Quantum computing with two independent control functions: Optimal solutions to the teleportation protocol

Autor(es)

de Lima, Emanuel F. ; Fernandes, Marllos E. F. ; Castelano, Leonardo K.

• Tipo de documento: Artigo Científico
• Fonte: PHYSICAL REVIEW A; v. 105, n. 3, p. 8-pg., 2022-03-30.

Resumo

A central problem in quantum computing is the finding of an unknown target state that encodes the solution of a certain computational task. To accomplish this goal, the evolution from a given initial state is performed with an associated total Hamiltonian, which is a time-dependent combination of two time-independent Hamiltonians: the problem-Hamiltonian, whose ground state is the unknown target, and a driving-Hamiltonian, whose ground state is the initial state. Here, we analyze this computational problem in the light of optimal control theory, considering each Hamiltonian modulated by an independent control function. For bounded controls, there is a minimum total evolution time beyond which the target state can be exactly prepared. We show that below this minimum time a possible optimal solution consists of both controls constantly tuned at their upper bound, provided the gradients of the associated control Hamiltonian with respect to the controls (the switching functions) are positive. We refer to this type of solution as the double-bang solution. We show that the double-bang solution is optimal for a teleportation protocol up to the minimum time. Additionally, we combine the double-bang solution and the adiabatic gate teleportation protocol to implement universal quantum computing. This approach to quantum computing is very appealing because of its simplicity and experimental feasibility. To corroborate our analytical results, we propose the use of a numerical quantum optimal control technique adapted to limit the amplitude of the controls, which converges to the double-bang solution when the final evolution time is shorter than the minimum time. We compare the fidelity of the teleported state obtained for the numerically optimized two control functions with the usual one-control function scheme and with the quantum approximate optimization algorithm (QAOA). We find that the two-control approach has a better performance than the other approaches. Moreover, we investigate the energetic cost and the robustness against systematic errors in the teleportation protocol, considering different schemes. (AU)

• Processo FAPESP: 14/23648-9 - Controle quântico da matéria ultrafria
• Beneficiário: Emanuel Fernandes de Lima
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 19/09624-3 - Controle ótimo e informação quântica em nanoestruturas semicondutoras
• Beneficiário: Leonardo Kleber Castelano
• Modalidade de apoio: Auxílio à Pesquisa - Regular