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arXiv:1912.11544 · IEEE Access

CMOS Position-Based Charge Qubits: Theoretical Analysis of Control and Entanglement

Elena Blokhina, Panagiotis Giounanlis, Andrew K. Mitchell, Dirk R. Leipold, Robert Bogdan Staszewski

Published Dec 19, 2019• 32 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1109/access.2019.2960684

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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.
We investigate the characteristics of purely electrostatic interactions with external gates in constructing full single-qubit manipulations. The quantum bit is naturally encoded in the spatial wave function of the electron system. Single-electron transistor arrays based on quantum dots or insulating interfaces typically allow for electrostatic controls where the interisland tunneling is considered constant, e.g., determined by the thickness of an insulating layer. A representative array of $3\ifmmode\times\else\texttimes\fi{}3$ quantum dots with two mobile electrons is analyzed using a Hubbard Hamiltonian and a capacitance matrix formalism. Our study shows that it is easy to realize the first quantum gate for single-qubit operations, but that a second quantum gate comes only at the cost of compromising the low-energy two-level system that encodes the qubit. We use perturbative arguments and the Feshbach formalism to show that this compromising of the two-level system is a rather general feature for electrostatically interacting qubits and is not just related to the specific details of the system chosen. We show further that full implementation requires tunable tunneling or external magnetic fields.
We present a generalized electrostatic SWAP gate realized in a chain of two double quantum dots operated in the single-electron regime. Using a minimalist tight-binding model, we derive analytical results and corroborate them with numerical simulations. We exploit the charge anticorrelation arising from Coulomb repulsion and quantify the resulting entanglement generation. We contrast classical and quantum descriptions and show how device geometry and coupling strengths govern entanglement dynamics and gate performance. The results are relevant to cryogenic, CMOS-compatible quantum technologies and suggest a route toward large-scale semiconductor implementations of quantum logic. Finally, we outline a systematic procedure for translating classical electrostatic logic gates into single-electron quantum gates.
We present a generalized electrostatic SWAP gate realized in a chain of two double quantum dots operated in the single-electron regime. Using a minimalist tight-binding model, we derive analytical results and corroborate them with numerical simulations. We exploit the charge anticorrelation arising from Coulomb repulsion and quantify the resulting entanglement generation. We contrast classical and quantum descriptions and show how device geometry and coupling strengths govern entanglement dynamics and gate performance. The results are relevant to cryogenic, CMOS-compatible quantum technologies and suggest a route toward large-scale semiconductor implementations of quantum logic. Finally, we outline a systematic procedure for translating classical electrostatic logic gates into single-electron quantum gates.
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.