A study of chaos and randomness in quantum systems
- URL: http://arxiv.org/abs/2402.00287v1
- Date: Thu, 1 Feb 2024 02:35:01 GMT
- Title: A study of chaos and randomness in quantum systems
- Authors: Sreeram PG
- Abstract summary: How classical chaos emerges from the underlying quantum world is a fundamental problem in physics.
One can understand the quantum signatures of classical chaos by studying a quantum system whose classical analogue is chaotic.
We study out-of-time-ordered computationors (OTOCs) and Loschmidt echo, the two well-known dynamical diagnostics of chaos.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: How classical chaos emerges from the underlying quantum world is a
fundamental problem in physics. The origin of this question is in the
correspondence principle. Classical chaos arises due to non-linear dynamics,
whereas quantum mechanics, driven by unitary evolution, is linear. The question
that still remains is - what are the footprints of classical chaos in the
quantum world? One can understand the quantum signatures of classical chaos by
studying a quantum system whose classical analogue is chaotic. In this thesis,
we use the quantum kicked top model of few qubits in the deep quantum regime to
investigate signatures that can be considered as a precursor to chaos in the
classical limit. In particular, we study out-of-time-ordered correlators
(OTOCs) and Loschmidt echo, the two well-known dynamical diagnostics of chaos.
We find vestiges of classical chaos even in such a deep quantum regime.
Another arena where one can study the effects of chaos and randomness is
quantum state tomography. We study quantum tomography from a continuous
measurement record obtained by measuring expectation values of a set of
Hermitian operators generated by a unitary evolution of an initial observable.
The rate of information gain and reconstruction fidelity shows vestiges of
chaos. As another contribution of this thesis, we have harnessed the power of
randomness inherent in the maximally mixed state to give an efficient quantum
algorithm to measure OTOCs. The protocol achieves an exponential speedup over
the best known classical algorithm, provided the OTOC operator to be estimated
admits an efficient gate decomposition. This protocol also helps benchmark
unitary gates, which is important from the quantum computation and control
perspective.
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