Grover Adaptive Search for Constrained Polynomial Binary Optimization

Abstract

In this paper we discuss Grover Adaptive Search (GAS) for Constrained Polynomial Binary Optimization (CPBO) problems, and in particular, Quadratic Unconstrained Binary Optimization (QUBO) problems, as a special case. GAS can provide a quadratic speed-up for combinatorial optimization problems compared to brute force search. However, this requires the development of efficient oracles to represent problems and flag states that satisfy certain search criteria. In general, this can be achieved using quantum arithmetic, however, this is expensive in terms of Toffoli gates as well as required ancilla qubits, which can be prohibitive in the near-term. Within this work, we develop a way to construct efficient oracles to solve CPBO problems using GAS algorithms. We demonstrate this approach and the potential speed-up for the portfolio optimization problem, i.e. a QUBO, using simulation and experimental results obtained on real quantum hardware. However, our approach applies to higher-degree polynomial objective functions as well as constrained optimization problems.

Fuzzy Logic on Quantum Annealers

“…However, in future studies the proposed approach will be compared with other quantum computing models, such as circuit model, quantum Turing machine, measurement-based quantum computation or quantum random access machine. Among these, the circuit model is surely the most widespread and used one and future studies involving this computational model may exploit some quantum algorithms present in literature for QUBO problems optimization, such as the those proposed in [23], [24], which respectively leverage approaches based on the Grover's algorithm [12] and quantum genetic algorithms. Finally, it is important to highlight that the goal achieved by this research is the proof of the quantum computers feasibility in doing basic fuzzy operations.…”

Quantum k-community detection: algorithm proposals and cross-architectural evaluation

“…We are currently experimenting with quantum algorithms other than QAOA, such as the Grover Adaptive Search [15], in our proposed hybrid algorithms. Furthermore, we are working on a concept, how to model the use of these algorithms according to Model Driven Software Engineering principles [5].…”

“…-Gate-based (GB) quantum computing, where operators are applied to a quantum system to manipulate its state. Within this paradigm, algorithms for combinatorial optimization (e.g., QAOA [10] or Grover Adaptive Search [15]) can be utilized for community detection. -Quantum Annealing (QA), where the function which has to be optimized is encoded in the Hamiltonian of the quantum system.…”

Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information

“…Quantum computing promises potential advances in many fields, such as quantum chemistry and physics [1][2][3], biology [4][5][6], optimization [7][8][9][10], finance [11], and machine learning [12][13][14]. While fault-tolerant quantum computers are not yet in reach, a computational paradigm particularly suitable for near-term, noisy quantum devices is that of variational quantum algorithms.…”