Realizing Controllable Quantum States

Preface.

CONTENTS.

We investigate the generation and detection of orbitally entangled states in electrical conductors. Orbital entanglement might be easier to detect than spin entanglement. We discuss a normal-superconducting hybrid structure in which entanglement is between pairs of electrons emitted at two different contacts. We also discuss a purely normal structure in which entanglement occurs in the form of electron-hole pairs or through post-selection on an unentangled many-electron state. A violation of a Bell inequality is used as an objective entanglement test.

An electron spin state teleportation scheme is described. It is based on the protocol of Bennett et al. and involves the production/detection by superconductors of entangled pairs of electrons from/with a s-wave superconductor. Quantum dots filter individual electron transitions, and the whole teleportation sequence is selected in a five-dot cell by electrostatic gating in the stationary regime: in the steady state, a spin-conserving current flows between the reservoirs, most exclusively carried by the teleportation channel. This current is perfectly correlated to a Cooper pair current flowing in the superconducting circuit. The average teleportation current is calculated using the Bloch equations. A diagnosis of teleportation is proposed using noise correlations.

We studied the pairwise-entanglement of a one-dimensional S = 1/2 transverse Ising model by the Lewenstein-Sanpera decomposition, ρ = Λρ_s + (1 − Λ)ρ_e, where ρ_s is a separable density matrix and ρ_e is a pure entangled state obtained by a linear combination of Bell states. By analyzing the pairwise-entanglement around the quantum phase transition point, we clarify that (i) the concurrence C(ρ_e) for the pure entangled state |Ψ_e〉 〈Ψ_e| shows a singular maximum at the quantum phase transition point and (ii) the weight (1 − Λ) of the pure part shows a singular minimum at the point.

We consider a hybrid system consisting of two normal metal leads connected to a superconductor through a tunnel barrier. We study current-current correlations of the normal leads at subgap voltages and temperatures. Only two processes contribute to the cross-correlation: the crossed Andreev reflection (emission of electrons in different leads) and the elastic cotunneling. Both processes are possible due to the finite size of the Cooper pair. Noise measurements can thus be used to probe directly the superconducting wave function without the drawbacks appearing in average current measurements where the current is dominated by direct Andreev reflection processes.

We evaluate the moments of transmission coefficients through a Y-shaped metallic diffusive conductor with incident waves from one arm and outgoing waves in another. We deduce the correlations between currents on different arms from these probabilities.

Fixed-number-of-electron mesoscopic or macromolecular conducting ring is shown to support persistent currents due to Aharonov-Bohm flux, and the “spontaneous” persistent currents without the flux when structural transformation in the ring is blocked by strong coupling to the externally azimuthal-symmetric environment. In the free-standing macromolecular ring, symmetry breaking removes the azimuthal periodicity which however is further restored at the increasing field. Three-site ring with one or three electrons represent an interesting quantum system which can serve as a qubit (quantum bit of information) and a qugate (quantum logical gate).

We investigate effects of the electron-electron interaction on the transmission probability of electrons through a tunnel junction in a quantum well in a magnetic quantum limit. We consider the system with which bulk states and edge states coexist. First we consider interaction effects in bulk states. We show that the treatment of the electron-electron interaction is very important. Next we investigate contributions of edge states on many-body effects in bulk states. Those contributions can be neglected within the approximation in consideration of only most divergent terms at low temperature.

Magnetic field with a spatial gradient breaks the symmetry of two-dimensional electron gas (2DEG) narrow channel with respect to the current flow direction. We have observed unidirectional flow behavior by measuring a differential resistance under dc bias current and a bend resistance in cross junction.

The transport properties of a quantum wire (QW) with a quantum dot (QD) coupled to one side has been studied. The structure is formed by metallic gates on a GaAs/AlGaAs heterostructure. The conductance of the QW oscillates periodically as the number of electrons in the QD is increased due to the tunnel coupling between the QW and the QD. We measured these oscillations in detail by changing the coupling strength, the wire width, and magnetic fields. The measurements indicate that the side-coupled QD scatters the conduction electrons in the QW.

In this work we investigate the low-dimensional electron gas confined in single quantum wires by employing magneto-transport measurements and far-infrared photoconductivity spectroscopy. The quantum wires were fabricated from InAs/InGaAs/InAlAs heterostructures ranging from 4 μm down to 400 nm in width. We demonstrate the feasibility of photoconductivity spectroscopy on single InAs quantum wires for the first time.

Collective-mode contribution to the thermoelectric properties in charge-density-wave systems is studied. Thermoelectric power and thermal conductivity is derived from Fröhlich Hamiltonian with linear response theory. In this study, we ignore quasi-particle contribution and impurity effects. Energy dissipation is attributed to nonlinear interaction between phase and amplitude modes. We find that temperature dependence of correlation function between electric and heat currents is the same as that of electric conductivity, and thermoelectric power is inversely proportional to temperatures. We also find that thermal conductivity has nearly constant value at the temperatures above amplitude mode gap, and has exponentially low value at the temperatures sufficiently below it.

New physical effects emerge from an interplay between the electron parity number and persistent currents in superconducting nanorings. An odd electron, being added to the ring, produces a countercurrent which may substantially modify the ground state properties of the system. In superconducting nanorings with an embedded normal metal layer a novel “π/N-junction” state can occur for the odd number of electrons. Changing this number from even to odd yields spontaneous supercurrent in the ground state of such rings without any externally applied magnetic flux.

