Testing accelerated stochastic algorithms in two dimensions

John B. Kogut

Xutao Han, Zhiyi Li, Wei Gu +1 more

Scenario-based stochastic optimization is a prevalent method for the economic dispatch of renewables-rich power systems. To reduce the time and space complexities for generating massive scenarios and solving pertinent mixed-integer stochastic optimization efficiently, quantum computing can provide critical assistance. To this end, we first propose the unified quantum amplitude estimation (UQAE) to generate massive scenarios with quadratic acceleration by a few qubits, after which the dimension of state variables embedded in the two-stage stochastic optimization also decreases exponentially. Then, by utilizing quantum-classical Benders decomposition, we accelerate the mixed integer master problem in the first stage on quantum processing units, while convex subproblems are solved on central processing units. Especially considering limited qubits in the noisy intermediate-scale quantum era, we propose to reduce the scale of master problem by scenario clustering and cut selection using the customized quantum approximation optimization algorithm (QAOA). Mathematically, we not only prove the decreases of complexities by UQAE-QAOA but also give the feasible ranges of penalty factors for transforming constrained problems into Ising models. Finally, we perform numerical experiments on modified IEEE systems to test the efficiency and accuracy of UQAE-QAOA, as well as the scalability of the designed quantum scheme.

Syed Asadullah Hashmi

Maria Paola Bianchi, Beatrice Palano

We study the stochastic events induced by MM-qfa's working on unary alphabets. We give two algorithms for unary MM-qfa's: the first computes the dimension of the ergodic and transient components of the non halting subspace, while the second tests whe

Piotr Garbaczewski

Jiangwei Shang, Otfried Gühne

A well-known strategy to characterize multiparticle entanglement utilizes the notion of stochastic local operations and classical communication (SLOCC), but characterizing the resulting entanglement classes is difficult. Given a multiparticle quantum state, we first show that Gilbert's algorithm can be adapted to prove separability or membership in a certain entanglement class. We then present two algorithms for convex optimization over SLOCC classes. The first algorithm uses a simple gradient approach, while the other one employs the accelerated projected-gradient method. For demonstration, the algorithms are applied to the likelihood-ratio test using experimental data on bound entanglement of a noisy four-photon Smolin state [Phys. Rev. Lett. 105, 130501 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.130501].