19,273 research outputs found
Bridging the gap between general probabilistic theories and the device-independent framework for nonlocality and contextuality
Characterizing quantum correlations in terms of information-theoretic
principles is a popular chapter of quantum foundations. Traditionally, the
principles adopted for this scope have been expressed in terms of conditional
probability distributions, specifying the probability that a black box produces
a certain output upon receiving a certain input. This framework is known as
"device-independent". Another major chapter of quantum foundations is the
information-theoretic characterization of quantum theory, with its sets of
states and measurements, and with its allowed dynamics. The different
frameworks adopted for this scope are known under the umbrella term "general
probabilistic theories". With only a few exceptions, the two programmes on
characterizing quantum correlations and characterizing quantum theory have so
far proceeded on separate tracks, each one developing its own methods and its
own agenda. This paper aims at bridging the gap, by comparing the two
frameworks and illustrating how the two programmes can benefit each other.Comment: 61 pages, no figures, published versio
Computational Complexity in Electronic Structure
In quantum chemistry, the price paid by all known efficient model chemistries
is either the truncation of the Hilbert space or uncontrolled approximations.
Theoretical computer science suggests that these restrictions are not mere
shortcomings of the algorithm designers and programmers but could stem from the
inherent difficulty of simulating quantum systems. Extensions of computer
science and information processing exploiting quantum mechanics has led to new
ways of understanding the ultimate limitations of computational power.
Interestingly, this perspective helps us understand widely used model
chemistries in a new light. In this article, the fundamentals of computational
complexity will be reviewed and motivated from the vantage point of chemistry.
Then recent results from the computational complexity literature regarding
common model chemistries including Hartree-Fock and density functional theory
are discussed.Comment: 14 pages, 2 figures, 1 table. Comments welcom
Foundations for a theory of emergent quantum mechanics and emergent classical gravity
Quantum systems are viewed as emergent systems from the fundamental degrees
of freedom. The laws and rules of quantum mechanics are understood as an
effective description, valid for the emergent systems and specially useful to
handle probabilistic predictions of observables. After introducing the
geometric theory of Hamilton-Randers spaces and reformulating it using Hilbert
space theory, a Hilbert space structure is constructed from the Hilbert space
formulation of the underlying Hamilton-Randers model and associated with the
space of wave functions of quantum mechanical systems. We can prove the
emergence of the Born rule from ergodic considerations. A geometric mechanism
for a natural spontaneous collapse of the quantum states based on the
concentration of measure phenomena as it appears in metric geometry is
discussed.We show the existence of stable vacua states for the quantized matter
Hamiltonian. Another consequence of the concentration of measure is the
emergence of a weak equivalence principle for one of the dynamics of the
fundamental degrees of freedom. We suggest that the reduction of the quantum
state is driven by a gravitational type interaction.
Such interaction appears only in the dynamical domain when localization of
quantum observables happens, it must be a classical interaction. We discuss the
double slit experiment in the context of the framework proposed, the
interference phenomena associated with a quantum system in an external
gravitational potential, a mechanism explaining non-quantum locality and also
provide an argument in favour of an emergent interpretation of every
macroscopic time parameter. Entanglement is partially described in the context
of Hamilton-Randers theory and how naturally Bell's inequalities should be
violated.Comment: Extensive changes in chapter 1 and chapter 2; minor changes in other
chapters; several refereces added and others update; 192 pages including
index of contents and reference
Tractable Simulation of Error Correction with Honest Approximations to Realistic Fault Models
In previous work, we proposed a method for leveraging efficient classical
simulation algorithms to aid in the analysis of large-scale fault tolerant
circuits implemented on hypothetical quantum information processors. Here, we
extend those results by numerically studying the efficacy of this proposal as a
tool for understanding the performance of an error-correction gadget
implemented with fault models derived from physical simulations. Our approach
is to approximate the arbitrary error maps that arise from realistic physical
models with errors that are amenable to a particular classical simulation
algorithm in an "honest" way; that is, such that we do not underestimate the
faults introduced by our physical models. In all cases, our approximations
provide an "honest representation" of the performance of the circuit composed
of the original errors. This numerical evidence supports the use of our method
as a way to understand the feasibility of an implementation of quantum
information processing given a characterization of the underlying physical
processes in experimentally accessible examples.Comment: 34 pages, 9 tables, 4 figure
Low dimensional manifolds for exact representation of open quantum systems
Weakly nonlinear degrees of freedom in dissipative quantum systems tend to
localize near manifolds of quasi-classical states. We present a family of
analytical and computational methods for deriving optimal unitary model
transformations based on representations of finite dimensional Lie groups. The
transformations are optimal in that they minimize the quantum relative entropy
distance between a given state and the quasi-classical manifold. This naturally
splits the description of quantum states into quasi-classical coordinates that
specify the nearest quasi-classical state and a transformed quantum state that
can be represented in fewer basis levels. We derive coupled equations of motion
for the coordinates and the transformed state and demonstrate how this can be
exploited for efficient numerical simulation. Our optimization objective
naturally quantifies the non-classicality of states occurring in some given
open system dynamics. This allows us to compare the intrinsic complexity of
different open quantum systems.Comment: Added section on semi-classical SR-latch, added summary of method,
revised structure of manuscrip
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