Geometric manipulation of a quantum system offers a method for fast, universal, and robust quantum information processing. Here, we propose a scheme for universal all-geometric quantum computation using non-adiabatic quantum holonomies. We propose three different realizations of the scheme based on an unconventional use of quantum dot and single-molecule magnet devices, which offer promising scalability and robust efficiency.
We show how to realize, by means of non-abelian quantum holonomies, a set of universal quantum gates acting on decoherence-free subspaces and subsystems. In this manner we bring together the quantum coherence stabilization virtues of decoherence-free subspaces and the fault-tolerance of all-geometric holonomic control. We discuss the implementation of this scheme in the context of quantum information processing using trapped ions and quantum dots.
Nonadiabatic holonomic quantum computation~(NHQC) provides an essential way to construct robust and high-fidelity quantum gates due to its geometric features. However, NHQC is more sensitive to the decay and dephasing errors than conventional dynamical gate since it requires an ancillary intermediate state. Here, we utilize the Hamiltonian reverse engineering technique to study the influence of the intermediate state-decoherence on the NHQC gate fidelity, and propose the novel schemes to construct the arbitrary single-qubit holonomic gate and nontrivial two-qubit holonomic gate with high fidel…
In this paper, we present a realistic application of the coherence protection method proposed in the previous article. A qubit of information encoded on the two spin states of a Rubidium isotope is protected from the action of electric and magnetic fields.
Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors. However, all the previous schemes have to use at least two sequentially implemented gates to realize a general one-qubit gate. Based on two recent works, we construct two Hamiltonians and experimentally realized nonadiabatic holonomic gates by a single-shot implementation in a two-qubit nuclear magnetic resonance (NMR) system. Two noncommuting one-qubit holonomic gates, rotating along $\hat{x}$ and $\hat{z}$ axes respectively, are implemented by evolving a work qubit and a…
We analyze the performance of holonomic quantum gates in semi-conductor quantum dots, driven by ultrafast lasers, under the effect of a dissipative environment. In agreement with the standard practice, the environment is modeled as a thermal bath of oscillators linearly coupled with the excitonic states of the quantum dot. Standard techniques of quantum dissipation make the problem amenable to a numerical treatment and allow to determine the fidelity (the common gate-performance estimator), as a function of all the relevant physical parameters. As a consequence of our analysis, we show that, b…
Among existing approaches to holonomic quantum computing, the adiabatic holonomic quantum gates (HQGs) suffer errors due to decoherence, while the non-adiabatic HQGs either require additional Hilbert spaces or are difficult to scale. Here, we report a systematic, scalable approach based on dynamical invariants to realize HQGs without using additional Hilbert spaces. While presenting the theoretical framework of our approach, we design and experimentally evaluate single-qubit and two-qubits HQGs for the nuclear magnetic resonance system. The single-qubit gates acquire average fidelity 0.9972 by…
High-fidelity quantum gates are essential for large-scale quantum computation, which can naturally be realized in a noise-resilient way. Geometric manipulation and decoherence-free subspace encoding are promising ways toward robust quantum computation. Here, by combining the advantages of both strategies, we propose and experimentally realize universal holonomic quantum gates in both a singleloop scheme and a composite scheme, based on nonadiabatic and non-Abelian geometric phases, in a decoherence-free subspace with nuclear magnetic resonance. Our experiment uses only two-body resonant spin-s…
We propose an implementation scheme for holonomic, i.e., geometrical, quantum information processing based on semiconductor nanostructures. Our quantum hardware consists of coupled semiconductor macroatoms addressed/controlled by ultrafast multicolor laser-pulse sequences. More specifically, logical qubits are encoded in excitonic states with different spin polarizations and manipulated by adiabatic time-control of the laser amplitudes . The two-qubit gate is realized in a geometric fashion by exploiting dipole-dipole coupling between excitons in neighboring quantum dots.
Reliable quantum information processing requires high-fidelity universal manipulation of quantum systems within the characteristic coherence times. Non-adiabatic holonomic quantum computation offers a promising approach to implement fast, universal, and robust quantum logic gates particularly useful in nano-fabricated solid-state architectures, which typically have short coherence times. Here, we propose an experimentally feasible scheme to realize high-speed universal geometric quantum gates in nano-engineered pseudo-spin charge qubits. We use a system of three coupled quantum dots containing…
The time evolution of entanglement for excitons in two quantum dots embedded in a single mode cavity is studied in a ``spin-boson'' regime. It is found that although with the dissipation from the boson mode, the excitons in the two quantum dots can be entangled by only modulating their energy bias $ε$ under the influence of external driving magnetic field. Initially, the two excitons are prepared in a pure separate state. When the time-dependent magnetic field is switched on, a highly entangled state is produced and maintained even in a very long time interval. The mechanism may be used to con…
A practical source of high fidelity entangled photons is desirable for quantum information applications and exploring quantum physics. Semiconductor quantum dots have recently been shown to conveniently emit entangled light when driven electrically, however the fidelity was not optimal. Here we show that the fidelity is not limited by decoherence, but by coherent interaction with nuclei. Furthermore we predict that on 100μs timescales, strongly enhanced fidelities could be achieved. This insight could allow tailoring of quantum logic to operate using quantum dots in the fault tolerant regime.
