NC State University

Quantum Computing

Although early demonstrations of quantum computing explored a wide variety of experimental methods, quantum computers based on solid-state systems, in spite of the potentially larger interactions limiting coherence, are believed to be worth serious investigation. Systems based on Josephson Junctions, electrons resident on the surface of superfluid Helium, compound semiconductors, electrons trapped in an acoustic wave, semiconductor quantum dots coupled via electromagnetic field, and solid-state nuclear magnetic resonance systems that have been proposed are described below. Previously we have investigated coherent coupling of electrons trapped at neighboring asymmetric quantum dots in a III-V pillar structure. However, we believe the best candidate is based on the coupled spin of electrons on trapped on adjacent quantum dots in a silicon environment currently being investigated in our research.

Quantum Josephson Junction Circuits

A superconductor can be characterized by the absolute value (number of the quasiparticles) and the phase f of the macroscopic wavefunction, representing the order parameter. As for any quantum system, both of them cannot be determined simultaneously. If a Josephson junction is formed by the two massive superconductors they are insensitive to the fluctuations of the quasiparticle number and the junction evolution can be described by the classical equations for the relative phase of the contacting superconductors. Small superconductors, however, have small capacitance ECE Nano Image - capacitance (C); if the charging energy exceeds the Josephson energy ECE Nano Image - Josephson energy (Ej), then the charge fluctuations are suppressed, and the circuit demonstrates essentially quantum behavior. It has been demonstrated that in this case it is possible to create a quantum superposition of the two different charge states of the superconductor, thus, forming a qubit. This is possible by biasing the additional gate contact [31] or applying a microwave radiation [32]. As a result, the Bloch oscillations of frequency ECE Nano Image - Bloch oscillations of frequency (~Ej/h) between the two charge states are inspired. Addressing of the qubit can be accomplished by the control of the duration of the gate voltage pulse, while the two-qubit operation can be organized by coupling of the different circuits. The obvious advantage of this scheme is that it exploits a quantum behavior of a macroscopic system that promises relatively easy control of the qubit. On the other hand, this concept is not free of some drawbacks. In particular, to inspire the Bloch oscillations, the applied voltage pulse must be sharp on the time scale ECE Nano Image - time scale (h/Ej). Although the Josephson energy can be controlled by external magnetic flux, to avoid decoherence during the computation, it should be kept at the level about 50 meV, as the London length and the coherence length of the Cooper which corresponds to about 10 GHz in the frequency domain. Obviously, it is a great challenge to achieve reliable operation at such high frequencies of massive circuits containing a large number of qubits. In addition, there are some restrictions in the possible miniaturization of the Josephson-junction circuits. Currently, the experiments accomplished where done with the superconductor having dimensions of the order of a micron that corresponds to the charging energy about 0.1 meV. Scaling down the junction dimensions increases the charging energy. As a result, a more precise adjustment of the gate voltage required for the resonance condition is necessary. What is more fundamental, the scaling of the junction dimensions is restricted by such scales pairs.

Electrons Confined at the Surface of Superfluid Helium

Close to the surface of the thin superfluid helium film an electron experiences Coulomb-like attraction caused by the electrostatic image forces. As a result, injected electrons are confined in the vicinity of the helium surface. Electron-electron interaction in such a system causes formation of a 2D Wigner crystal. The positions of the electrons in this crystal can be pinned by means of an electrodes patterned at the bottom of the cell. The ground and excited states of an electron in the Coulomb-like potential are proposed to be used as basis states of a qubit. [33] Addressing of the qubit can be accomplished by the resonance microwave radiation causing Rabi oscillations. Adjustment of the resonance frequency of a particular qubit can be made by the electrodes to allow control of one-qubit rotations and two-qubit operation, caused by the electron-electron coupling. Since the wavefunction of the ground state in the classically forbidden region decays faster than that of the excited state, the tunneling of the electron is sensitive to the state of the qubit. Therefore, the electron tunneling current measurement by an additional electrode can accomplish the qubit readout. Relatively weak electron interaction with the elementary excitations of helium, surface capillary waves and ripplons, ensures long decoherence times for the qubit and the possibility to implement the reliable quantum computations. However, it is unclear whether two-qubit coupling can be properly controlled for the quantum gate implementation. The possibility of the proposed readout procedure is also questionable. If a single electron is used as qubit, then its readout is complemented by the electron removal. This, obviously, creates a defect in the Wigner crystal and can strongly disturb the neighbor electrons. This difficulty can be overcome by using a cluster of electrons as a single qubit. In this case, however, it is more difficult to achieve the necessary decoherence level. One more serious disadvantage of this scheme is that even weak vibrations caused by the environment strongly disturb the superfluid helium surface giving rise additional electron decoherence or even complete destruction of the electron Wigner crystal. Obviously, this would establish very tough conditions for the mechanical isolation of such QC and restrict the area of its applications.

