20 research outputs found
No imminent quantum supremacy by boson sampling
It is predicted that quantum computers will dramatically outperform their
conventional counterparts. However, large-scale universal quantum computers are
yet to be built. Boson sampling is a rudimentary quantum algorithm tailored to
the platform of photons in linear optics, which has sparked interest as a rapid
way to demonstrate this quantum supremacy. Photon statistics are governed by
intractable matrix functions known as permanents, which suggests that sampling
from the distribution obtained by injecting photons into a linear-optical
network could be solved more quickly by a photonic experiment than by a
classical computer. The contrast between the apparently awesome challenge faced
by any classical sampling algorithm and the apparently near-term experimental
resources required for a large boson sampling experiment has raised
expectations that quantum supremacy by boson sampling is on the horizon. Here
we present classical boson sampling algorithms and theoretical analyses of
prospects for scaling boson sampling experiments, showing that near-term
quantum supremacy via boson sampling is unlikely. While the largest boson
sampling experiments reported so far are with 5 photons, our classical
algorithm, based on Metropolised independence sampling (MIS), allowed the boson
sampling problem to be solved for 30 photons with standard computing hardware.
We argue that the impact of experimental photon losses means that demonstrating
quantum supremacy by boson sampling would require a step change in technology.Comment: 25 pages, 9 figures. Comments welcom
The Classical Complexity of Boson Sampling
We study the classical complexity of the exact Boson Sampling problem where
the objective is to produce provably correct random samples from a particular
quantum mechanical distribution. The computational framework was proposed by
Aaronson and Arkhipov in 2011 as an attainable demonstration of `quantum
supremacy', that is a practical quantum computing experiment able to produce
output at a speed beyond the reach of classical (that is non-quantum) computer
hardware. Since its introduction Boson Sampling has been the subject of intense
international research in the world of quantum computing. On the face of it,
the problem is challenging for classical computation. Aaronson and Arkhipov
show that exact Boson Sampling is not efficiently solvable by a classical
computer unless and the polynomial hierarchy collapses to
the third level.
The fastest known exact classical algorithm for the standard Boson Sampling
problem takes time to produce samples for a
system with input size and output modes, making it infeasible for
anything but the smallest values of and . We give an algorithm that is
much faster, running in time and
additional space. The algorithm is simple to implement and has low constant
factor overheads. As a consequence our classical algorithm is able to solve the
exact Boson Sampling problem for system sizes far beyond current photonic
quantum computing experimentation, thereby significantly reducing the
likelihood of achieving near-term quantum supremacy in the context of Boson
Sampling.Comment: 15 pages. To appear in SODA '1
A faster hafnian formula for complex matrices and its benchmarking on a supercomputer
We introduce new and simple algorithms for the calculation of the number of
perfect matchings of complex weighted, undirected graphs with and without
loops. Our compact formulas for the hafnian and loop hafnian of
complex matrices run in time, are embarrassingly
parallelizable and, to the best of our knowledge, are the fastest exact
algorithms to compute these quantities. Despite our highly optimized algorithm,
numerical benchmarks on the Titan supercomputer with matrices up to size indicate that one would require the 288000 CPUs of this machine for
about a month and a half to compute the hafnian of a matrix.Comment: 11 pages, 7 figures. The source code of the library is available at
https://github.com/XanaduAI/hafnian . Accepted for publication in Journal of
Experimental Algorithmic
Validating multi-photon quantum interference with finite data
Multi-particle interference is a key resource for quantum information
processing, as exemplified by Boson Sampling. Hence, given its fragile nature,
an essential desideratum is a solid and reliable framework for its validation.
However, while several protocols have been introduced to this end, the approach
is still fragmented and fails to build a big picture for future developments.
In this work, we propose an operational approach to validation that encompasses
and strengthens the state of the art for these protocols. To this end, we
consider the Bayesian hypothesis testing and the statistical benchmark as most
favorable protocols for small- and large-scale applications, respectively. We
numerically investigate their operation with finite sample size, extending
previous tests to larger dimensions, and against two adversarial algorithms for
classical simulation: the Mean-Field sampler and the Metropolized Independent
Sampler. To evidence the actual need for refined validation techniques, we show
how the assessment of numerically simulated data depends on the available
sample size, as well as on the internal hyper-parameters and other practically
relevant constraints. Our analyses provide general insights into the challenge
of validation, and can inspire the design of algorithms with a measurable
quantum advantage.Comment: 10 pages, 7 figure
High performance Boson Sampling simulation via data-flow engines
In this work, we generalize the Balasubramanian-Bax-Franklin-Glynn (BB/FG)
permanent formula to account for row multiplicities during the permanent
evaluation and reduce the complexity of permanent evaluation in scenarios where
such multiplicities occur. This is achieved by incorporating n-ary Gray code
ordering of the addends during the evaluation. We implemented the designed
algorithm on FPGA-based data-flow engines and utilized the developed accessory
to speed up boson sampling simulations up to photons, by drawing samples
from a mode interferometer at an averaged rate of seconds per
sample utilizing FPGA chips. We also show that the performance of our BS
simulator is in line with the theoretical estimation of Clifford \& Clifford
\cite{clifford2020faster} providing a way to define a single parameter to
characterize the performance of the BS simulator in a portable way. The
developed design can be used to simulate both ideal and lossy boson sampling
experiments.Comment: 25 page
Validating multi-photon quantum interference with finite data
Multi-particle interference is a key resource for quantum information processing, as exemplified by Boson Sampling. Hence, given its fragile nature, an essential desideratum is a solid and reliable framework for its validation. However, while several protocols have been introduced to this end, the approach is still fragmented and fails to build a big picture for future developments. In this work, we propose an operational approach to validation that encompasses and strengthens the state of the art for these protocols. To this end, we consider the Bayesian hypothesis testing and the statistical benchmark as most favorable protocols for small- and large-scale applications, respectively. We numerically investigate their operation with finite sample size, extending previous tests to larger dimensions, and against two adversarial algorithms for classical simulation: the mean-field sampler and the metropolized independent sampler. To evidence the actual need for refined validation techniques, we show how the assessment of numerically simulated data depends on the available sample size, as well as on the internal hyper-parameters and other practically relevant constraints. Our analyses provide general insights into the challenge of validation, and can inspire the design of algorithms with a measurable quantum advantage