Quantum-enhanced analysis of discrete stochastic processes
Quantum Physics
Physics
QC1-999
Electronic computers. Computer science
Probability (math.PR)
FOS: Mathematics
FOS: Physical sciences
QA75.5-76.95
Quantum Physics (quant-ph)
Mathematics - Probability
DOI:
10.48550/arxiv.2008.06443
Publication Date:
2020-01-01
AUTHORS (3)
ABSTRACT
Discrete stochastic processes (DSP) are instrumental for modelling the dynamics of probabilistic systems and have a wide spectrum applications in science engineering. DSPs usually analyzed via Monte Carlo methods since number realizations increases exponentially with time steps, importance sampling is often required to reduce variance. We propose quantum algorithm calculating characteristic function DSP, which completely defines its probability distribution, using circuit elements that grows only linearly steps. The takes all trajectories into account hence eliminates need sampling. can be further furnished amplitude estimation provide quadratic speed-up Both these strategies improve variance beyond classical capabilities. method combined Fourier approximation estimate an expectation value any integrable random variable. Applications finance correlated walks presented exemplify usefulness our results. Proof-of-principle experiments performed IBM cloud platform.
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