23 research outputs found
Quantum Inference on Bayesian Networks
Performing exact inference on Bayesian networks is known to be #P-hard.
Typically approximate inference techniques are used instead to sample from the
distribution on query variables given the values of evidence variables.
Classically, a single unbiased sample is obtained from a Bayesian network on
variables with at most parents per node in time
, depending critically on , the probability the
evidence might occur in the first place. By implementing a quantum version of
rejection sampling, we obtain a square-root speedup, taking
time per sample. We exploit the Bayesian
network's graph structure to efficiently construct a quantum state, a q-sample,
representing the intended classical distribution, and also to efficiently apply
amplitude amplification, the source of our speedup. Thus, our speedup is
notable as it is unrelativized -- we count primitive operations and require no
blackbox oracle queries.Comment: 8 pages, 3 figures. Submitted to PR
Continuous-variable quantum neural networks
We introduce a general method for building neural networks on quantum
computers. The quantum neural network is a variational quantum circuit built in
the continuous-variable (CV) architecture, which encodes quantum information in
continuous degrees of freedom such as the amplitudes of the electromagnetic
field. This circuit contains a layered structure of continuously parameterized
gates which is universal for CV quantum computation. Affine transformations and
nonlinear activation functions, two key elements in neural networks, are
enacted in the quantum network using Gaussian and non-Gaussian gates,
respectively. The non-Gaussian gates provide both the nonlinearity and the
universality of the model. Due to the structure of the CV model, the CV quantum
neural network can encode highly nonlinear transformations while remaining
completely unitary. We show how a classical network can be embedded into the
quantum formalism and propose quantum versions of various specialized model
such as convolutional, recurrent, and residual networks. Finally, we present
numerous modeling experiments built with the Strawberry Fields software
library. These experiments, including a classifier for fraud detection, a
network which generates Tetris images, and a hybrid classical-quantum
autoencoder, demonstrate the capability and adaptability of CV quantum neural
networks
Quantum bayesian decision‑making
As a compact representation of joint probability distributions over a dependence graph of
random variables, and a tool for modelling and reasoning in the presence of uncertainty,
Bayesian networks are of great importance for artificial intelligence to combine domain
knowledge, capture causal relationships, or learn from incomplete datasets. Known as a
NP-hard problem in a classical setting, Bayesian inference pops up as a class of algorithms worth to explore in a quantum framework. This paper explores such a research direction and improves on previous proposals by a judicious use of the utility function in an entangled configuration. It proposes a completely quantum mechanical decision-making process with a proven computational advantage. A prototype implementation in Qiskit (a Python based program development kit for the IBM Q machine) is discussed as a proof-of-concept.This work is fnanced by the ERDF–European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation–COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT, within project POCI-01- 0145-FEDER-030947. The frst author was further supported by project NORTE-01-0145- FEDER-000037, funded by Norte Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement
Quantum Natural Gradient for Variational Bayes
Variational Bayes (VB) is a critical method in machine learning and
statistics, underpinning the recent success of Bayesian deep learning. The
natural gradient is an essential component of efficient VB estimation, but it
is prohibitively computationally expensive in high dimensions. We propose a
hybrid quantum-classical algorithm to improve the scaling properties of natural
gradient computation and make VB a truly computationally efficient method for
Bayesian inference in highdimensional settings. The algorithm leverages matrix
inversion from the linear systems algorithm by Harrow, Hassidim, and Lloyd
[Phys. Rev. Lett. 103, 15 (2009)] (HHL). We demonstrate that the matrix to be
inverted is sparse and the classical-quantum-classical handoffs are
sufficiently economical to preserve computational efficiency, making the
problem of natural gradient for VB an ideal application of HHL. We prove that,
under standard conditions, the VB algorithm with quantum natural gradient is
guaranteed to converge. Our regression-based natural gradient formulation is
also highly useful for classical VB
A Programmable True Random Number Generator Using Commercial Quantum Computers
Random number generators (RNG) are essential elements in many cryptographic
systems. True random number generators (TRNG) rely upon sources of randomness
from natural processes such as those arising from quantum mechanics phenomena.
We demonstrate that a quantum computer can serve as a high-quality, weakly
random source for a generalized user-defined probability mass function (PMF).
Specifically, QC measurement implements the process of variate sampling
according to a user-specified PMF resulting in a word comprised of electronic
bits that can then be processed by an extractor function to address
inaccuracies due to non-ideal quantum gate operations and other system biases.
We introduce an automated and flexible method for implementing a TRNG as a
programmed quantum circuit that executes on commercially-available, gate-model
quantum computers. The user specifies the desired word size as the number of
qubits and a definition of the desired PMF. Based upon the user specification
of the PMF, our compilation tool automatically synthesizes the desired TRNG as
a structural OpenQASM file containing native gate operations that are optimized
to reduce the circuit's quantum depth. The resulting TRNG provides multiple
bits of randomness for each execution/measurement cycle; thus, the number of
random bits produced in each execution is limited only by the size of the QC.
We provide experimental results to illustrate the viability of this approach.Comment: 15 pages, 7 figures, SPIE Defense + Commercial Sensing: Quantum
Information Science, Sensing, and Computation X
Quantum belief function
The belief function in Dempster Shafer evidence theory can express more
information than the traditional Bayesian distribution. It is widely used in
approximate reasoning, decision-making and information fusion. However, its
power exponential explosion characteristics leads to the extremely high
computational complexity when handling large amounts of elements in classic
computers. In order to solve the problem, we encode the basic belief assignment
(BBA) into quantum states, which makes each qubit correspond to control an
element. Besides the high efficiency, this quantum expression is very conducive
to measure the similarity between two BBAs, and the measuring quantum algorithm
we come up with has exponential acceleration theoretically compared to the
corresponding classical algorithm. In addition, we simulate our quantum version
of BBA on Qiskit platform, which ensures the rationality of our algorithm
experimentally. We believe our results will shed some light on utilizing the
characteristic of quantum computation to handle belief function more
conveniently