Spin-Split States in Compound Semiconductor Quantum Dots with Spin Injection

This design of the QC [34] has a lot in common with that proposed by us. The two main differences are as follows: (i) instead of silicon, a compound semiconductor is proposed as a quantum-dot material. In this case the two-level system is formed by the spin-split state, originated as a result of relatively strong spin-orbital coupling in compound semiconductors lacking inversion symmetry (Rashba effect). As a result, an effective voltage-control of the energy gap between the two states is possible with no magnetic field required; (ii) the initial spin-polarized state is created by the injection of a spin-polarized carrier from a magnetic material surrounding the quantum dot. Analogously, the readout of the qubit state is accomplished by measuring the spin-dependent current from the quantum dot to the magnetic material. Although this design could provide easier control of the energy splitting of the two states representing a qubit, it sacrifices such an advantage of silicon as very long spin decoherence time. In addition, injection of the spin-polarized carriers in semiconductors is a great challenge. Currently, it was observed in a few materials. In general, it seems to be very difficult to find a pair semiconductor-ferromagnetic material or semiconductor-semimagnetic semiconductor with good-quality interface causing no strong spin decoherence.

Quantum Josephson Junction Circuits

This approach [35] is based on a specific method to create 0D electron states and arrange their coupling. Recent experiments demonstrate that the piezoelectric potential of a gigahertz surface acoustic wave (SAW) can effectively trap 2D electrons confined near the semiconductor surface. If a quasi-1D channel is formed in the 2D electron gas by gate electrodes or etching, the SAW traveling along the channel drags the electrons. It is possible to calibrate the parameters of the SAW and 2D electrons to capture a single electron from the channel in each potential minimum of the SAW. In this case the qubit is represented by the spin-split electron states in the external magnetic filed. A two-qubit logic gate can be achieved by patterning a set of parallel 1D channels. In this case the electrons from the adjacent channels captured in the same potential well of the SAW are coupled due to the exchange interaction. This approach allows control of the two-qubit logic gates by bringing the two adjacent channels closer for some portion of the channel, thus, controlling the exchange-induced two-qubit coupling by the geometry of the structure. However, it is questionable if it is possible to achieve a low enough level of electron spin decoherence for this design, since it assumes using GaAs-based structures where the decoherence is much stronger than for silicon. Furthermore, some additional source of decoherence can be brought about by the SAW-generating circuit and the SAW itself.

Semiconductor Quantum Dots Coupled via Electromagnetic Field of a Microcavity

In this approach it is proposed to implement in solid-state systems a method of quantum computation using cavity QED [36]. In this case a number of quantum dots are put into a common microcavity characterized by a high quality factor. The computation process utilizes the three lowest levels of a quantum dot; two of them represent a state of a qubit, while the third one is used to arrange an electron interaction with the electromagnetic field. The two-qubit operation in this system is realized by the nonlinear interaction of the electron with the coherent electromagnetic radiation having the frequency different from the eigen-frequency of the cavity. The readout procedure is accomplished by means of the radiation detector. The advantage of this approach is that it allows entanglement of an arbitrary pair of qubits by tuning the energy levels of the individual quantum dots by the gate electrodes. However, the relatively high decoherence rate in such structure requires use of the terahertz-range radiation; currently, it is a significant challenge to create high-quality microelectronic sources of terahertz radiation as well as terahertz detectors. In addition, it is necessary to mention that this approach requires manufacturing a very sophisticated structure that integrates a set of individually controlled quantum dots, the cavity, laser, and detector, which comprises a significant technological challenge.

Solid-State NMR Quantum Computers

Demonstration of the elements of the QC employing NMR in molecular systems inspired researches to investigate the possibility to use NMR in solids for the same purpose. Basically, the main principles of quantum computation based on nuclear and electron spins are similar. The main advantage of the nuclear spins is their weak coupling to the environment, ensuring a long decoherence time. On the other hand, the weak coupling makes the control of a qubit more difficult and reduces the possible clock frequency of the QC. A number of propositions were generated that use either electrical [2] or optical [37] methods to control the two-qubit rotations in NMR solid-state QC. Both of these schemes require the high-precision implantation of individual donor atoms in a silicon substrate, which is extremely hard to achieve, especially in many-qubit circuits. There is also an alternative NMR-based scheme for the quantum computation [38]. Here an original method of the spin detection is proposed. It is based on the interaction of the nonuniform magnetic field of a ferromagnetic particle and the spins subject to the resonance radio frequency field. This interaction causes the mechanical oscillations of a micrometer cantilever, where the ferromagnetic particle is deposited. In turn, the mechanical oscillations are detected by the optical methods. Although this scheme can provide very weak decoherence, it would be extremely hard technologically to implement it for the many-qubit systems. More recently this scheme has been augmented by the suggestion that Si29 atoms can be preferentially deposited by MBE at the steps produced on a vicinal Si (111) 77 surface [39]. With this structure placed in an extremely large magnetic field gradient to allow addressing, the readout is provided by magnetic resonance force microscopy. It is suggested by initial state preparation could be aided by optical pumping and spin transfer from electrons. On the order of 105 identical systems are required to obtain adequate signal detection for ensemble measurement of the final state.

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