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AIP conference proceedings

Implementation of quantum gates on quantum dot register

Fedor Pavlovich Meshchaninov, Alikhan Magomedrasulov, Leonid Evgenevich Fedichkin

Published Jan 1, 2021• 0 citations
Publisher

Abstract

A two-qubit register is simulated using a graph of four quantum dots, each of which has a point contact. One-qubit Pauli gates and two-qubit gates CNOT CZ and CP(π) were implemented, the effect of dephasing created by point contacts on the accuracy of two-qubit gates was calculated numerically, and this system was calculated using the model potential.

DOI
10.1063/5.0056736

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A two-qubit register is simulated using a graph of four quantum dots, each of which has a point contact. One-qubit Pauli gates and two-qubit gates CNOT CZ and CP(π) were implemented, the effect of dephasing created by point contacts on the accuracy of two-qubit gates was calculated numerically, and this system was calculated using the model potential.
We propose a method for implementation of a quantum computer using artificial molecules. The artificial molecule consists of two coupled quantum dots stacked along z direction and one single electron. One-qubit and two-qubit gates are constructed by one molecule and two coupled molecules, respectively.The ground state and the first excited state of the molecule are used to encode the |0> and |1> states of a qubit. The qubit is manipulated by a resonant electromagnetic wave that is applied directly to the qubit through a microstrip line. The coupling between two qubits in a quantum controlled NOT gate is switched on (off) by floating (grounding) the metal film electrodes. We study the operations of the gates by using a box-shaped quantum dot model and numerically solving a time-dependent Schridinger equation, and demonstrate that the quantum gates can perform the quantum computation. The operating speed of the gates is about one operation per 4ps. The reading operation of the output of the quantum computer can be performed by detecting the polarization of the qubits.
We propose a method for implementing a quantum computer using artificial molecules. The artificial molecule consists of two coupled quantum dots stacked along the z direction and one single electron. One-qubit and two-qubit gates are constructed by one molecule and two coupled molecules, respectively. The ground state and the first excited state of the molecule are used to encode the |0> and |1> states of a qubit. The qubit is manipulated by a resonant electromagnetic wave that is applied directly to the qubit through a microstrip line. The coupling between two qubits in a quantum-controlled NOT gate is switched on (off) by floating (grounding) the metal film electrodes. We study the operations of the gates using a box-shaped quantum dot model and numerically solving a time-dependent Schrödinger equation, and demonstrate that the quantum gates can perform quantum computations. The operating speed of the gates is about one operation per 4 ps. The reading operation of the output of the quantum computer can be performed by detecting the polarization of the qubits.
This work tries to model Single, Double and Triple electrons, spins based gates using quantum dot. These gates form universal gates in quantum computation and are building block of all logic circuits based on quantum gates. These spins are based on electrons which now days can be easily confined in quantum dots using a combination of hetero-structure and metal electrodes [5]. The modelling has taken analytical approach (One and Two Electron System [15], [10], [14]) wherever possible and numerical approach (Three Electron System). The spin manipulations in above three system, show us how to implement some of the important gates in quantum computing [NOT, CNOT,TOFFOLI etc.] in spin based quantum dot system. We think the TOFFOLI implementation is a novel architecture for a electron spin based system. We will also comment on the physical aspect of the simulation work wherever possible . We will also workout the aspect of quantum noise of the system which would be based on Davies Master(DM) Equation [8] based on Markovian approximation and Weak Coupling to the surrounding
This thesis addresses the concept of quantum computing with semiconductor quantum dots. The basic unit of a quantum computer is a quantum mechanical two-level system, the so-called quantum bit (qubit). The qubit can be defined as the spin of an electron confined in a quantum dot or as a two-dimensional subspace of the Hilbert space for several spins. Some semiconductors have several minima in their conduction band, socalled valleys. A two-dimensional valley degree of freedom can also be considered as a qubit. In this thesis, quantum registers storing spin as well as valley qubits are described theoretically. Virtual hopping yields an exchange interaction between neighboring quantum dots, which reduces the energy of antisymmetric spin-valley states according to the Pauli principle. Considering the spin and the valley degrees of freedom of two electrons in neighboring quantum dots as qubits, the exchange interaction is a four-qubit interaction. In this thesis, it will be shown that it is, nevertheless, possible to generate a universal two-qubit gate for spin qubits or for valley qubits by combining the exchange interaction and individual single-qubit gates. The exchange interaction in this two-electron double quantum dot directly provides a universal two-qubit gate for one spin and one valley qubit as well. For this, the qubits are defined as suitable subspaces, spanned by the singlet and one triplet state of the spin and the valley states, respectively, Using those gates, arbitrary quantum operations can be performed for single-spin and single-valley qubits in the same quantum register, where in one double quantum dot the quantum states are restricted to the singlet-triplet subspace. While in this register single-spin and single-valley rotations are required, these gates are dispensable in a quantum register storing spin and valley singlet-triplet qubits. The single-qubit operations, in this case, can be provided by the exchange interaction and a gradient in the energy splitting of spin and valley states when the spin qubit is stored in a double quantum dot with spin degrees of freedom only and when the spin states in the double quantum dot which stores the valley qubit are polarized. For providing the two-qubit gate, the spin and the valley qubits need to be stored in the same double quantum dot. The crucial task for this register is to interchange the spin of a spin-only and a spin-valley quantum dot in order to switch between the single-qubit and the two-qubit operation mode. This interchanging of the spin can be achieved by a valley-depending virtual hopping between the quantum dots. Furthermore, echo sequences for a so-called exchange-only qubit are considered. An exchange-only qubit is defined as a subspace in a system of three electron spins in a triple quantum dot. An inhomogeneous magnetic field, which may be caused by nuclear spins in the semiconductor, can lead to decoherence and leakage, i.e., the state might leave the qubit subspace. Suppressing this effect by an echo sequence which consists of pulses interchanging neighboring spin states, so-called SWAP gates, was proposed. Controllability over these quantum operations is provided via the exchange interaction. In this thesis, the performance of different such sequences is investigated. The analysis shows that optimization strategies developed for single spin echoes can be adapted for the three spin system. The echo sequences can be different in their order of applied SWAP gates interchanging the spins in the first and second dots or in the second and third dots. The noise suppression performance depends slightly on this order of SWAP gates. For two spins in a double quantum dot a scheme for quantum state tomography is presented. The corresponding measurement operators are constructed from a set of mutually unbiased bases of the four-dimensional two-qubit Hilbert space. These measurements are represented by short sequences of no more than three elementary quantum gates and projective measurements by the well-established spin-to-charge conversion.
In the last decade, a lot of effort have gone to find the most appropriate physical implementation of quantum computer. Quantum dot based system is one of the most promising system owing to its integrability with classical computation hardware and its versatility in realizing qubits and quantum gates. In this work, we propose a model for quantum dot based realization of qubits and quantum gates. The proposed system makes use of semiconductor hetrostructure based quantum dots and gate voltages to confine electrons and thus defining the qubits. Electron spin resonance is used to manipulate the spin state of the electrons. We implement single, double and triple qubit systems and two most widely used universal sets of quantum gates. We show full control of Bloch sphere in single qubit system, CNOT gate implementation in double qubit system and a novel way to implement Toffoli gate in triple qubit system.