publications

2023

1. arxiv

   Hamiltonian-Oriented Homotopy QAOA

   Akash Kundu, Ludmila Botelho, and Adam Glos

   quant-ph arXiv, 2023

   Abs arXiv

   The classical homotopy optimization approach has the potential to deal with highly nonlinear landscape, such as the energy landscape of QAOA problems. Following this motivation, we introduce Hamiltonian-Oriented Homotopy QAOA (HOHo-QAOA), that is a heuristic method for combinatorial optimization using QAOA, based on classical homotopy optimization. The method consists of a homotopy map that produces an optimization problem for each value of interpolating parameter. Therefore, HOHo-QAOA decomposes the optimization of QAOA into several loops, each using a mixture of the mixer and the objective Hamiltonian for cost function evaluation. Furthermore, we conclude that the HOHo-QAOA improves the search for low energy states in the nonlinear energy landscape and outperforms other variants of QAOA.

2022

1. Phys. Rev. A

   Error mitigation for variational quantum algorithms through mid-circuit measurements

   Ludmila Botelho, Adam Glos, Akash Kundu, and 3 more authors

   Phys. Rev. A, Feb 2022

   Abs arXiv HTML

   Noisy intermediate-scale quantum algorithms require novel paradigms of error mitigation. To obtain noise-robust quantum computers, each logical qubit is equipped with hundreds or thousands of physical qubits. However, it is not possible to use memory-consuming techniques for current quantum devices having at most hundreds or thousands of physical qubits on their own. For specific problems, valid quantum states have a unique structure as in the case of Fock states and W states where the Hamming weight is fixed, and the evolution takes place in a smaller subspace of the full Hilbert space. With this preknowledge, some errors can be detected during the evolution of the circuit, by filtering the states not obeying the pattern through postselection. In this paper, we present mid-circuit postselection schemes for frequently used encodings such as one-hot, binary, gray, and domain-wall encoding. For the particular subspace of one-hot states, we propose a method that works by compressing the full Hilbert space to a smaller subspace, allowing projecting to the desired subspace without using any ancilla qubits. We demonstrate the effectiveness of the approach for the quantum alternating operator ansatz algorithm. Our method is particularly suitable for the currently available hardware, where measuring and r esetting are possible, but classical conditional operators are not.

2. Springer

   Applications of Quantum Annealing to Music Theory

   Ashish Arya, Ludmila Botelho, Fabiola Cañete, and 2 more authors

   Nov 2022

   Abs arXiv HTML

   "With the emergence of quantum computers, a new field of algorithmic music composition has been initiated. The vast majority of previous work focuses on music generation using gate-based quantum computers. An alternative model of computation is adiabatic quantum computing (AQC), and a heuristic algorithm known as quantum annealing running in the framework of AQC is a promising method for solving optimization problems. In this chapter, we lay the groundwork for music composition using quantum annealing. We approach the process of music composition as an optimization problem. We describe the fundamental methodologies needed for generating different aspects of music including melody, rhythm, and harmony. The discussed techniques are illustrated through examples to ease the understanding. The music pieces generated using D-Wave’s quantum annealers are among the first examples of their kind and presented within the scope of the chapter.

2020

1. EPJD

   Efficient quantum tomography of two-mode Wigner functions

   Ludmila Botelho, and Reinaldo Vianna

   The European Physical Journal D, Jan 2020

   Abs arXiv HTML

   We introduce an efficient method to reconstruct the Wigner function of many-mode continuous variable systems. It is based on convex optimization with semidefinite programs, and also includes a version of the maximum entropy principle, in order to yield unbiased states. A key ingredient of the proposed approach is the representation of the state in a truncated Fock basis. As a bonus, the discrete finite representation allows to easily quantify the entanglement.

2019

1. Msc Thesis

   Tomography on Continuous Variable Quantum States

   Ludmila Botelho

   Master Thesis, UFMG, Jan 2019

   Abs arXiv HTML

   In this work we have explored few tools in Quantum State Tomography for Continuous Variable Systems. The concept of quantum states in phase space representation is introduced in a simple manner by using a few statistical concepts. Unlike most texts of Quantum information in which the Wigner function for a single mode is often more used, in this text the multi-modes state Wigner function is also developed. Our numerical investigations indicate that the reconstructed method using back-projection add some error due the choice of cutoff frequency, therefore it is necessary to use data post-processing, like the semi-definite programs, which provides sufficient conditions correctly estimate the state. Once the information about the state is recovered, important features such as entanglement can also be investigated.