Strong spin-momentum coupling in topological insulators give rise to topological surface states, protected against disorder scattering by time reversal symmetry. The study of these exotic quantum states not only provides an opportunity to explore fundamental phenomenon in condensed matter physics such as the spin hall effect, but also lays the foundation for applications in quantum computing to spintronics. Conventional electrical measurements suffer from substantial bulk interference, making it difficult to clearly identify topological surface state from the bulk. We use terahertz time-domain spectroscopy to study the temperature-dependent optical behavior of a 23-quintuple-thick film of bismuth selenide (Bi2Se3) allowing the deconvolution of the surface state response from the bulk. The signatures of the topological surface state at low temperatures (< 30 K) with the optical conductance of Bi2Se3 exhibiting a metallic behavior are observed. Measurement of carrier dynamics, obtain an optical mobility, exceeding 2000 cm2/V•s at 4 K, indicative of a surface-dominated response. A scattering lifetime of ~0.18 ps and a carrier density of 6×1012 cm-2 at 4 K were obtained from the terahertz time-domain spectroscopy measurement. The terahertz conductance spectra reveal characteristic features at ~1.9 THz, attributed to the optical phonon mode, which becomes less prominent with temperature. The electrical transport measurements reveal weak antilocalization behavior in our Bi2Se3 sample. We obtain the number of surface state modes, α as 0.5, and the coherence length, Lφ, as 380 nm at low temperatures < 10 K, further confirming the presence of a single topological surface state mode.
We investigate the groups generated by the sets of $CP$, $CNOT$ and $SWAP^\alpha$ (power-of-SWAP) quantum gate operations acting on $n$ qubits. Isomorphisms to standard groups are found, and using techniques from representation theory, we are able to determine the invariant subspaces of the $n-$qubit Hilbert space under the action of each group. For the $CP$ operation, we find isomorphism to the direct product of $n(n-1)/2$ cyclic groups of order $2$, and determine $2^n$ $1$-dimensional invariant subspaces corresponding to the computational state-vectors. For the $CNOT$ operation, we find isomorphism to the general linear group of an $n$-dimensional space over a field of $2$ elements, $GL(n,2)$, and determine two $1$-dimensional invariant subspaces and one $(2^n-2)$-dimensional invariant subspace. For the $SWAP^\alpha$ operation we determine a complex structure of invariant subspaces with varying dimensions and occurrences and present a recursive procedure to construct them. As an example of an application for our work, we suggest that these invariant subspaces can be used to construct simple formal verification procedures to assess the operation of quantum computers of arbitrary size.
We demonstrate the possibility of engineering a single donor transistor directly from a phosphorous doped quantum dot by making use of the intrinsic glassy behaviour of the structure as well as the complex electron dynamics during cooldown. Characterisation of the device at low temperatures and in magnetic field shows single donors can be electrostatically isolated near one of the tunnel barrier with either a single or a doubly occupancy. Such a model is well supported by capacitance-based simulations. Ability of using the D0 of such isolated donor as a charge detector is demonstrated by observing the charge stability diagram of a nearby and capacitively coupled semi-connected double quantum dot.
We fabricated silicon metal-oxide-semiconductor field effect transistors where an additional sodium-doped layer was incorporated into the oxide to create potential fluctuations at the Si-SiO2 interface. The amplitude of these fluctuations is controlled by both the density of ions in the oxide and their position relative to the Si-SiO2 interface. Owing to the high mobility of the ions at room temperature, it is possible to move them with the application of a suitable electric field. We show that, in this configuration, such a device can be used to control both the disorder and the electron-electron interaction strength at the Si-SiO2 interface.
We present a numerically-optimized multipulse framework for the quantum control of a single-electron double quantum dot qubit. Our framework defines a set of pulse sequences, necessary for the manipulation of the ideal qubit basis, that avoids errors associated with excitations outside the computational subspace. A novel control scheme manipulates the qubit adiabatically, while also retaining high speed and ability to perform a general single-qubit rotation. This basis generates spatially localized logical qubit states, making readout straightforward. We consider experimentally realistic semiconductor qubits with finite pulse rise and fall times and determine the fastest pulse sequence yielding the highest fidelity. We show that our protocol leads to improved control of a qubit. We present simulations of a double quantum dot in a semiconductor device to visualize and verify our protocol. These results can be generalized to other physical systems since they depend only on pulse rise and fall times and the energy gap between the two lowest eigenstates.
Quantum computation offers ways of solving problems which are unreachable for classical computers [1]. Double quantum dots are of great interest as candidates for implementing solid state quantum bits (qubits) because of the long electron coherence times. The use of geometrically isolated structures (with the detectors coupled capacitively) improves the electrical isolation of the dots, however, it makes the detection more challenging [2].
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