Electronic Qubits Research Articles

Electrons Take Their Places on a Liquid Helium Grid

A device that efficiently transfers single electrons from one grid point to another on the surface of liquid helium could provide a scalable way to make arrays of electron qubits.

Spin-entanglement in a three electron system produced in double Auger decay

The simultaneous emission of two electrons in photoionization, or in the non-radiative spontaneous decay of an inner-shell vacancy, are two of the best known examples of the failure of the independent-particle model of atoms and molecules. The later of these provides also one of the two competitive processes, following inner-shell photoionization, for producing three flying electrons which can, for example, be used in implementing many protocols hitherto developed in quantum information. The correlation properties of the three-particle system consisting of these two electrons plus the photoelectron are analyzed using methods from quantum information theory. The entanglement of the consequent tripartite spin-state is shown to be completely independent of the mechanism(s) which may be responsible for the emission of these three electronic qubits in two different steps in the absence of spin-orbit interaction. Our analysis shows that the tripartite state formed in the present case is more like a |W〉 class of states possessing pairwise entanglement. The experimental characterization of these states is fully achieved merely by the measurements of the energies of three flying electrons, without requiring any entanglement witness or other similar protocols hitherto developed in quantum information. Changes in these entanglement properties of a tripartite state of electronic qubits on the inclusion of the spin-orbit interaction have also been discussed.

Optimized planar Penning traps for quantum information studies

Single electron qubits are attractive for quantum information processing because they offer, for example, the possibility of extremely long coherence times. For scaling up to a large number of coupled qubits, an array of planar Penning traps is a much more promising option than the cylindrical Penning traps within which one-quantum transitions have been observed. This report summarizes optimized trap configurations, discussed at length in Goldman and Gabrielse (Phys Rev A 81:052335, 2010), which promise to make it possible to realize one-electron qubits in a scalable configuration for the first time.

Spin–orbit qubit in a semiconductor nanowire

Motion of electrons can influence their spins through a fundamental effect called spin-orbit interaction. This interaction provides a way to control spins electrically and thus lies at the foundation of spintronics. Even at the level of single electrons, the spin-orbit interaction has proven promising for coherent spin rotations. Here we implement a spin-orbit quantum bit (qubit) in an indium arsenide nanowire, where the spin-orbit interaction is so strong that spin and motion can no longer be separated. In this regime, we realize fast qubit rotations and universal single-qubit control using only electric fields; the qubits are hosted in single-electron quantum dots that are individually addressable. We enhance coherence by dynamically decoupling the qubits from the environment. Nanowires offer various advantages for quantum computing: they can serve as one-dimensional templates for scalable qubit registers, and it is possible to vary the material even during wire growth. Such flexibility can be used to design wires with suppressed decoherence and to push semiconductor qubit fidelities towards error correction levels. Furthermore, electrical dots can be integrated with optical dots in p-n junction nanowires. The coherence times achieved here are sufficient for the conversion of an electronic qubit into a photon, which can serve as a flying qubit for long-distance quantum communication.

Experimental and theoretical challenges for the trapped electron quantum computer

We discuss quantum information processing with trapped electrons. After recalling the operation principle of planar Penning traps, we sketch the experimental conditions to load, cool and detect single electrons. Here we present a detailed investigation of a scalable scheme including feasibility studies and the analysis of all important elements, relevant for the experimental stage. On the theoretical side, we discuss different methods to couple electron qubits. We estimate the relevant qubit coherence times and draw implications for the experimental setting. A critical assessment of quantum information processing with trapped electrons concludes the paper.

