99,341 research outputs found
Parquet approach to nonlocal vertex functions and electrical conductivity of disordered electrons
A diagrammatic technique for two-particle vertex functions is used to
describe systematically the influence of spatial quantum coherence and
backscattering effects on transport properties of noninteracting electrons in a
random potential. In analogy with many-body theory we construct parquet
equations for topologically distinct {\em nonlocal} irreducible vertex
functions into which the {\em local} one-particle propagator and two-particle
vertex of the coherent-potential approximation (CPA) enter as input. To
complete the two-particle parquet equations we use an integral form of the Ward
identity and determine the one-particle self-energy from the known irreducible
vertex. In this way a conserving approximation with (Herglotz) analytic
averaged Green functions is obtained. We use the limit of high spatial
dimensions to demonstrate how nonlocal corrections to the (CPA)
solution emerge. The general parquet construction is applied to the calculation
of vertex corrections to the electrical conductivity. With the aid of the
high-dimensional asymptotics of the nonlocal irreducible vertex in the
electron-hole scattering channel we derive a mean-field approximation for the
conductivity with vertex corrections. The impact of vertex corrections onto the
electronic transport is assessed quantitatively within the proposed mean-field
description on a binary alloy.Comment: REVTeX 19 pages, 9 EPS diagrams, 6 PS figure
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Quantum Algorithms for Matrix Problems and Machine Learning
This dissertation presents a study of quantum algorithms for problems that can be posed as matrix function tasks. In Chapter 1 we demonstrate a simple unifying framework for implementing of smooth functions of matrices on a quantum computer. This framework captures a variety of problems that can be solved by evaluating properties of some function of a matrix, and we identify speedups over classical algorithms for some problem classes. The analysis combines ideas from the classical theory of function approximation with the quantum algorithmic primitive of implementing linear combinations of unitary operators.
In Chapter 2 we continue this study by looking at the role of sparsity of input matrices in constructing efficient quantum algorithms. We show that classically pre-processing an input matrix by spectral sparsification can be profitable for quantum Hamiltonian simulation algorithms, without compromising the simulation error or complexity. Such preprocessing incurs a one time cost linear in the size of the matrix, but can be exploited to exponentially speed up subsequent subroutines such as inversion.
In Chapter 3, we give an application of this theory of matrix functions to the problem of estimating the Renyi entropy of an unknown quantum state. We combine matrix function techniques with mixed state quantum computation in the one-clean qubit model, and are able to bound of the expected runtime of our algorithm in terms of the unknown target quantity.
In addition to the theme of analysing the complexity of our algorithms, we also identify instances that are of practical relevance, leading us to some problems of machine learning. In Chapter 4 we investigate kernel based learning methods using random features. We work
with the QRAM input model suitable for big data, and show how matrix functions and the quantum Fourier transform can be used to devise a quantum algorithm for sampling random features that are optimised for given input data and choice of kernel. We obtain a potential exponential speedup over the best known classical algorithm even without explicit assumptions of sparsity or low rank.
Finally in Chapter 5 we consider the technique of beamsearch decoding used in natural language processing. We work in the query model, and show how quantum search with advice can be used to construct a quantum search decoder that can find the optimal parse (which may for instance be a best translation, or text-to-speech transcript) at least quadratically faster than the best known classical algorithms, and obtain super-quadratic speedups in the expected runtime.Science and Engineering Research Board (Department of Science and Technology), Government of Indi
Block encryption of quantum messages
In modern cryptography, block encryption is a fundamental cryptographic
primitive. However, it is impossible for block encryption to achieve the same
security as one-time pad. Quantum mechanics has changed the modern
cryptography, and lots of researches have shown that quantum cryptography can
outperform the limitation of traditional cryptography.
This article proposes a new constructive mode for private quantum encryption,
named , which is a very simple method to construct quantum
encryption from classical primitive. Based on mode, we
construct a quantum block encryption (QBE) scheme from pseudorandom functions.
If the pseudorandom functions are standard secure, our scheme is
indistinguishable encryption under chosen plaintext attack. If the pseudorandom
functions are permutation on the key space, our scheme can achieve perfect
security. In our scheme, the key can be reused and the randomness cannot, so a
-bit key can be used in an exponential number of encryptions, where the
randomness will be refreshed in each time of encryption. Thus -bit key can
perfectly encrypt qubits, and the perfect secrecy would not be broken
if the -bit key is reused for only exponential times.
