431 research outputs found
Decoupling with random quantum circuits
Decoupling has become a central concept in quantum information theory with
applications including proving coding theorems, randomness extraction and the
study of conditions for reaching thermal equilibrium. However, our
understanding of the dynamics that lead to decoupling is limited. In fact, the
only families of transformations that are known to lead to decoupling are
(approximate) unitary two-designs, i.e., measures over the unitary group which
behave like the Haar measure as far as the first two moments are concerned.
Such families include for example random quantum circuits with O(n^2) gates,
where n is the number of qubits in the system under consideration. In fact, all
known constructions of decoupling circuits use \Omega(n^2) gates.
Here, we prove that random quantum circuits with O(n log^2 n) gates satisfy
an essentially optimal decoupling theorem. In addition, these circuits can be
implemented in depth O(log^3 n). This proves that decoupling can happen in a
time that scales polylogarithmically in the number of particles in the system,
provided all the particles are allowed to interact. Our proof does not proceed
by showing that such circuits are approximate two-designs in the usual sense,
but rather we directly analyze the decoupling property.Comment: 25 page
Short random circuits define good quantum error correcting codes
We study the encoding complexity for quantum error correcting codes with
large rate and distance. We prove that random Clifford circuits with gates can be used to encode qubits in qubits with a distance
provided . In
addition, we prove that such circuits typically have a depth of .Comment: 5 page
Scrambling speed of random quantum circuits
Random transformations are typically good at "scrambling" information.
Specifically, in the quantum setting, scrambling usually refers to the process
of mapping most initial pure product states under a unitary transformation to
states which are macroscopically entangled, in the sense of being close to
completely mixed on most subsystems containing a fraction fn of all n particles
for some constant f. While the term scrambling is used in the context of the
black hole information paradox, scrambling is related to problems involving
decoupling in general, and to the question of how large isolated many-body
systems reach local thermal equilibrium under their own unitary dynamics.
Here, we study the speed at which various notions of scrambling/decoupling
occur in a simplified but natural model of random two-particle interactions:
random quantum circuits. For a circuit representing the dynamics generated by a
local Hamiltonian, the depth of the circuit corresponds to time. Thus, we
consider the depth of these circuits and we are typically interested in what
can be done in a depth that is sublinear or even logarithmic in the size of the
system. We resolve an outstanding conjecture raised in the context of the black
hole information paradox with respect to the depth at which a typical quantum
circuit generates an entanglement assisted encoding against the erasure
channel. In addition, we prove that typical quantum circuits of poly(log n)
depth satisfy a stronger notion of scrambling and can be used to encode alpha n
qubits into n qubits so that up to beta n errors can be corrected, for some
constants alpha, beta > 0.Comment: 24 pages, 2 figures. Superseded by http://arxiv.org/abs/1307.063
Quantum Chaos, Delocalization, and Entanglement in Disordered Heisenberg Models
We investigate disordered one- and two-dimensional Heisenberg spin lattices
across a transition from integrability to quantum chaos from both a statistical
many-body and a quantum-information perspective. Special emphasis is devoted to
quantitatively exploring the interplay between eigenvector statistics,
delocalization, and entanglement in the presence of nontrivial symmetries. The
implications of basis dependence of state delocalization indicators (such as
the number of principal components) is addressed, and a measure of {\em
relative delocalization} is proposed in order to robustly characterize the
onset of chaos in the presence of disorder. Both standard multipartite and {\em
generalized entanglement} are investigated in a wide parameter regime by using
a family of spin- and fermion- purity measures, their dependence on
delocalization and on energy spectrum statistics being examined. A distinctive
{\em correlation between entanglement, delocalization, and integrability} is
uncovered, which may be generic to systems described by the two-body random
ensemble and may point to a new diagnostic tool for quantum chaos. Analytical
estimates for typical entanglement of random pure states restricted to a proper
subspace of the full Hilbert space are also established and compared with
random matrix theory predictions.Comment: 17 pages, 10 figures, revised versio
Experimentally Accessible Witnesses of Many-Body Localization
The phenomenon of many-body localized (MBL) systems has attracted significant interest in recent years, for its intriguing implications from a perspective of both condensed-matter and statistical physics: they are insulators even at non-zero temperature and fail to thermalize, violating expectations from quantum statistical mechanics. What is more, recent seminal experimental developments with ultra-cold atoms in optical lattices constituting analog quantum simulators have pushed many-body localized systems into the realm of physical systems that can be measured with high accuracy. In this work, we introduce experimentally accessible witnesses that directly probe distinct features of MBL, distinguishing it from its Anderson counterpart. We insist on building our toolbox from techniques available in the laboratory, including on-site addressing, super-lattices, and time-of-flight measurements, identifying witnesses based on fluctuations, density–density correlators, densities, and entanglement. We build upon the theory of out of equilibrium quantum systems, in conjunction with tensor network and exact simulations, showing the effectiveness of the tools for realistic models
Parameters of Pseudorandom Quantum Circuits
Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudorandom circuits, with the goal of identifying relevant tradeoffs and optimizing convergence. The parameters we explore include the choice of single- and two-qubit gates, the topology of the underlying physical qubit architecture, the probabilistic application of two-qubit gates, as well as circuit size, initialization, and the effect of control constraints. Building on the equivalence between pseudorandom circuits and approximate t-designs, a Markov matrix approach is employed to analyze asymptotic convergence properties of pseudorandom second-order moments to a 2-design. Quantitative results on the convergence rate as a function of the circuit size are presented for qubit topologies with a sufficient degree of symmetry. Our results may be useful towards optimizing the efficiency of random state and operator generation
Addressing Water Quality Issues in Rural Cameroon with Household Biosand Filters
This paper describes an ongoing collaboration between the Hope College student chapter of Engineers Without Borders – USA and the rural community of Nkuv in the Northwest Province of Cameroon related to improving drinking water quality using Manz biosand filters. The collaboration began in 2006 and focused on developing a community-based construction and distribution model for household water treatment units. Results from microbiology testing of the constructed filters indicate that this water treatment method is effective for improving water quality in rural areas. The results also highlight the need for ongoing assessment and adapting community education programs to provide necessary training for filter construction and maintenance. The critical finding from this study is that transferring this technology in rural settings in developing countries may require years of iterative intervention and site specific adjustments to the construction and distribution model
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