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arXiv:quant-ph/0312196 · Quantum Information Processing

Geometric Approach to Digital Quantum Information

Chad T. Rigetti, Rémy Mosseri, Michel Devoret

Published Dec 1, 2004• 13 citations
arXivHTMLPDF
DOI
10.1007/s11128-004-7875-2

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With the development of science and technology, the way to represent information becomes more powerful and diversified. Recent research on digital coding metasurfaces has built an alternative bridge between wave-behaviors and information science. Different from the logic information in traditional circuits, the digital bit in coding metasurfaces is based on wave-structure interaction, which is capable of exploiting multiple degrees of freedom (DoFs). However, to what extent the digital coding metasurface can expand the information representation has not been discussed. In this work, it is shown that classical metasurfaces have the ability to mimic qubit and quantum information. An approach for simulating a two-level spin system with meta-atoms is proposed, from which the superposition for two optical spin states is constructed. It is further proposed that using geometric-phase elements with nonseparable coding states can induce the classical entanglement between polarization and spatial modes, and give the condition to achieve the maximal entanglement. This study expands the information representing range of coding metasurfaces and provides an ultrathin platform to mimic quantum information.

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With the development of science and technology, the way to represent information becomes more powerful and diversified. Recent research on digital coding metasurfaces has built an alternative bridge between wave-behaviors and information science. Different from the logic information in traditional circuits, the digital bit in coding metasurfaces is based on wave-structure interaction, which is capable of exploiting multiple degrees of freedom (DoFs). However, to what extent the digital coding metasurface can expand the information representation has not been discussed. In this work, it is shown that classical metasurfaces have the ability to mimic qubit and quantum information. An approach for simulating a two-level spin system with meta-atoms is proposed, from which the superposition for two optical spin states is constructed. It is further proposed that using geometric-phase elements with nonseparable coding states can induce the classical entanglement between polarization and spatial modes, and give the condition to achieve the maximal entanglement. This study expands the information representing range of coding metasurfaces and provides an ultrathin platform to mimic quantum information.
Geometric phases are used to construct quantum gates since it naturally resists local noises, acting as the modularized units of geometric quantum computing. Meanwhile, fast nonadiabatic geometric gates are required for reducing the information loss induced by decoherence. Here, we propose a digital simulation of nonadiabatic geometric quantum gates in terms of shortcuts to adiabaticity (STA). More specifically, we combine the invariant-based inverse engineering with optimal control theory for designing the fast and robust Abelian geometric gates against systematic error, in the context of two-level qubit systems. We exemplify X and T gates, in which the fidelities and robustness are evaluated by simulations in ideal quantum circuits. Our results can also be extended to constructing two-qubit gates, for example, a controlled-PHASE gate, which shares the equivalent effective Hamiltonian with rotation around the Z-axis of a single qubit. These STA-inspired nonadiabatic geometric gates can realize quantum error correction physically, leading to fault-tolerant quantum computing in the Noisy Intermediate-Scale Quantum (NISQ) era.
Information is physically measurable as a selection from a set of possibilities, the domain of information. This defines the term "information". The domain of the information must be known together reproducibly beforehand. As a practical consequence, digital information exchange can be made globally efficient, interoperable, and searchable to a large extent by online definition of application-optimized domains of information. There are even more far-reaching consequences for physics. The purpose of this article is to present prerequisites and possibilities for a physical approach that is consistent with the precise definition of information. This concerns not only the discretization of the sets of possible experimental results but also the order of their definition over time. The access to or comparison with the domain of information is more frequent, the earlier it was defined. The geometrical appearance of our space is apparently a delayed statistical consequence of a very frequent connection with the common primary domain of information.