Comparing with quantum one-time pad (QOTP), our scheme can be the same secure
as QOTP, and the secret key can be reused (no matter whether the eavesdropping
exists or not). Thus, the limitation of perfectly secure encryption (Shannon's
theory) is broken in the quantum setting. Moreover, our scheme can be viewed as
a positive answer to the open problem in quantum cryptography "how to
unconditionally reuse or recycle the whole key of private-key quantum
encryption". In order to physically implement the QBE scheme, we only need to
implement two kinds of single-qubit gates (Pauli gate and Hadamard gate),
so it is within reach of current quantum technology.Comment: 13 pages, 1 figure. Prior version appears in
eprint.iacr.org(iacr/2017/1247). This version adds some analysis about
multiple-message encryption, and modifies lots of contents. There are no
changes about the fundamental result
Localization landscape for Dirac fermions
In the theory of Anderson localization, a landscape function predicts where
wave functions localize in a disordered medium, without requiring the solution
of an eigenvalue problem. It is known how to construct the localization
landscape for the scalar wave equation in a random potential, or equivalently
for the Schr\"{o}dinger equation of spinless electrons. Here we generalize the
concept to the Dirac equation, which includes the effects of spin-orbit
coupling and allows to study quantum localization in graphene or in topological
insulators and superconductors. The landscape function is defined on a
lattice as a solution of the differential equation ,
where is the Ostrowsky comparison matrix of the Dirac
Hamiltonian. Random Hamiltonians with the same (positive definite) comparison
matrix have localized states at the same positions, defining an equivalence
class for Anderson localization. This provides for a mapping between the
Hermitian and non-Hermitian Anderson model.Comment: 6 pages, 6 figure
Random Oracles in a Quantum World
The interest in post-quantum cryptography - classical systems that remain
secure in the presence of a quantum adversary - has generated elegant proposals
for new cryptosystems. Some of these systems are set in the random oracle model
and are proven secure relative to adversaries that have classical access to the
random oracle. We argue that to prove post-quantum security one needs to prove
security in the quantum-accessible random oracle model where the adversary can
query the random oracle with quantum states.
We begin by separating the classical and quantum-accessible random oracle
models by presenting a scheme that is secure when the adversary is given
classical access to the random oracle, but is insecure when the adversary can
make quantum oracle queries. We then set out to develop generic conditions
under which a classical random oracle proof implies security in the
quantum-accessible random oracle model. We introduce the concept of a
history-free reduction which is a category of classical random oracle
reductions that basically determine oracle answers independently of the history
of previous queries, and we prove that such reductions imply security in the
quantum model. We then show that certain post-quantum proposals, including ones
based on lattices, can be proven secure using history-free reductions and are
therefore post-quantum secure. We conclude with a rich set of open problems in
this area.Comment: 38 pages, v2: many substantial changes and extensions, merged with a
related paper by Boneh and Zhandr
Quantum Lightning Never Strikes the Same State Twice
Public key quantum money can be seen as a version of the quantum no-cloning
theorem that holds even when the quantum states can be verified by the
adversary. In this work, investigate quantum lightning, a formalization of
"collision-free quantum money" defined by Lutomirski et al. [ICS'10], where
no-cloning holds even when the adversary herself generates the quantum state to
be cloned. We then study quantum money and quantum lightning, showing the
following results:
- We demonstrate the usefulness of quantum lightning by showing several
potential applications, such as generating random strings with a proof of
entropy, to completely decentralized cryptocurrency without a block-chain,
where transactions is instant and local.
- We give win-win results for quantum money/lightning, showing that either
signatures/hash functions/commitment schemes meet very strong recently proposed
notions of security, or they yield quantum money or lightning.
- We construct quantum lightning under the assumed multi-collision resistance
of random degree-2 systems of polynomials.
- We show that instantiating the quantum money scheme of Aaronson and
Christiano [STOC'12] with indistinguishability obfuscation that is secure
against quantum computers yields a secure quantum money schem
- …