29,669 research outputs found
Black holes, complexity and quantum chaos
We study aspects of black holes and quantum chaos through the behavior of
computational costs, which are distance notions in the manifold of unitaries of
the theory. To this end, we enlarge Nielsen geometric approach to quantum
computation and provide metrics for finite temperature/energy scenarios and
CFT's. From the framework, it is clear that costs can grow in two different
ways: operator vs `simple' growths. The first type mixes operators associated
to different penalties, while the second does not. Important examples of simple
growths are those related to symmetry transformations, and we describe the
costs of rotations, translations, and boosts. For black holes, this analysis
shows how infalling particle costs are controlled by the maximal Lyapunov
exponent, and motivates a further bound on the growth of chaos. The analysis
also suggests a correspondence between proper energies in the bulk and average
`local' scaling dimensions in the boundary. Finally, we describe these
complexity features from a dual perspective. Using recent results on SYK we
compute a lower bound to the computational cost growth in SYK at infinite
temperature. At intermediate times it is controlled by the Lyapunov exponent,
while at long times it saturates to a linear growth, as expected from the
gravity description.Comment: 30 page
Quantum Computation of Scattering in Scalar Quantum Field Theories
Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally, and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great computational complexity and can generally be performed only when the interaction strength is weak. A full understanding of the foundations and rich consequences of quantum field theory remains an outstanding challenge. We develop a quantum algorithm to compute relativistic scattering amplitudes in massive phi-fourth theory in spacetime of four and fewer dimensions. The algorithm runs in a time that is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. Thus, it offers exponential speedup over existing classical methods at high precision or strong coupling
NP-complete Problems and Physical Reality
Can NP-complete problems be solved efficiently in the physical universe? I
survey proposals including soap bubbles, protein folding, quantum computing,
quantum advice, quantum adiabatic algorithms, quantum-mechanical
nonlinearities, hidden variables, relativistic time dilation, analog computing,
Malament-Hogarth spacetimes, quantum gravity, closed timelike curves, and
"anthropic computing." The section on soap bubbles even includes some
"experimental" results. While I do not believe that any of the proposals will
let us solve NP-complete problems efficiently, I argue that by studying them,
we can learn something not only about computation but also about physics.Comment: 23 pages, minor correction
Simulating quantum field theory with a quantum computer
Forthcoming exascale digital computers will further advance our knowledge of
quantum chromodynamics, but formidable challenges will remain. In particular,
Euclidean Monte Carlo methods are not well suited for studying real-time
evolution in hadronic collisions, or the properties of hadronic matter at
nonzero temperature and chemical potential. Digital computers may never be able
to achieve accurate simulations of such phenomena in QCD and other
strongly-coupled field theories; quantum computers will do so eventually,
though I'm not sure when. Progress toward quantum simulation of quantum field
theory will require the collaborative efforts of quantumists and field
theorists, and though the physics payoff may still be far away, it's worthwhile
to get started now. Today's research can hasten the arrival of a new era in
which quantum simulation fuels rapid progress in fundamental physics.Comment: 22 pages, The 36th Annual International Symposium on Lattice Field
Theory - LATTICE201
Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
We propose an optimization procedure for Euclidean path-integrals that
evaluate CFT wave functionals in arbitrary dimensions. The optimization is
performed by minimizing certain functional, which can be interpreted as a
measure of computational complexity, with respect to background metrics for the
path-integrals. In two dimensional CFTs, this functional is given by the
Liouville action. We also formulate the optimization for higher dimensional
CFTs and, in various examples, find that the optimized hyperbolic metrics
coincide with the time slices of expected gravity duals. Moreover, if we
optimize a reduced density matrix, the geometry becomes two copies of the
entanglement wedge and reproduces the holographic entanglement entropy. Our
approach resembles a continuous tensor network renormalization and provides a
concrete realization of the proposed interpretation of AdS/CFT as tensor
networks. The present paper is an extended version of our earlier report
arXiv:1703.00456 and includes many new results such as evaluations of
complexity functionals, energy stress tensor, higher dimensional extensions and
time evolutions of thermofield double states.Comment: 63 pages, 10 figure
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