Generation of tripartite states of flying electronic qubits and their characterization by energy measurements

A scheme for generating states of three free electrons entangled with respect to their spins is suggested. It consists of sequential ejection of two Auger electrons (${e}_{2}$ and ${e}_{3}$) in the nonradiative decay of an inner-shell vacancy created due to the emission of photoelectron ${e}_{1}$ from an atom, say $A$. In the absence of spin-orbit interaction, the entanglement among the spin angular momenta of the flying $({e}_{1},{e}_{2},{e}_{3})$ is generated simply by the Coulomb interaction experienced by them inside $A$. Their states are classified according to the hierarchic structure suggested by D\"ur, Cirac, and Tarrach [Phys. Rev. Lett. 83, 3562 (1999); D\"ur and Cirac, Phys. Rev. A 61, 042314 (2000)]. The generation of fully separable, 1-electron biseparable, fully inseparable, or ``$1\ensuremath{\rightarrow}2$ entangled'' tripartite (in addition to various kinds of bipartite) states is shown to be completely determined only by the spin multiplicities of the electronic states of $A$ and of its ionic species $({A}^{{+}^{\ensuremath{\ast}}},{A}^{2{+}^{\ensuremath{\ast}}},{A}^{3+})$ participating in the suggested scheme. The entanglement of three electrons is Greenberger-Horne-Zeilinger type. The experimental characterization of these states is fully achieved merely by the measurements of the energies of $({e}_{1},{e}_{2},{e}_{3})$, without requiring any entanglement witness or other similar protocols hitherto developed in quantum information.

Sequential double Auger decay in atoms: A quantum informatic analysis

We theoretically show that the process of inner-shell photoionization in an atom A, followed by the spontaneous sequential emission of two Auger electrons, produces various kinds of spin-entangled states of three flying electronic qubits. All properties of these states are completely pre-determined by the total spin quantum numbers of the electronic states of four atomic species (i.e., A, A + ∗ , A 2 + ∗ , A 3 + ) participating in this process in the Russell–Saunders coupling. These tripartite states are readily characterized experimentally by measuring only energies of the three emitted electrons, without requiring any entanglement witness or other such protocols.

Controlled-NOT gate for multiparticle qubits and topological quantum computation based on parity measurements

We discuss a measurement-based implementation of a controlled-NOT (CNOT) quantum gate. Such a gate has recently been discussed for free electron qubits. Here we extend this scheme for qubits encoded in product states of two (or more) spins-1/2 or in equivalent systems. The key to such an extension is to find a feasible qubit-parity meter. We present a general scheme for reducing this qubit-parity meter to a local spin-parity measurement performed on two spins, one from each qubit. Two possible realizations of a multiparticle CNOT gate are further discussed: electron spins in double quantum dots in the singlet-triplet encoding, and nu=5/2 Ising non-Abelian anyons using topological quantum computation braiding operations and nontopological charge measurements.

Quantum computing using molecular electronic and vibrational states

We numerically constructed elementary phase-correct global quantum gates by using molecular electronic and vibrational states to encode two qubits and implement the Deutsch–Jozsa algorithm. The calculations were based on optimal control theory (OCT). The molecular species we chose were Na 2 and Li 2. The electronic X 1 Σ g + and A 1 Σ u + states were taken as two orthonormalized energy levels of the electronic qubit. The vibrational qubits were those involved in these electronic states. The time duration of the optimized pulses with high fidelity was typically 500–900 fs, which reflects the wavepacket dynamics in electronically ground and excited states. When implementing the Deutsch–Jozsa algorithm by combining these elementary gates, we obtained a maximum probability 83.12% for Li 2 molecule, which indicates that the electronic–vibrational qubits are worse than the vibrational–vibrational and the vibrational–rotational qubits reported so far.

Deterministic quantum state transfer from an electronic charge qubit to a photonic polarization qubit

Building on an earlier proposal for the production of polarization-entangled microwaves by means of intraband transitions in a pair of quantum dots, we show how this device can be used to transfer an unknown single-qubit state from electronic charge to photonic polarization degrees of freedom. No postselection is required, meaning that the quantum state transfer happens deterministically. Decoherence of the charge qubit causes a nonmonotonic decay of the fidelity of the transferred state with an increasing decoherence rate.

Single photoelectron trapping, storage, and detection in a one-electron quantum dot

There has been considerable progress in electrostatically emptying, and refilling, quantum dots with individual electrons. Typically the quantum dot is defined by electrostatic gates on a GaAs∕AlyGa1−yAs modulation-doped heterostructure. We report the filling of such a quantum dot by a single photoelectron, originating from an individual photon. The electrostatic dot can be emptied and reset in a controlled fashion before the arrival of each photon. The trapped photoelectron is detected by a point contact transistor integrated adjacent to the electrostatic potential trap. Each stored photoelectron causes a persistent negative step in the transistor channel current. Such a controllable, benign, single photoelectron detector could allow for information transfer between flying photon qubits and stored electron qubits.

