258 research outputs found
Quantum Causal Graph Dynamics
Consider a graph having quantum systems lying at each node. Suppose that the
whole thing evolves in discrete time steps, according to a global, unitary
causal operator. By causal we mean that information can only propagate at a
bounded speed, with respect to the distance given by the graph. Suppose,
moreover, that the graph itself is subject to the evolution, and may be driven
to be in a quantum superposition of graphs---in accordance to the superposition
principle. We show that these unitary causal operators must decompose as a
finite-depth circuit of local unitary gates. This unifies a result on Quantum
Cellular Automata with another on Reversible Causal Graph Dynamics. Along the
way we formalize a notion of causality which is valid in the context of quantum
superpositions of time-varying graphs, and has a number of good properties.
Keywords: Quantum Lattice Gas Automata, Block-representation,
Curtis-Hedlund-Lyndon, No-signalling, Localizability, Quantum Gravity, Quantum
Graphity, Causal Dynamical Triangulations, Spin Networks, Dynamical networks,
Graph Rewriting.Comment: 8 pages, 1 figur
Causal Dynamics of Discrete Surfaces
We formalize the intuitive idea of a labelled discrete surface which evolves
in time, subject to two natural constraints: the evolution does not propagate
information too fast; and it acts everywhere the same.Comment: In Proceedings DCM 2013, arXiv:1403.768
Birhythmicity in a model for the cyclic AMP signalling system of the slime mold Dictyostelium discoideum
AbstractWe demonstrate the coexistence of two simultaneously stable periodic regimes in a model based on receptor desensitization for the cyclic AMP signalling system of the slime mold Dictyostelium discoideum. These results provide the first example of autonomous birhythmicity in a biochemical model closely related to experimental observations. Whereas the transition from one stable mode of oscillations to the other can be elicited by suprathreshold stimuli, the two periodic regimes differ in their sensitivity to perturbations. That multiple oscillations occur in a model based on a single feedback loop suggests that the conditions for birhythmicity are widely satisfied in biological systems
Benchmarking quantum co-processors in an application-centric, hardware-agnostic and scalable way
Existing protocols for benchmarking current quantum co-processors fail to
meet the usual standards for assessing the performance of
High-Performance-Computing platforms. After a synthetic review of these
protocols -- whether at the gate, circuit or application level -- we introduce
a new benchmark, dubbed Atos Q-score (TM), that is application-centric,
hardware-agnostic and scalable to quantum advantage processor sizes and beyond.
The Q-score measures the maximum number of qubits that can be used effectively
to solve the MaxCut combinatorial optimization problem with the Quantum
Approximate Optimization Algorithm. We give a robust definition of the notion
of effective performance by introducing an improved approximation ratio based
on the scaling of random and optimal algorithms. We illustrate the behavior of
Q-score using perfect and noisy simulations of quantum processors. Finally, we
provide an open-source implementation of Q-score that makes it easy to compute
the Q-score of any quantum hardware
Phase polynomials synthesis algorithms for NISQ architectures and beyond
We present a framework for the synthesis of phase polynomials that addresses
both cases of full connectivity and partial connectivity for NISQ
architectures. In most cases, our algorithms generate circuits with lower CNOT
count and CNOT depth than the state of the art or have a significantly smaller
running time for similar performances. We also provide methods that can be
applied to our algorithms in order to trade an increase in the CNOT count for a
decrease in execution time, thereby filling the gap between our algorithms and
faster ones
Optimal Hadamard gate count for Clifford synthesis of Pauli rotations sequences
The Clifford gate set is commonly used to perform universal quantum
computation. In such setup the gate is typically much more expensive to
implement in a fault-tolerant way than Clifford gates. To improve the
feasibility of fault-tolerant quantum computing it is then crucial to minimize
the number of gates. Many algorithms, yielding effective results, have been
designed to address this problem. It has been demonstrated that performing a
pre-processing step consisting of reducing the number of Hadamard gates in the
circuit can help to exploit the full potential of these algorithms and thereby
lead to a substantial -count reduction. Moreover, minimizing the number of
Hadamard gates also restrains the number of additional qubits and operations
resulting from the gadgetization of Hadamard gates, a procedure used by some
compilers to further reduce the number of gates. In this work we tackle the
Hadamard gate reduction problem, and propose an algorithm for synthesizing a
sequence of Pauli rotations with a minimal number of Hadamard gates. Based on
this result, we present an algorithm which optimally minimizes the number of
Hadamard gates lying between the first and the last gate of the circuit
Costes
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