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arXiv:2001.02513

Analytical view on tunnable electrostatic quantum swap gate in tight-binding model

Krzysztof Dominik Pomorski

Published Jan 7, 2020• 6 citations
arXivHTMLPDF

Abstract

Generalized electrostatic quantum swap gate implemented in the chain of 2 double coupled quantum dots using single electron in semiconductor is presented in tight-binding simplistic model specifying both analytic and numerical results. The anticorrelation principle coming from Coulomb electrostatic repulsion is exploited in single electron devices. The formation of quantum entanglement is specified and supported by analytical results. The difference between classical and quantum picture is given. The correlations between geometry of quantum structures and entanglement dynamics are shown in analytical way. Effective wavefunction of single electrons is extracted from 2 electron electrostatic interactions. The presented results have its significance in cryogenic CMOS quantum technologies that gives perspective of implementation of semiconductor quantum computer on massive scale. Keyword: electrostatic quantum swap gate, entanglement, anticorrelation, tight-binding model, two-body wavefunction, correlation-anticorrelation crossover, density matrix of 2 electron system, single electron devices, coupled quantum dots

DOI
10.48550/arxiv.2001.02513

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Generalized electrostatic quantum swap gate implemented in the chain of 2 double coupled quantum dots using single electron in semiconductor is presented in tight-binding simplistic model specifying both analytic and numerical results. The anticorrelation principle coming from Coulomb electrostatic repulsion is exploited in single electron devices. The formation of quantum entanglement is specified and supported by analytical results. The difference between classical and quantum picture is given. The correlations between geometry of quantum structures and entanglement dynamics are shown in analytical way. Effective wavefunction of single electrons is extracted from 2 electron electrostatic interactions. The presented results have its significance in cryogenic CMOS quantum technologies that gives perspective of implementation of semiconductor quantum computer on massive scale. Keyword: electrostatic quantum swap gate, entanglement, anticorrelation, tight-binding model, two-body wavefunction, correlation-anticorrelation crossover, density matrix of 2 electron system, single electron devices, coupled quantum dots
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.
Analytical solutions describing quantum swap and Hadamard gate are given with the use of tight-binding approximation. Decoherence effects are described analytically for 2 interacting electrons confined by local potentials with use of tight-binding simplistic model and in Schroedinger formalism with omission of spin degree of freedom. The obtained results can be generalized for the case of [Formula: see text] electrostatically interacting quantum bodies confined by local potentials ([Formula: see text]-qubit) system representing any electrostatic quantum gate with [Formula: see text] inputs/outputs. The mathematical structure of system evolution with time is specified.
Abstract The fundamental properties of two electrostatically interacting single-electron lines (SEL) are determined from a minimalistic tight-binding model. The lines are represented by a chain of coupled quantum wells that can be implemented in a mainstream nanoscale CMOS process technology and tuned electrostatically by DC or AC voltage biases. The obtained results show an essential qualitative difference with two capacitively coupled classical electrical lines. The derived equations and their solutions prove that the two coupled SET lines can create an entanglement between electrons. The correlation function characterizing the correlation/anticorrelation in electron position is introduced both in quantum and classical descriptions of capacitively coupled SELs. The quantum measurement conducted on quantum and classical SELs is described. The difference in quantum and classical ground states can be used as the probe determining the ‘quantumness’ of the SEL system. The results indicate a possibility of constructing electrostatic (non-spin) coupled qubits that could be used as a building block in a CMOS quantum computer.
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.
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.