Ajinkya Borle, Vincent E. Elfving, Samuel J. Lomonaco
SciPost Phys. Core 4, 031 (2021) ·
published 30 November 2021

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The quantum approximate optimization algorithm (QAOA) by Farhi et al. is a quantum computational framework for solving quantum or classical optimization tasks. Here, we explore using QAOA for binary linear least squares (BLLS); a problem that can serve as a building block of several other hard problems in linear algebra, such as the nonnegative binary matrix factorization (NBMF) and other variants of the nonnegative matrix factorization (NMF) problem. Most of the previous efforts in quantum computing for solving these problems were done using the quantum annealing paradigm. For the scope of this work, our experiments were done on noiseless quantum simulators, a simulator including a devicerealistic noisemodel, and two IBM Q 5qubit machines. We highlight the possibilities of using QAOA and QAOAlike variational algorithms for solving such problems, where trial solutions can be obtained directly as samples, rather than being amplitudeencoded in the quantum wavefunction. Our numerics show that even for a small number of steps, simulated annealing can outperform QAOA for BLLS at a QAOA depth of $p\leq3$ for the probability of sampling the ground state. Finally, we point out some of the challenges involved in currentday experimental implementations of this technique on cloudbased quantum computers.
SciPost Phys. Core 4, 030 (2021) ·
published 18 November 2021

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We find the complete family of manybody quantum Hamiltonians with groundstate of Jastrow form involving the pairwise product of a pair function in an arbitrary spatial dimension. The parent Hamiltonian generally includes a twobody pairwise potential as well as a threebody potential. We thus generalize the CalogeroMarchioro construction for the threedimensional case to arbitrary spatial dimensions. The resulting family of models is further extended to include a onebody term representing an external potential, which gives rise to an additional longrange twobody interaction. Using this framework, we provide the generalization to an arbitrary spatial dimension of wellknown systems such as the CalogeroSutherland and CalogeroMoser models. We also introduce novel models, generalizing the McGuire manybody quantum bright soliton solution to higher dimensions and considering groundstates which involve e.g., polynomial, Gaussian, exponential, and hyperbolic pair functions. Finally, we show how the pair function can be reverseengineered to construct models with a given potential, such as a pairwise Yukawa potential, and to identify models governed exclusively by threebody interactions.
Edoardo G. Carnio, Andreas Buchleitner, Frank Schlawin
SciPost Phys. Core 4, 028 (2021) ·
published 15 October 2021

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We investigate how entanglement can enhance twophoton absorption in a threelevel system. First, we employ the Schmidt decomposition to determine the entanglement properties of the optimal twophoton state to drive such a transition, and the maximum enhancement which can be achieved in comparison to the optimal classical pulse. We then adapt the optimization problem to realistic experimental constraints, where photon pairs from a downconversion source are manipulated by local operations such as spatial light modulators. We derive optimal pulse shaping functions to enhance the absorption efficiency, and compare the maximal enhancement achievable by entanglement to the yield of optimally shaped, separable pulses.
Parth Bhargava, Sayantan Choudhury, Satyaki Chowdhury, Anurag Mishara, Sachin Panneer Selvam, Sudhakar Panda, Gabriel D. Pasquino
SciPost Phys. Core 4, 026 (2021) ·
published 7 October 2021

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$Circuit~ Complexity$, a well known computational technique has recently
become the backbone of the physics community to probe the chaotic behaviour and
random quantum fluctuations of quantum fields. This paper is devoted to the
study of outofequilibrium aspects and quantum chaos appearing in the universe
from the paradigm of two well known bouncing cosmological solutions viz.
$Cosine~ hyperbolic$ and $Exponential$ models of scale factors. Besides
$circuit~ complexity$, we use the $OutofTime~ Ordered~ correlation~ (OTOC)$
functions for probing the random behaviour of the universe both at early and
the late times. In particular, we use the techniques of well known twomode
squeezed state formalism in cosmological perturbation theory as a key
ingredient for the purpose of our computation. To give an appropriate
theoretical interpretation that is consistent with the observational
perspective we use the scale factor and the number of efoldings as a dynamical
variable instead of conformal time for this computation. From this study, we
found that the period of post bounce is the most interesting one. Though it may
not be immediately visible, but an exponential rise can be seen in the
$complexity$ once the post bounce feature is extrapolated to the present time
scales. We also find within the very small acceptable error range a universal
connecting relation between Complexity computed from two different kinds of
cost functionals$linearly~ weighted$ and $geodesic~ weighted$ with the OTOC.
Furthermore, from the $complexity$ computation obtained from both the
cosmological models and also using the well known MSS bound on quantum Lyapunov
exponent, $\lambda\leq 2\pi/\beta$ for the saturation of chaos, we estimate the
lower bound on the equilibrium temperature of our universe at late time scale.
Finally, we provide a rough estimation of the scrambling time in terms of the
conformal time.