14,388 research outputs found
Optimal signal processing in small stochastic biochemical networks
We quantify the influence of the topology of a transcriptional regulatory
network on its ability to process environmental signals. By posing the problem
in terms of information theory, we may do this without specifying the function
performed by the network. Specifically, we study the maximum mutual information
between the input (chemical) signal and the output (genetic) response
attainable by the network in the context of an analytic model of particle
number fluctuations. We perform this analysis for all biochemical circuits,
including various feedback loops, that can be built out of 3 chemical species,
each under the control of one regulator. We find that a generic network,
constrained to low molecule numbers and reasonable response times, can
transduce more information than a simple binary switch and, in fact, manages to
achieve close to the optimal information transmission fidelity. These
high-information solutions are robust to tenfold changes in most of the
networks' biochemical parameters; moreover they are easier to achieve in
networks containing cycles with an odd number of negative regulators (overall
negative feedback) due to their decreased molecular noise (a result which we
derive analytically). Finally, we demonstrate that a single circuit can support
multiple high-information solutions. These findings suggest a potential
resolution of the "cross-talk" dilemma as well as the previously unexplained
observation that transcription factors which undergo proteolysis are more
likely to be auto-repressive.Comment: 41 pages 7 figures, 5 table
Quantum Algorithm Implementations for Beginners
As quantum computers become available to the general public, the need has
arisen to train a cohort of quantum programmers, many of whom have been
developing classical computer programs for most of their careers. While
currently available quantum computers have less than 100 qubits, quantum
computing hardware is widely expected to grow in terms of qubit count, quality,
and connectivity. This review aims to explain the principles of quantum
programming, which are quite different from classical programming, with
straightforward algebra that makes understanding of the underlying fascinating
quantum mechanical principles optional. We give an introduction to quantum
computing algorithms and their implementation on real quantum hardware. We
survey 20 different quantum algorithms, attempting to describe each in a
succinct and self-contained fashion. We show how these algorithms can be
implemented on IBM's quantum computer, and in each case, we discuss the results
of the implementation with respect to differences between the simulator and the
actual hardware runs. This article introduces computer scientists, physicists,
and engineers to quantum algorithms and provides a blueprint for their
implementations
Polar Varieties and Efficient Real Elimination
Let be a smooth and compact real variety given by a reduced regular
sequence of polynomials . This paper is devoted to the
algorithmic problem of finding {\em efficiently} a representative point for
each connected component of . For this purpose we exhibit explicit
polynomial equations that describe the generic polar varieties of . This
leads to a procedure which solves our algorithmic problem in time that is
polynomial in the (extrinsic) description length of the input equations and in a suitably introduced, intrinsic geometric parameter, called
the {\em degree} of the real interpretation of the given equation system .Comment: 32 page
Optimized Compilation of Aggregated Instructions for Realistic Quantum Computers
Recent developments in engineering and algorithms have made real-world
applications in quantum computing possible in the near future. Existing quantum
programming languages and compilers use a quantum assembly language composed of
1- and 2-qubit (quantum bit) gates. Quantum compiler frameworks translate this
quantum assembly to electric signals (called control pulses) that implement the
specified computation on specific physical devices. However, there is a
mismatch between the operations defined by the 1- and 2-qubit logical ISA and
their underlying physical implementation, so the current practice of directly
translating logical instructions into control pulses results in inefficient,
high-latency programs. To address this inefficiency, we propose a universal
quantum compilation methodology that aggregates multiple logical operations
into larger units that manipulate up to 10 qubits at a time. Our methodology
then optimizes these aggregates by (1) finding commutative intermediate
operations that result in more efficient schedules and (2) creating custom
control pulses optimized for the aggregate (instead of individual 1- and
2-qubit operations). Compared to the standard gate-based compilation, the
proposed approach realizes a deeper vertical integration of high-level quantum
software and low-level, physical quantum hardware. We evaluate our approach on
important near-term quantum applications on simulations of superconducting
quantum architectures. Our proposed approach provides a mean speedup of
, with a maximum of . Because latency directly affects the
feasibility of quantum computation, our results not only improve performance
but also have the potential to enable quantum computation sooner than otherwise
possible.Comment: 13 pages, to apper in ASPLO
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