793 research outputs found
Efficient Quantum Algorithms for State Measurement and Linear Algebra Applications
We present an algorithm for measurement of -local operators in a quantum
state, which scales logarithmically both in the system size and the output
accuracy. The key ingredients of the algorithm are a digital representation of
the quantum state, and a decomposition of the measurement operator in a basis
of operators with known discrete spectra. We then show how this algorithm can
be combined with (a) Hamiltonian evolution to make quantum simulations
efficient, (b) the Newton-Raphson method based solution of matrix inverse to
efficiently solve linear simultaneous equations, and (c) Chebyshev expansion of
matrix exponentials to efficiently evaluate thermal expectation values. The
general strategy may be useful in solving many other linear algebra problems
efficiently.Comment: 17 pages, 3 figures (v2) Sections reorganised, several clarifications
added, results unchange
Operand Folding Hardware Multipliers
This paper describes a new accumulate-and-add multiplication algorithm. The
method partitions one of the operands and re-combines the results of
computations done with each of the partitions. The resulting design turns-out
to be both compact and fast.
When the operands' bit-length is 1024, the new algorithm requires only
additions (on average), this is about half the number of additions
required by the classical accumulate-and-add multiplication algorithm
()
Secure Quantized Training for Deep Learning
We have implemented training of neural networks in secure multi-party
computation (MPC) using quantization commonly used in the said setting. To the
best of our knowledge, we are the first to present an MNIST classifier purely
trained in MPC that comes within 0.2 percent of the accuracy of the same
convolutional neural network trained via plaintext computation. More
concretely, we have trained a network with two convolution and two dense layers
to 99.2% accuracy in 25 epochs. This took 3.5 hours in our MPC implementation
(under one hour for 99% accuracy).Comment: 17 page
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RSA in hardware
textThis report presents the RSA encryption and decryption schemes and discusses several methods for expediting the computations required, specifically the modular exponentiation operation that is required for RSA. A hardware implementation of the CIOS (Coarsely Integrated Operand Scanning) algorithm for modular multiplication is attempted on a XILINX Spartan3 FPGA in the TLL-5000 development platform used at the University of Texas at Austin. The development of the hardware is discussed in detail and some Verilog source code is provided for an implementation of modular multiplication. Some source code is also provided for an RSA executable to run on the TLL-6219 ARM-based development platform, to be used to generate test vectors.Electrical and Computer Engineerin
Coarse Grainings and Irreversibility in Quantum Field Theory
In this paper we are interested in the studying coarse-graining in field
theories using the language of quantum open systems. Motivated by the ideas of
Calzetta and Hu on correlation histories we employ the Zwanzig projection
technique to obtain evolution equations for relevant observables in
self-interacting scalar field theories. Our coarse-graining operation consists
in concentrating solely on the evolution of the correlation functions of degree
less than , a treatment which corresponds to the familiar from statistical
mechanics truncation of the BBKGY hierarchy at the n-th level. We derive the
equations governing the evolution of mean field and two-point functions thus
identifying the terms corresponding to dissipation and noise. We discuss
possible applications of our formalism, the emergence of classical behaviour
and the connection to the decoherent histories framework.Comment: 25 pages, Late
Customisable arithmetic hardware designs
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Fast Digital Convolutions using Bit-Shifts
An exact, one-to-one transform is presented that not only allows digital
circular convolutions, but is free from multiplications and quantisation errors
for transform lengths of arbitrary powers of two. The transform is analogous to
the Discrete Fourier Transform, with the canonical harmonics replaced by a set
of cyclic integers computed using only bit-shifts and additions modulo a prime
number. The prime number may be selected to occupy contemporary word sizes or
to be very large for cryptographic or data hiding applications. The transform
is an extension of the Rader Transforms via Carmichael's Theorem. These
properties allow for exact convolutions that are impervious to numerical
overflow and to utilise Fast Fourier Transform algorithms.Comment: 4 pages, 2 figures, submitted to IEEE Signal Processing Letter
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