We study experimentally and theoretically the in-plane magnetic field dependence of the coupling between dots forming a vertically stacked double dot molecule. The InAsP molecule is grown epitaxially in an InP nanowire and interrogated optically at millikelvin temperatures. The strength of interdot tunneling, leading to the formation of the bonding-antibonding pair of molecular orbitals, is investigated by adjusting the sample geometry. For specific geometries, we show that the interdot coupling can be controlled in-situ using a magnetic field-mediated redistribution of interdot coupling stren…
By the application of an in-plane magnetic field, we demonstrate control of the fine structure polarisation splitting of the exciton emission lines in individual InAs quantum dots. The selection of quantum dots with certain barrier composition and confinement energies is found to determine the magnetic field dependent increase or decrease of the separation of the bright exciton emission lines, and has enabled the splitting to be tuned to zero within the resolution of our experiments. Observed behaviour allows us to determine g-factors and exchange splittings for different types of dots.
We use the entanglement measure to study the evolution of quantum correlations in two-electron axially-symmetric parabolic quantum dots under a perpendicular magnetic field. We found that the entanglement indicates on the shape transition in the density distribution of two electrons in the lowest state with zero angular momentum projection at the specific value of the applied magnetic field.
We analyze distinct sources of spin-dependent energy level shifts and their impact on the tunneling magnetoresistance (TMR) of interacting quantum dots coupled to collinearly polarized ferromagnetic leads. Level shifts due to virtual charge fluctuations can be quantitatively evaluated within a diagrammatic representation of our transport theory. The theory is valid for multilevel quantum dot systems and we exemplarily apply it to carbon nanotube quantum dots, where we show that the presence of many levels can qualitatively influence the TMR effect.
We present full atomistic calculations of the spin-flip time (T$_{1}$) of electrons and holes mediated by acoustic phonons in self-assembled In$_{1-x}$Ga$_x$As/GaAs quantum dots at zero magnetic field. At low magnetic field, the first-order process is suppressed, and the second-order process becomes dominant. We find that the spin-phonon-interaction induced spin relaxation time is 40 - 80 s for electrons, and 1 - 20 ms for holes at 4.2 K. The calculated hole-spin relaxation times are in good agreement with recent experiments, which suggests that the two-phonon process is the main relaxation me…
We study the band structures of hybrid graphene quantum dots subject to a magnetic flux and electrostatic potential. The system is consisting of a circular single layer graphene surrounded by an infinite bilayer graphene. By solving the Dirac equation we obtain the solution of the energy spectrum in two regions. For the valley $K$, it is found that the magnetic flux strongly acts by decreasing the gap and shifting energy levels away from zero radius with some oscillations, which are note observed for null flux case. As for the valley $K'$, the energy levels rapidly increase when the radius inc…
The electromagnetic-vacuum-field fluctuations are intimately linked to the process of spontaneous emission of light. Atomic emitters cannot probe electric- and magnetic-field fluctuations simultaneously because electric and magnetic transitions correspond to different selection rules. In this paper we show that semiconductor quantum dots are fundamentally different and are capable of mediating electric-dipole, magnetic-dipole, and electric-quadrupole transitions on a single electronic resonance. As a consequence, quantum dots can probe electric and magnetic fields simultaneously and can thus b…
We show that the Coulomb blockade in parallel dots pierced by magnetic flux $Φ$ completely blocks the resonant current for any value of $Φ$ except for integer multiples of the flux quantum $Φ_0$. This non-analytic (switching) dependence of the current on $Φ$ arises only when the dot states that carry the current are of the same energy. The time needed to reach the steady state, however, diverges when $Φ\to nΦ_0$.
We consider the motion of electrons confined to a two dimensional plane with an externally applied perpendicular inhomogeneous magnetic field, both with and without a Coulomb potential. We find that as long as the magnetic field is slowly-decaying, bound states in magnetic quantum dots are indeed possible. Several example cases of such magnetic quantum dots are considered in which one can find the eigenvalues and eigenfunctions in closed form, including two hitherto unknown quasi-exactly solvable models treated with confluent and biconfluent Heun polynomials. It is shown how a modulation of th…
We present an analytical solution to the Schrödinger equation for electron in a two-dimensional circular quantum dot in the presence of both external magnetic field and the Rashba spin-orbit interaction. The confinement is described by the realistic potential well of finite depth.