Microwave saturation and the Rabi frequency of the Rydberg states of electrons on helium

We present measurements of the resonant microwave excitation of the Rydberg energy levels of surface state electrons on superfluid helium. The temperature dependent line width γ( T) agrees well with theoretical predictions and is very small below 300 mK . Absorption saturation and power broadening were observed as the fraction of electrons in the first excited state was increased to 0.49, close to the thermal excitation limit of 0.5. The Rabi frequency was determined as a function of microwave power. The experiments show that the conditions are met for the use of these states in an electronic qubit.

Decoherence of electron spin qubits in Si-based quantum computers

Direct phonon spin-lattice relaxation of an electron qubit bound by a donor impurity or quantum dot in SiGe heterostructures is investigated. The aim is to evaluate the importance of decoherence from this mechanism in several important solid-state quantum computer designs operating at low temperatures. We calculate the relaxation rate $1/T_1$ as a function of [100] uniaxial strain, temperature, magnetic field, and silicon/germanium content for Si:P bound electrons. The quantum dot potential is much smoother, leading to smaller splittings of the valley degeneracies. We have estimated these splittings in order to obtain upper bounds for the relaxation rate. In general, we find that the relaxation rate is strongly decreased by uniaxial compressive strain in a SiGe-Si-SiGe quantum well, making this strain an important positive design feature. Ge in high concentrations (particularly over 85%) increases the rate, making Si-rich materials preferable. We conclude that SiGe bound electron qubits must meet certain conditions to minimize decoherence but that spin-phonon relaxation does not rule out the solid-state implementation of error-tolerant quantum computing.

The manipulation of massive ro-vibronic superpositions using time–frequency-resolved coherent anti-Stokes Raman scattering (TFRCARS): from quantum control to quantum computing

Molecular ro-vibronic coherences, joint energy-time distributions of quantum amplitudes, are selectively prepared, manipulated, and imaged in time–frequency-resolved coherent anti-Stokes Raman scattering (TFRCARS) measurements using femtosecond laser pulses. The studies are implemented in iodine vapor, with its thermally occupied statistical ro-vibrational density serving as initial state. The evolution of the massive ro-vibronic superpositions, consisting of 10 3 eigenstates, is followed through two-dimensional images. The first- and second-order coherences are captured using time-integrated frequency-resolved CARS, while the third-order coherence is captured using time-gated frequency-resolved CARS. The Fourier filtering provided by time-integrated detection projects out single ro-vibronic transitions, while time-gated detection allows the projection of arbitrary ro-vibronic superpositions from the coherent third-order polarization. A detailed analysis of the data is provided to highlight the salient features of this four-wave mixing process. The richly patterned images of the ro-vibrational coherences can be understood in terms of phase evolution in rotation–vibration–electronic Hilbert space, using time-circuit diagrams. Beside the control and imaging of chemistry, the controlled manipulation of massive quantum coherences suggests the possibility of quantum computing. We argue that the universal logic gates necessary for arbitrary quantum computing – all single qubit operations and the two-qubit controlled-NOT (CNOT) gate – are available in time-resolved four-wave mixing in a molecule. The molecular rotational manifold is naturally “wired” for carrying out all single qubit operations efficiently, and in parallel. We identify vibronic coherences as one example of a naturally available two-qubit CNOT gate, wherein the vibrational qubit controls the switching of the targeted electronic qubit.

Ion Trap Quantum Computing with Warm Ions

We describe two schemes to manipulate the electronic qubit states of trapped ions independent of the collective vibrational state of the ions. The first scheme uses an adiabatic method, and thus is intrinsically slow. The second scheme takes the opposite approach and uses fast pulses to produce an effective direct coupling between the electronic qubits. This last scheme enables the simulation of a number of nonlinear quantum systems including systems that exhibit phase transitions, and other semiclassical bifurcations. Quantum tunnelling and entangled states occur in such systems.