6,352 research outputs found
Quantum Bilinear Optimization
We study optimization programs given by a bilinear form over noncommutative variables subject to linear inequalities. Problems of this form include the entangled value of two-prover games, entanglement-assisted coding for classical channels, and quantum-proof randomness extractors. We introduce an asymptotically converging hierarchy of efficiently computable semidefinite programming (SDP) relaxations for this quantum optimization. This allows us to give upper bounds on the quantum advantage for all of these problems. Compared to previous work of Pironio, Navascués, and Acín [SIAM J. Optim., 20 (2010), pp. 2157-2180], our hierarchy has additional constraints. By means of examples, we illustrate the importance of these new constraints both in practice and for analytical properties. Moreover, this allows us to give a hierarchy of SDP outer approximations for the completely positive semidefinite cone introduced by Laurent and Piovesan
Hybrid GRU-CNN Bilinear Parameters Initialization for Quantum Approximate Optimization Algorithm
The Quantum Approximate Optimization Algorithm (QAOA), a pivotal paradigm in
the realm of variational quantum algorithms (VQAs), offers promising
computational advantages for tackling combinatorial optimization problems.
Well-defined initial circuit parameters, responsible for preparing a
parameterized quantum state encoding the solution, play a key role in
optimizing QAOA. However, classical optimization techniques encounter
challenges in discerning optimal parameters that align with the optimal
solution. In this work, we propose a hybrid optimization approach that
integrates Gated Recurrent Units (GRU), Convolutional Neural Networks (CNN),
and a bilinear strategy as an innovative alternative to conventional optimizers
for predicting optimal parameters of QAOA circuits. GRU serves to
stochastically initialize favorable parameters for depth-1 circuits, while CNN
predicts initial parameters for depth-2 circuits based on the optimized
parameters of depth-1 circuits. To assess the efficacy of our approach, we
conducted a comparative analysis with traditional initialization methods using
QAOA on Erd\H{o}s-R\'enyi graph instances, revealing superior optimal
approximation ratios. We employ the bilinear strategy to initialize QAOA
circuit parameters at greater depths, with reference parameters obtained from
GRU-CNN optimization. This approach allows us to forecast parameters for a
depth-12 QAOA circuit, yielding a remarkable approximation ratio of 0.998
across 10 qubits, which surpasses that of the random initialization strategy
and the PPN2 method at a depth of 10. The proposed hybrid GRU-CNN bilinear
optimization method significantly improves the effectiveness and accuracy of
parameters initialization, offering a promising iterative framework for QAOA
that elevates its performance
Renormalization algorithm for the calculation of spectra of interacting quantum systems
We present an algorithm for the calculation of eigenstates with definite
linear momentum in quantum lattices. Our method is related to the Density
Matrix Renormalization Group, and makes use of the distribution of multipartite
entanglement to build variational wave--functions with translational symmetry.
Its virtues are shown in the study of bilinear--biquadratic S=1 chains.Comment: Corrected version. We have added an appendix with an extended
explanation of the implementation of our algorith
Quantum annealing for systems of polynomial equations
Numerous scientific and engineering applications require numerically solving
systems of equations. Classically solving a general set of polynomial equations
requires iterative solvers, while linear equations may be solved either by
direct matrix inversion or iteratively with judicious preconditioning. However,
the convergence of iterative algorithms is highly variable and depends, in
part, on the condition number. We present a direct method for solving general
systems of polynomial equations based on quantum annealing, and we validate
this method using a system of second-order polynomial equations solved on a
commercially available quantum annealer. We then demonstrate applications for
linear regression, and discuss in more detail the scaling behavior for general
systems of linear equations with respect to problem size, condition number, and
search precision. Finally, we define an iterative annealing process and
demonstrate its efficacy in solving a linear system to a tolerance of
.Comment: 11 pages, 4 figures. Added example for a system of quadratic
equations. Supporting code is available at
https://github.com/cchang5/quantum_poly_solver . This is a post-peer-review,
pre-copyedit version of an article published in Scientific Reports. The final
authenticated version is available online at:
https://www.nature.com/articles/s41598-019-46729-
Bilinear noise subtraction at the GEO 600 observatory
We develop a scheme to subtract off bilinear noise from the gravitational wave strain data and demonstrate it at the GEO 600 observatory. Modulations caused by test mass misalignments on longitudinal control signals are observed to have a broadband effect on the mid-frequency detector sensitivity ranging from 50 Hz to 500 Hz. We estimate this bilinear coupling by making use of narrow-band signal injections that are already in place for noise projection purposes. A coherent bilinear signal is constructed by a two-stage system identification process where the involved couplings are approximated in terms of stable rational functions. The time-domain filtering efficiency is observed to depend upon the system identification process especially when the involved transfer functions cover a large dynamic range and have multiple resonant features. We improve upon the existing filter design techniques by employing a Bayesian adaptive directed search strategy that optimizes across the several key parameters that affect the accuracy of the estimated model. The resulting post-offline subtraction leads to a suppression of modulation side-bands around the calibration lines along with a broadband reduction of the mid-frequency noise floor. The filter coefficients are updated periodically to account for any non-stationarities that can arise within the coupling. The observed increase in the astrophysical range and a reduction in the occurrence of non-astrophysical transients suggest that the above method is a viable data cleaning technique for current and future gravitational wave observatories
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