Propose a implementation of a universal set of one-and two-qubit gates for quantum computation using the spin states of coupled single-electron quantum dots. Superoperator of the gate quality are computed within a newly derived spin master equation incorporating decoherence in the Born and Markov approximation.
We propose an implementation of a universal set of one- and two-quantum-bit gates for quantum computation using the spin states of coupled single-electron quantum dots. Desired operations are effected by the gating of the tunneling barrier between neighboring dots. Several measures of the gate quality are computed within a recently derived spin master equation incorporating decoherence caused by a prototypical magnetic environment. Dot-array experiments that would provide an initial demonstration of the desired nonequilibrium spin dynamics are proposed.
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
A scheme to possibly implement the quantum computer is proposed based on the idea to build up the single qubit from two coupled quantum dots. The spatial separation of the two logic states of the qubit can greatly reduce the decoherence time, which allows one to perform the coherent quantum logic operations at a fairly high ratio. Together with the realization of the universal quantum logic gates, and the proper scheme of quantum measurement, the present proposal can satisfy all the essential criteria for quantum computing.
We propose a universal quantum computing scheme in which the orthogonal qubit states \ensuremath{\mid}0⟩ and \ensuremath{\mid}1⟩ are identical in their single-particle spin and charge properties. Each qubit is contained in a single quantum dot, and gate operations are induced all electrically by changes in the confinement potential. Within the computational space, these qubits are robust against environmental influences that couple to the system through single-particle channels. Due to the identical spin and charge properties of the \ensuremath{\mid}0⟩, \ensuremath{\mid}1⟩ states, the lowest-order relaxation and decoherence rates 1∕T1 and 1∕T2, within the Born-Markov approximation, both vanish for a large class of environmental couplings. We give explicit pulse sequences for a universal set of gates (phase, $\ensuremath{\pi}∕8$, Hadamard, and CNOT) and discuss state preparation, manipulation, and detection.
Quantum computation in solid state quantum dots faces two significant challenges: Decoherence from interactions with the environment and the difficulty of generating local magnetic fields for the single qubit rotations. This paper presents a design of composite qubits to overcome both challenges. Each qubit is encoded in the degenerate ground-state of four (or six) electrons in a system of five quantum dots arranged in a two-dimensional pattern. This decoherence-free subspace is immune to both collective and local decoherence, and resists other forms of decoherence, which must raise the energy. The gate operations for universal computation are simple and physically intuitive, and are controlled by modifying the tunneling barriers between the dots--Control of local magnetic fields is not required. A controlled-phase gate can be implemented in a single pulse.
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.