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arXiv:1911.02094 · AIP conference proceedings

Towards quantum internet and non-local communication in position-based qubits

Krzysztof Dominik Pomorski, Robert Bogdan Staszewski

Published Jan 1, 2020• 17 citations
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Abstract

Non-local communication between position-based qubits is described for a system of a quantum electromagnetic resonator entangled to two semiconductor electrostatic qubits via an interaction between matter and radiation by Jaynes-Cummings tight-binding Hamiltonian. Principle of quantum communication between position-dependent qubits is explained. Further prospects of the model development are given. The obtained results bring foundation for the construction of quantum internet and quantum communication networks between position-based qubits that are implementable in semiconductor single-electron devices that can be realized in current CMOS technologies. The case of two semiconductor position-dependent qubits interacting with quantum electromagnetic cavity is discussed and general form of tight-binding Hamiltonian is derived with renormalized tight-binding coefficients. The considerations also describe the situation of mutual qubit-qubit electrostatic interaction.

DOI
10.1063/5.0011369

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Non-local communication between position-based qubits is described for a system of a quantum electromagnetic resonator entangled to two semiconductor electrostatic qubits via an interaction between matter and radiation by Jaynes-Cummings tight-binding Hamiltonian. Principle of quantum communication between position-dependent qubits is explained. Further prospects of the model development are given. The obtained results bring foundation for the construction of quantum internet and quantum communication networks between position-based qubits that are implementable in semiconductor single-electron devices that can be realized in current CMOS technologies. The case of two semiconductor position-dependent qubits interacting with quantum electromagnetic cavity is discussed and general form of tight-binding Hamiltonian is derived with renormalized tight-binding coefficients. The considerations also describe the situation of mutual qubit-qubit electrostatic interaction.
Analytical solutions for a tight-binding model are presented for a position-based qubit and N interacting qubits realized by quasi-one-dimensional network of coupled quantum dots expressed by connected or disconnected graphs of any topology in 2 and 3 dimensions where one electron is presented at each separated graphs. Electron(s) quantum dynamic state is described under various electromagnetic circumstances with an omission spin degree-of-freedom. The action of Hadamard and phase rotating gate is given by analytical formulas derived and formulated for any case of physical field evolution preserving the occupancy of two-energy level system. The procedure for heating up and cooling down of the quantum state placed in position based qubit is described. The interaction of position-based qubit with electromagnetic cavity is described. In particular non-local communication between position based qubits is given. It opens the perspective of implementation of quantum internet among electrostatic CMOS quantum computers (quantum chips). The interface between superconducting Josephson junction and semiconductor position-based qubit implemented in coupled semiconductor q-dots is described such that it can be the base for electrostatic interface between superconducting and semiconductor quantum computer. Modification of Andreev Bound State in Josephson junction by the presence of semiconductor qubit in its proximity and electrostatic interaction with superconducting qubit is spotted by the minimalistic tight-binding model. The obtained results allow in creating interface between semiconductor quantum computer and superconducting quantum computer. They open the perspective of construction of QISKIT like software that will describe both types of quantum computers as well as their interface.
In this study, a formal definition, robustness analysis and discussion on the control of a position-based semiconductor charge qubit are presented. Such a qubit can be realized in a chain of coupled quantum dots, forming a register of charge-coupled transistor-like devices, and is intended for CMOS implementation in scalable quantum computers. We discuss the construction and operation of this qubit, its Bloch sphere, and relation with maximally localized Wannier functions which define its position-based nature. We then demonstrate how to build a tight-binding model of single and multiple interacting qubits from first principles of the Schrödinger formalism. We provide all required formulae to calculate the maximally localized functions and the entries of the Hamiltonian matrix in the presence of interaction between qubits. We use three illustrative examples to demonstrate the electrostatic interaction of electrons and discuss how to build a model for many-electron (qubit) system. To conclude this study, we show that charge qubits can be entangled through electrostatic interaction.
CMOS technologies facilitate the possibility of implementing quantum logic in silicon. In this work, we discuss a minimalistic modelling of entangled photon communication in semiconductor qubits. We demonstrate that electrostatic actuation is sufficient to construct and control desired potential energy profiles along a Si quantum dot (QD) structure allowing the formation of position-based qubits. We further discuss a basic mathematical formalism to define the position-based qubits and their evolution under the presence of external driving fields. Then, based on Jaynes–Cummings–Hubbard formalism, we expand the model to include the description of the position-based qubits involving four energy states coupled with a cavity. We proceed with showing an anti-correlation between the various quantum states. Moreover, we simulate an example of a quantum trajectory as a result of transitions between the quantum states and we plot the emitted/absorbed photos in the system with time. Lastly, we examine the system of two coupled position-based qubits via a waveguide. We demonstrate a mechanism to achieve a dynamic interchange of information between these qubits over larger distances, exploiting both an electrostatic actuation/control of qubits and their photon communication. We define the entanglement entropy between two qubits and we find that their quantum states are in principle entangled.
Dynamics of N bodies interacting with quantum cavity is presented. The rotating frame approximation is not used and obtained solutions are the most basic in the framework of generalized Jaynes-Cummings tight-binding model. All presented solutions are entirely analytical and are expressed in terms of elementary functions. Presented scheme can easily be generalized into N bodies (qubits) with M energetic levels interacting with quantum electromagnetic cavity with K energetic levels. Presented framework can be used for construction of software modeling quantum communication between semi-conductor single-electron position-based qubits. Keywords: Jaynes-Cummings tight-binding model, quantum communication, Rabi oscillations, position-based qubit, CMOS quantum computer, single-electron devices
Analytical solutions for a tight-binding model are presented for position-based charge qubits and N-interacting qubits realized by quasi-one-dimensional network of coupled quantum dots (QD) expressed by connected or disconnected graphs of any topology in two and three dimensions where one electron is present at each separated graph. Electron(s) quantum dynamical state is described under various electromagnetic circumstances with omission spin degree-of-freedom. The action of Hadamard and phase-rotating gates is given by analytical formulas derived and formulated for any case of a physical field evolution preserving the occupancy of a two-energetic-level system. The interface between a superconducting Josephson junction and semiconductor position-based qubit implemented in coupled semiconductor QDs is described, which can be the base for electrostatic interface between superconducting and semiconductor quantum computer. Modification of Andreev Bound State in Josephson junction by the presence of semiconductor qubit in its proximity and electrostatic interaction with superconducting qubit is supported by the minimalistic tight-binding model that also can indicate topological phase transition. The obtained results can be generalized for a case of electrostatic interaction of the semiconductor qubit with the different types of Josephson junctions. The operation of phase rotating gate implemented in semiconductor position-based qubit with use of electrical and magnetic field is presented with use of analytical approach.
The interface between a superconducting Josephson junction and a semiconductor position-based qubit implemented in coupled semiconductor q-dots is described as a possible base for an electrostatic interface between superconducting and semiconductor quantum computers.A modification of an Andreev bound state in a Josephson junction by the presence of a semiconductor qubit in its proximity and electrostatic interaction with a superconducting qubit is spotted by the minimalist tight-binding model.The obtained results allow for the creation of an interface between a semiconductor quantum computer and a superconducting quantum computer.The existence of topological states of matter is indicated.They open a perspective for the construction of QISKIT-like software that will describe both types of quantum computers as well as their interface.