23,949 research outputs found
On connectivity-dependent resource requirements for digital quantum simulation of -level particles
A primary objective of quantum computation is to efficiently simulate quantum
physics. Scientifically and technologically important quantum Hamiltonians
include those with spin-, vibrational, photonic, and other bosonic degrees
of freedom, i.e. problems composed of or approximated by -level particles
(qudits). Recently, several methods for encoding these systems into a set of
qubits have been introduced, where each encoding's efficiency was studied in
terms of qubit and gate counts. Here, we build on previous results by including
effects of hardware connectivity. To study the number of SWAP gates required to
Trotterize commonly used quantum operators, we use both analytical arguments
and automatic tools that optimize the schedule in multiple stages. We study the
unary (or one-hot), Gray, standard binary, and block unary encodings, with
three connectivities: linear array, ladder array, and square grid. Among other
trends, we find that while the ladder array leads to substantial efficiencies
over the linear array, the advantage of the square over the ladder array is
less pronounced. These results are applicable in hardware co-design and in
choosing efficient qudit encodings for a given set of near-term quantum
hardware. Additionally, this work may be relevant to the scheduling of other
quantum algorithms for which matrix exponentiation is a subroutine.Comment: Accepted to QCE20 (IEEE Quantum Week). Corrected erroneous circuits
in Figure
Variable-Length Coding of Two-Sided Asymptotically Mean Stationary Measures
We collect several observations that concern variable-length coding of
two-sided infinite sequences in a probabilistic setting. Attention is paid to
images and preimages of asymptotically mean stationary measures defined on
subsets of these sequences. We point out sufficient conditions under which the
variable-length coding and its inverse preserve asymptotic mean stationarity.
Moreover, conditions for preservation of shift-invariant -fields and
the finite-energy property are discussed and the block entropies for stationary
means of coded processes are related in some cases. Subsequently, we apply
certain of these results to construct a stationary nonergodic process with a
desired linguistic interpretation.Comment: 20 pages. A few typos corrected after the journal publicatio
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