that cooperation
remains rather stable by applying the reinforcement learning strategy adoption
rule, Q-learning on a variety of random, regular, small-word, scale-free and
modular network models in repeated, multi-agent Prisoners Dilemma and Hawk-Dove
games. Furthermore, we found that using the above model systems other long-term
learning strategy adoption rules also promote cooperation, while introducing a
low level of noise (as a model of innovation) to the strategy adoption rules
makes the level of cooperation less dependent on the actual network topology.
Our results demonstrate that long-term learning and random elements in the
strategy adoption rules, when acting together, extend the range of network
topologies enabling the development of cooperation at a wider range of costs
and temptations. These results suggest that a balanced duo of learning and
innovation may help to preserve cooperation during the re-organization of
real-world networks, and may play a prominent role in the evolution of
self-organizing, complex systems.Comment: 14 pages, 3 Figures + a Supplementary Material with 25 pages, 3
Tables, 12 Figures and 116 reference
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