353 research outputs found
Non-locality and Communication Complexity
Quantum information processing is the emerging field that defines and
realizes computing devices that make use of quantum mechanical principles, like
the superposition principle, entanglement, and interference. In this review we
study the information counterpart of computing. The abstract form of the
distributed computing setting is called communication complexity. It studies
the amount of information, in terms of bits or in our case qubits, that two
spatially separated computing devices need to exchange in order to perform some
computational task. Surprisingly, quantum mechanics can be used to obtain
dramatic advantages for such tasks.
We review the area of quantum communication complexity, and show how it
connects the foundational physics questions regarding non-locality with those
of communication complexity studied in theoretical computer science. The first
examples exhibiting the advantage of the use of qubits in distributed
information-processing tasks were based on non-locality tests. However, by now
the field has produced strong and interesting quantum protocols and algorithms
of its own that demonstrate that entanglement, although it cannot be used to
replace communication, can be used to reduce the communication exponentially.
In turn, these new advances yield a new outlook on the foundations of physics,
and could even yield new proposals for experiments that test the foundations of
physics.Comment: Survey paper, 63 pages LaTeX. A reformatted version will appear in
Reviews of Modern Physic
The Quantum and Classical Streaming Complexity of Quantum and Classical Max-Cut
We investigate the space complexity of two graph streaming problems: Max-Cut
and its quantum analogue, Quantum Max-Cut. Previous work by Kapralov and
Krachun [STOC `19] resolved the classical complexity of the \emph{classical}
problem, showing that any -approximation requires
space (a -approximation is trivial with
space). We generalize both of these qualifiers, demonstrating space
lower bounds for -approximating Max-Cut and Quantum Max-Cut,
even if the algorithm is allowed to maintain a quantum state. As the trivial
approximation algorithm for Quantum Max-Cut only gives a -approximation, we
show tightness with an algorithm that returns a -approximation to the Quantum Max-Cut value of a graph in
space. Our work resolves the quantum and classical
approximability of quantum and classical Max-Cut using space.
We prove our lower bounds through the techniques of Boolean Fourier analysis.
We give the first application of these methods to sequential one-way quantum
communication, in which each player receives a quantum message from the
previous player, and can then perform arbitrary quantum operations on it before
sending it to the next. To this end, we show how Fourier-analytic techniques
may be used to understand the application of a quantum channel
A survey on the complexity of learning quantum states
We survey various recent results that rigorously study the complexity of
learning quantum states. These include progress on quantum tomography, learning
physical quantum states, alternate learning models to tomography and learning
classical functions encoded as quantum states. We highlight how these results
are paving the way for a highly successful theory with a range of exciting open
questions. To this end, we distill 25 open questions from these results.Comment: Invited article by Nature Review Physics. 39 pages, 6 figure
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
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