On entropy growth and the hardness of simulating time evolution

@article{Schuch2008OnEG,
  title={On entropy growth and the hardness of simulating time evolution},
  author={N. Schuch and M. Wolf and K. Vollbrecht and J. Cirac},
  journal={New Journal of Physics},
  year={2008},
  volume={10},
  pages={033032}
}
The simulation of quantum systems is a task for which quantum computers are believed to give an exponential speed up as compared with classical ones. While ground states of one-dimensional systems can be efficiently approximated using matrix product states (MPS), their time evolution can encode quantum computations, so that simulating the latter should be hard classically. However, one might believe that for systems with high enough symmetry, and thus insufficient parameters to encode a quantum… Expand
Supersonic quantum communication.
TLDR
It is proved that one can encounter accelerating excitations under the natural dynamics that allow for reliable transmission of information faster than any finite speed of sound. Expand
Practical recipes for the model order reduction, dynamical simulation, and compressive sampling of large-scale open quantum systems
TLDR
Practical recipes are presented for simulating high-temperature and nonequilibrium quantum spin systems that are continuously measured and controlled, and the high-fidelity projection of numerically computed quantum trajectories onto low dimensionality K?hler state-space manifolds is demonstrated. Expand
Entanglement dynamics after quantum quenches in generic integrable systems
The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, byExpand
Quantum information dynamics in multipartite integrable systems
In a non-equilibrium many-body system, the quantum information dynamics between non-complementary regions is a crucial feature to understand the local relaxation towards statistical ensembles.Expand
Can one trust quantum simulators?
TLDR
It is found that disorder can decrease the reliability of an analog quantum simulator of this model, although large errors in local observables are introduced only for strong levels of disorder. Expand
Entanglement bounds on the performance of quantum computing architectures
TLDR
It is shown that a quantity known as the isoperimetric number establishes a lower bound on the time required to create highly entangled states, and this metric is used to evaluate the hierarchical architecture proposed by A. Bapat et al. and find it to be a promising alternative to the conventional grid architecture. Expand
Instantaneous Quantum Computation
We examine theoretic architectures and an abstract model for a restricted class of quantum computation, called here temporally unstructured (“instantaneous”) quantum computation because it allows forExpand
Discrete Time Quantum Lattice Systems
Discrete time quantum lattice systems recently have come into the focus of quantum computation because they provide a versatile tool for many different applications and they are potentiallyExpand
Se p 20 08 Instantaneous Quantum Computation
We examine theoretic architectures and an abstract model for a restricted class of quantum computation, called here instantaneous quantum computation because it allows for essentially no temporalExpand
Entanglement Spreading in a Minimal Model of Maximal Many-Body Quantum Chaos
The spreading of entanglement in out-of-equilibrium quantum systems is currently at the center of intense interdisciplinary research efforts involving communities with interests ranging fromExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 78 REFERENCES
Efficient approximation of the dynamics of one-dimensional quantum spin systems.
  • T. Osborne
  • Physics, Medicine
  • Physical review letters
  • 2006
In this Letter we show that an arbitrarily good approximation to the propagator e(itH) for a 1D lattice of n quantum spins with Hamiltonian H may be obtained with polynomial computational resourcesExpand
Exact relaxation in a class of nonequilibrium quantum lattice systems.
TLDR
This work rigorously proves that the evolving state locally relaxes to a steady state with maximum entropy constrained by second moments--thus maximizing the entanglement. Expand
Quantum simulators, continuous-time automata, and translationally invariant systems.
TLDR
It is shown that a quantum computer can be built in a 1D chain with a fixed, translationally invariant Hamitonian consisting of nearest-neighbor interactions only. Expand
Efficient simulation of one-dimensional quantum many-body systems.
  • G. Vidal
  • Computer Science, Physics
  • Physical review letters
  • 2004
TLDR
Numerical analysis indicates that this method can be used, for instance, to efficiently compute time-dependent properties of low-energy dynamics in sufficiently regular but otherwise arbitrary one-dimensional quantum many-body systems. Expand
Evolution of entanglement entropy in one-dimensional systems
We study the unitary time evolution of the entropy of entanglement of a one-dimensional system between the degrees of freedom in an interval of length and its complement, starting from a pure stateExpand
Entropy and entanglement in quantum ground states
We consider the relationship between correlations and entanglement in gapped quantum systems, with application to matrix product state representations. We prove that there exist gappedExpand
Quantum-Merlin-Arthur-complete translationally invariant Hamiltonian problem and the complexity of finding ground-state energies in physical systems
Here we present a problem related to the local Hamiltonian problem (identifying whether the ground-state energy falls within one of two ranges) which is restricted to being translationally invariant.Expand
Simulation of quantum dynamics with quantum optical systems
TLDR
The use of quantum optical systems to perform universal simulation of quantum dynamics and average Hamiltonian techniques are used to achieve evolutions in time according to a large class of Hamiltonians. Expand
An Area Law for One Dimensional Quantum Systems
We prove an area law for the entanglement entropy in gapped one-dimensional quantum systems. The bound on the entropy grows surprisingly rapidly with the correlation length; we discuss this in termsExpand
Entropy scaling and simulability by matrix product states.
TLDR
It is applied to illustrate that quantum computers might outperform classical computers in simulating the time evolution of quantum systems, even for completely translational invariant systems subject to a time-independent Hamiltonian. Expand
...
1
2
3
4
5
...