6,556 research outputs found
Computational Difficulty of Computing the Density of States
We study the computational difficulty of computing the ground state
degeneracy and the density of states for local Hamiltonians. We show that the
difficulty of both problems is exactly captured by a class which we call #BQP,
which is the counting version of the quantum complexity class QMA. We show that
#BQP is not harder than its classical counting counterpart #P, which in turn
implies that computing the ground state degeneracy or the density of states for
classical Hamiltonians is just as hard as it is for quantum Hamiltonians.Comment: v2: Accepted version. 9 pages, 1 figur
Testing product states, quantum Merlin-Arthur games and tensor optimisation
We give a test that can distinguish efficiently between product states of n
quantum systems and states which are far from product. If applied to a state
psi whose maximum overlap with a product state is 1-epsilon, the test passes
with probability 1-Theta(epsilon), regardless of n or the local dimensions of
the individual systems. The test uses two copies of psi. We prove correctness
of this test as a special case of a more general result regarding stability of
maximum output purity of the depolarising channel. A key application of the
test is to quantum Merlin-Arthur games with multiple Merlins, where we obtain
several structural results that had been previously conjectured, including the
fact that efficient soundness amplification is possible and that two Merlins
can simulate many Merlins: QMA(k)=QMA(2) for k>=2. Building on a previous
result of Aaronson et al, this implies that there is an efficient quantum
algorithm to verify 3-SAT with constant soundness, given two unentangled proofs
of O(sqrt(n) polylog(n)) qubits. We also show how QMA(2) with log-sized proofs
is equivalent to a large number of problems, some related to quantum
information (such as testing separability of mixed states) as well as problems
without any apparent connection to quantum mechanics (such as computing
injective tensor norms of 3-index tensors). As a consequence, we obtain many
hardness-of-approximation results, as well as potential algorithmic
applications of methods for approximating QMA(2) acceptance probabilities.
Finally, our test can also be used to construct an efficient test for
determining whether a unitary operator is a tensor product, which is a
generalisation of classical linearity testing.Comment: 44 pages, 1 figure, 7 appendices; v6: added references, rearranged
sections, added discussion of connections to classical CS. Final version to
appear in J of the AC
Distributed PCP Theorems for Hardness of Approximation in P
We present a new distributed model of probabilistically checkable proofs
(PCP). A satisfying assignment to a CNF formula is
shared between two parties, where Alice knows , Bob knows
, and both parties know . The goal is to have
Alice and Bob jointly write a PCP that satisfies , while
exchanging little or no information. Unfortunately, this model as-is does not
allow for nontrivial query complexity. Instead, we focus on a non-deterministic
variant, where the players are helped by Merlin, a third party who knows all of
.
Using our framework, we obtain, for the first time, PCP-like reductions from
the Strong Exponential Time Hypothesis (SETH) to approximation problems in P.
In particular, under SETH we show that there are no truly-subquadratic
approximation algorithms for Bichromatic Maximum Inner Product over
{0,1}-vectors, Bichromatic LCS Closest Pair over permutations, Approximate
Regular Expression Matching, and Diameter in Product Metric. All our
inapproximability factors are nearly-tight. In particular, for the first two
problems we obtain nearly-polynomial factors of ; only
-factor lower bounds (under SETH) were known before
The Quantum PCP Conjecture
The classical PCP theorem is arguably the most important achievement of
classical complexity theory in the past quarter century. In recent years,
researchers in quantum computational complexity have tried to identify
approaches and develop tools that address the question: does a quantum version
of the PCP theorem hold? The story of this study starts with classical
complexity and takes unexpected turns providing fascinating vistas on the
foundations of quantum mechanics, the global nature of entanglement and its
topological properties, quantum error correction, information theory, and much
more; it raises questions that touch upon some of the most fundamental issues
at the heart of our understanding of quantum mechanics. At this point, the jury
is still out as to whether or not such a theorem holds. This survey aims to
provide a snapshot of the status in this ongoing story, tailored to a general
theory-of-CS audience.Comment: 45 pages, 4 figures, an enhanced version of the SIGACT guest column
from Volume 44 Issue 2, June 201
Technical Design Report for PANDA Electromagnetic Calorimeter (EMC)
This document presents the technical layout and the envisaged performance of the Electromagnetic Calorimeter (EMC) for the
PANDA target spectrometer. The EMC has been designed to meet the physics goals of the PANDA experiment. The performance figures are based on extensive prototype tests and radiation hardness studies. The document shows that the EMC is ready for construction up to the front-end electronics interface
Fast Quantum Algorithm for Solving Multivariate Quadratic Equations
In August 2015 the cryptographic world was shaken by a sudden and surprising
announcement by the US National Security Agency NSA concerning plans to
transition to post-quantum algorithms. Since this announcement post-quantum
cryptography has become a topic of primary interest for several standardization
bodies. The transition from the currently deployed public-key algorithms to
post-quantum algorithms has been found to be challenging in many aspects. In
particular the problem of evaluating the quantum-bit security of such
post-quantum cryptosystems remains vastly open. Of course this question is of
primarily concern in the process of standardizing the post-quantum
cryptosystems. In this paper we consider the quantum security of the problem of
solving a system of {\it Boolean multivariate quadratic equations in
variables} (\MQb); a central problem in post-quantum cryptography. When ,
under a natural algebraic assumption, we present a Las-Vegas quantum algorithm
solving \MQb{} that requires the evaluation of, on average,
quantum gates. To our knowledge this is the fastest algorithm for solving
\MQb{}
A review of advances in pixel detectors for experiments with high rate and radiation
The Large Hadron Collider (LHC) experiments ATLAS and CMS have established
hybrid pixel detectors as the instrument of choice for particle tracking and
vertexing in high rate and radiation environments, as they operate close to the
LHC interaction points. With the High Luminosity-LHC upgrade now in sight, for
which the tracking detectors will be completely replaced, new generations of
pixel detectors are being devised. They have to address enormous challenges in
terms of data throughput and radiation levels, ionizing and non-ionizing, that
harm the sensing and readout parts of pixel detectors alike. Advances in
microelectronics and microprocessing technologies now enable large scale
detector designs with unprecedented performance in measurement precision (space
and time), radiation hard sensors and readout chips, hybridization techniques,
lightweight supports, and fully monolithic approaches to meet these challenges.
This paper reviews the world-wide effort on these developments.Comment: 84 pages with 46 figures. Review article.For submission to Rep. Prog.
Phy
Derandomization with Minimal Memory Footprint
Existing proofs that deduce BPL = ? from circuit lower bounds convert randomized algorithms into deterministic algorithms with large constant overhead in space. We study space-bounded derandomization with minimal footprint, and ask what is the minimal possible space overhead for derandomization. We show that BPSPACE[S] ? DSPACE[c ? S] for c ? 2, assuming space-efficient cryptographic PRGs, and, either: (1) lower bounds against bounded-space algorithms with advice, or: (2) lower bounds against certain uniform compression algorithms. Under additional assumptions regarding the power of catalytic computation, in a new setting of parameters that was not studied before, we are even able to get c ? 1.
Our results are constructive: Given a candidate hard function (and a candidate cryptographic PRG) we show how to transform the randomized algorithm into an efficient deterministic one. This follows from new PRGs and targeted PRGs for space-bounded algorithms, which we combine with novel space-efficient evaluation methods. A central ingredient in all our constructions is hardness amplification reductions in logspace-uniform TC?, that were not known before
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