9,129 research outputs found
Quantum Circuit Cosmology: The Expansion of the Universe Since the First Qubit
We consider cosmological evolution from the perspective of quantum
information. We present a quantum circuit model for the expansion of a comoving
region of space, in which initially-unentangled ancilla qubits become entangled
as expansion proceeds. We apply this model to the comoving region that now
coincides with our Hubble volume, taking the number of entangled degrees of
freedom in this region to be proportional to the de Sitter entropy. The quantum
circuit model is applicable for at most 140 -folds of inflationary and
post-inflationary expansion: we argue that no geometric description was
possible before the time when our comoving region was one Planck length
across, and contained one pair of entangled degrees of freedom. This approach
could provide a framework for modeling the initial state of inflationary
perturbations.Comment: v2, minor correction
Geometrical bounds on irreversibility in open quantum systems
Clausius inequality has deep implications for reversibility and the arrow of
time. Quantum theory is able to extend this result for closed systems by
inspecting the trajectory of the density matrix on its manifold. Here we show
that this approach can provide an upper and lower bound to the irreversible
entropy production for open quantum systems as well. These provide insights on
the thermodynamics of the information erasure. Limits of the applicability of
our bounds are discussed, and demonstrated in a quantum photonic simulator
From quantum circuits to adiabatic algorithms
This paper explores several aspects of the adiabatic quantum computation
model. We first show a way that directly maps any arbitrary circuit in the
standard quantum computing model to an adiabatic algorithm of the same depth.
Specifically, we look for a smooth time-dependent Hamiltonian whose unique
ground state slowly changes from the initial state of the circuit to its final
state. Since this construction requires in general an n-local Hamiltonian, we
will study whether approximation is possible using previous results on ground
state entanglement and perturbation theory. Finally we will point out how the
adiabatic model can be relaxed in various ways to allow for 2-local partially
adiabatic algorithms as well as 2-local holonomic quantum algorithms.Comment: Version accepted by and to appear in Phys. Rev.
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
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