2,994 research outputs found
Can biological quantum networks solve NP-hard problems?
There is a widespread view that the human brain is so complex that it cannot
be efficiently simulated by universal Turing machines. During the last decades
the question has therefore been raised whether we need to consider quantum
effects to explain the imagined cognitive power of a conscious mind.
This paper presents a personal view of several fields of philosophy and
computational neurobiology in an attempt to suggest a realistic picture of how
the brain might work as a basis for perception, consciousness and cognition.
The purpose is to be able to identify and evaluate instances where quantum
effects might play a significant role in cognitive processes.
Not surprisingly, the conclusion is that quantum-enhanced cognition and
intelligence are very unlikely to be found in biological brains. Quantum
effects may certainly influence the functionality of various components and
signalling pathways at the molecular level in the brain network, like ion
ports, synapses, sensors, and enzymes. This might evidently influence the
functionality of some nodes and perhaps even the overall intelligence of the
brain network, but hardly give it any dramatically enhanced functionality. So,
the conclusion is that biological quantum networks can only approximately solve
small instances of NP-hard problems.
On the other hand, artificial intelligence and machine learning implemented
in complex dynamical systems based on genuine quantum networks can certainly be
expected to show enhanced performance and quantum advantage compared with
classical networks. Nevertheless, even quantum networks can only be expected to
efficiently solve NP-hard problems approximately. In the end it is a question
of precision - Nature is approximate.Comment: 38 page
Neural-network solutions to stochastic reaction networks
The stochastic reaction network is widely used to model stochastic processes
in physics, chemistry and biology. However, the size of the state space
increases exponentially with the number of species, making it challenging to
investigate the time evolution of the chemical master equation for the reaction
network. Here, we propose a machine-learning approach using the variational
autoregressive network to solve the chemical master equation. The approach is
based on the reinforcement learning framework and does not require any data
simulated in prior by another method. Different from simulating single
trajectories, the proposed approach tracks the time evolution of the joint
probability distribution in the state space of species counts, and supports
direct sampling on configurations and computing their normalized joint
probabilities. We apply the approach to various systems in physics and biology,
and demonstrate that it accurately generates the probability distribution over
time in the genetic toggle switch, the early life self-replicator, the epidemic
model and the intracellular signaling cascade. The variational autoregressive
network exhibits a plasticity in representing the multi-modal distribution by
feedback regulations, cooperates with the conservation law, enables
time-dependent reaction rates, and is efficient for high-dimensional reaction
networks with allowing a flexible upper count limit. The results suggest a
general approach to investigate stochastic reaction networks based on modern
machine learning
Adiabatic evolution on a spatial-photonic Ising machine
Combinatorial optimization problems are crucial for widespread applications
but remain difficult to solve on a large scale with conventional hardware.
Novel optical platforms, known as coherent or photonic Ising machines, are
attracting considerable attention as accelerators on optimization tasks
formulable as Ising models. Annealing is a well-known technique based on
adiabatic evolution for finding optimal solutions in classical and quantum
systems made by atoms, electrons, or photons. Although various Ising machines
employ annealing in some form, adiabatic computing on optical settings has been
only partially investigated. Here, we realize the adiabatic evolution of
frustrated Ising models with 100 spins programmed by spatial light modulation.
We use holographic and optical control to change the spin couplings
adiabatically, and exploit experimental noise to explore the energy landscape.
Annealing enhances the convergence to the Ising ground state and allows to find
the problem solution with probability close to unity. Our results demonstrate a
photonic scheme for combinatorial optimization in analogy with adiabatic
quantum algorithms and enforced by optical vector-matrix multiplications and
scalable photonic technology.Comment: 9 pages, 4 figure
Superior memory efficiency of quantum devices for the simulation of continuous-time stochastic processes
Continuous-time stochastic processes pervade everyday experience, and the
simulation of models of these processes is of great utility. Classical models
of systems operating in continuous-time must typically track an unbounded
amount of information about past behaviour, even for relatively simple models,
enforcing limits on precision due to the finite memory of the machine. However,
quantum machines can require less information about the past than even their
optimal classical counterparts to simulate the future of discrete-time
processes, and we demonstrate that this advantage extends to the
continuous-time regime. Moreover, we show that this reduction in the memory
requirement can be unboundedly large, allowing for arbitrary precision even
with a finite quantum memory. We provide a systematic method for finding
superior quantum constructions, and a protocol for analogue simulation of
continuous-time renewal processes with a quantum machine.Comment: 13 pages, 8 figures, title changed from original versio
Density Matrix Emulation of Quantum Recurrent Neural Networks for Multivariate Time Series Prediction
Quantum Recurrent Neural Networks (QRNNs) are robust candidates to model and
predict future values in multivariate time series. However, the effective
implementation of some QRNN models is limited by the need of mid-circuit
measurements. Those increase the requirements for quantum hardware, which in
the current NISQ era does not allow reliable computations. Emulation arises as
the main near-term alternative to explore the potential of QRNNs, but existing
quantum emulators are not dedicated to circuits with multiple intermediate
measurements. In this context, we design a specific emulation method that
relies on density matrix formalism. The mathematical development is explicitly
provided as a compact formulation by using tensor notation. It allows us to
show how the present and past information from a time series is transmitted
through the circuit, and how to reduce the computational cost in every time
step of the emulated network. In addition, we derive the analytical gradient
and the Hessian of the network outputs with respect to its trainable
parameters, with an eye on gradient-based training and noisy outputs that would
appear when using real quantum processors. We finally test the presented
methods using a novel hardware-efficient ansatz and three diverse datasets that
include univariate and multivariate time series. Our results show how QRNNs can
make accurate predictions of future values by capturing non-trivial patterns of
input series with different complexities.Comment: 16 pages, 6 figure
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