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Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie

Quantum mathematics: holonomic computing algorithms and their applications. Pt. 2

Anatoliy K. Prykarpatsky, Ufuk Taneri, Denis Blackmore

Published Jan 1, 2004• 0 citations
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This is a sequel to the papers (quant-ph/9910063) and (quant-ph/0004102). The aim of this paper is to give mathematical foundations to Holonomic Quantum Computation (Computer) proposed by Zanardi and Rasetti (quant-ph/9904011) and Pachos and Chountasis (quant-ph/9912093). In 2-qubit case we give an explicit form to non-abelian Berry connection of quantum computational bundle which is associated with Holonomic Quantum Computation, on some parameter space. We also suggest a possibility that not only usual holonomy but also higherdimensional holonomies must be used to prove a universality of our Holonomic
Nonadiabatic holonomic quantum computation (NHQC) offers a way to realize geometric quantum gates beyond the adiabatic regime. To extend the flexibility and control robustness, many NHQC schemes have been proposed. Here, we propose to use quantum optimal control theory to search control sequences that can realize holonomic gates. Given a target gate and the corresponding computational subspace, our optimization algorithm can find the control sequence automatically. Furthermore, by defining an averaged target function, our method can improve the robustness of the holonomic gates against the errors such as thermal noises and amplitude errors. As an application, we search the control sequences for the Hadamard, not, and cnot gates in a nitrogen-vacancy-center system.
This is a sequel to the papers (quant-ph/9910063) and (quant-ph/0004102). The aim of this paper is to give mathematical foundations to Holonomic Quantum Computation (Computer) proposed by Zanardi and Rasetti (quant-ph/9904011) and Pachos and Chountasis (quant-ph/9912093). In 2-qubit case we give an explicit form to non-abelian Berry connection of quantum computational bundle which is associated with Holonomic Quantum Computation, on some parameter space. We also suggest a possibility that not only usual holonomy but also higher-dimensional holonomies must be used to prove a universality of our Holonomic Quantum Computation.