4,252 research outputs found
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
Boson sampling with displaced single-photon Fock states versus single-photon-added coherent states---The quantum-classical divide and computational-complexity transitions in linear optics
Boson sampling is a specific quantum computation, which is likely hard to
implement efficiently on a classical computer. The task is to sample the output
photon number distribution of a linear optical interferometric network, which
is fed with single-photon Fock state inputs. A question that has been asked is
if the sampling problems associated with any other input quantum states of
light (other than the Fock states) to a linear optical network and suitable
output detection strategies are also of similar computational complexity as
boson sampling. We consider the states that differ from the Fock states by a
displacement operation, namely the displaced Fock states and the photon-added
coherent states. It is easy to show that the sampling problem associated with
displaced single-photon Fock states and a displaced photon number detection
scheme is in the same complexity class as boson sampling for all values of
displacement. On the other hand, we show that the sampling problem associated
with single-photon-added coherent states and the same displaced photon number
detection scheme demonstrates a computational complexity transition. It
transitions from being just as hard as boson sampling when the input coherent
amplitudes are sufficiently small, to a classically simulatable problem in the
limit of large coherent amplitudes.Comment: 7 pages, 3 figures; published versio
Boson sampling with non-identical single photons
The boson sampling problem has triggered a lot of interest in the scientific
community because of its potential of demonstrating the computational power of
quantum interference without the need of non-linear processes. However, the
intractability of such a problem with any classical device relies on the
realization of single photons approximately identical in their spectra. In this
paper we discuss the physics of boson sampling with non-identical single photon
sources, which is strongly relevant in view of scalable experimental
realizations and triggers fascinating questions in complexity theory
Exact Boson Sampling using Gaussian continuous variable measurements
BosonSampling is a quantum mechanical task involving Fock basis state
preparation and detection and evolution using only linear interactions. A
classical algorithm for producing samples from this quantum task cannot be
efficient unless the polynomial hierarchy of complexity classes collapses, a
situation believe to be highly implausible. We present method for constructing
a device which uses Fock state preparations, linear interactions and Gaussian
continuous-variable measurements for which one can show exact sampling would be
hard for a classical algorithm in the same way as Boson Sampling. The detection
events used from this arrangement does not allow a similar conclusion for the
classical hardness of approximate sampling to be drawn. We discuss the details
of this result outlining some specific properties that approximate sampling
hardness requires
Tensor network states in time-bin quantum optics
The current shift in the quantum optics community towards large-size
experiments -- with many modes and photons -- necessitates new classical
simulation techniques that go beyond the usual phase space formulation of
quantum mechanics. To address this pressing demand we formulate linear quantum
optics in the language of tensor network states. As a toy model, we extensively
analyze the quantum and classical correlations of time-bin interference in a
single fiber loop. We then generalize our results to more complex time-bin
quantum setups and identify different classes of architectures for
high-complexity and low-overhead boson sampling experiments
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