Interference of electronic waves undergoing Andreev reflection in diffusive conductors determines the energy profile of the conductance on the scale of the Thouless energy. A similar dependence exists in the current noise, but its behavior is known only in few limiting cases. We consider a metallic diffusive wire connected to a superconducting reservoir through an interface characterized by an arbitrary distribution of channel transparencies. Within the quasiclassical theory for current fluctuations we provide a general expression for the energy dependence of the current noise. We derive closed analytical expressions for large energy.

Based on the interaction between the radiation field and a superconductor, we propose a way to engineer quantum states using a SQUID charge qubit inside a microcavity. This device can act as a deterministic single photon source as well as generate any Fock states and an arbitrary superposition of Fock states for the cavity field. The controllable interaction between the cavity field and the qubit can be realized by the tunable gate voltage and classical magnetic field applied to the SQUID.

In this paper we generalize the formalism for studying pumping in hybrid normal/superconductor systems to include several superconducting leads with different order parameters. This formalism is applied to investigate Andreev-interference effects on adiabatically pumped charge in a 3-arm beam splitter attached to one normal and two superconducting leads. We derive a formula for the charge pumped through the normal lead, and we elucidate the effects due to Andreev interference. In contrast to what happens for voltage-driven transport, Andreev interference does not yield in general a pumped current which is a symmetric function of the superconducting-phase difference.

We find that Cooper-pair breaking is strongly suppressed against applied high fields in multi-walled carbon nanotube(MWNT), which was interfaced to niobium electrode, within proximity-induced superconductivity. We reveals that the inhomogeneously leaked Cooper pairs into the MWNTs are primarily responsible for these and that the suppression becomes significant as the one-dimensional anisotropy of these MWNTs becomes stronger. The weak electron-phonon interaction induced in the one-dimensionality is discussed as a possible origin for this. This result is a manifestation that MWNTs can strongly maintain Cooper-pair and spin entanglement against high fields and will open up the door to realizing magnetically-controlled molecular quantum-bits.

We study the weak link between current-carrying superconductors, both conventional and d-wave. The state of the system is controlled by two parameters: the order parameter phase difference ϕ and the superfluid velocity v_s, which parameterizes the parallel to the boundary transport supercurrent which is injected externally. The low-temperature current-phase relations are derived. We consider two models of weak links: a constriction between two conventional superconductors and a plane boundary between two differently orientated d-wave superconductors. We show that for some relation between ϕ and υ_s quasiparticles create the current along the boundary which flows in the direction opposite to the transport supercurrent.

Josephson current through a Luttinger liquid (LL) under a magnetic field is theoretically studied. We derive an analytical expression of Josephson current for clean interfaces, by using quasiclassical Green’s function and functional bosonization procedure. Because of spin-dependent energy shift in Andreev bound states, current-phase relations acquire positive slopes at phase difference χ=π (π-state). Renormalization of the critical current, due to electron-electron interactions, is found. Further, we show that repulsive interactions detabilize the π-state, while attractive ones stabilize.

We prove that efficient electron cooling can be realized using ferromagnet-superconductor junctions. Cooling power densities up to 600 nW/μm² can be achieved in this system, leading to electronic temperature reductions largely exceeding those obtained with existing superconductor-insulator-normal metal tunnel contacts. Furthermore, cooling efficiencies largely exceeding 20% can be reached in such microrefrigerators. Half-metallic CrO₂/Al bilayers are suggested as ideal candidates for the implementation of the device.

Anomalous charge transport properties in mesoscopic normal metal /triplet superconductor (DN/TP) junctions are studied based on a generalized circuit theory. It has been previously revealed that the formation of mid gap Andreev resonant states (MARS) competes with the proximity effect in singlet superconductor junctions. Here we verify that the formation of the MARS does enhance the proximity effect in the normal metal and that the resulting conductance spectra of the junction show giant zero-bias conductance peaks. The most striking effect predicted is that the total resistance of a diffusive normal metal / triplet superconductor junctions becomes completely independent of the resistance of the normal metal when the MARS are formed for all injection angles.

The YBa₂Cu₄O₈ ceramic superconductor shows successive superconducting transitions and is considered as a random Josephson-coupled networks of 0- and π-junctions. We have investigated the magnetic properties in order to clarify the inter-grain glass and Paramagnetic Meissner behavior at low field. A thermodynamically stable chiral-glass state in the field cooled-cooling and a metastable paramagnetic one in the field cooled-warming are observed below the inter-grain transition temperature. The results agree well the so-called d-wave mechanism leading to Paramagnetic Meissner effects in ceramic high-T_c superconductors.

In absence of external fields the ground state in triplet superconductors with broken time-reversal symmetry is degenerate, corresponding to two values of chirality N. Chirality corresponds to clockwise (N=1) and counter-clockwise (N=−1) spontaneous non-dissipative currents in single-domain superconductors. Interactions lift the degeneracy and yield a possibility of macroscopic quantum tunneling between the chiral states, observable in sufficiently small samples. For an appropriate initial state, coherent oscillations of the order parameter (and simultaneously, orbital and magnetic momentum) should take place with sign alternations of non-dissipative currents. Understanding the details of quantum properties of the ground state is the objective of this work. The method of investigation is in linking the phenomenological description of the superconductor with the spin-boson Hamiltonian approach.

We numerically study the Josephson current and its fluctuations through dirty normal metals in p wave superconducting junctions. Effects of a zero-energy state at junction interfaces and the proximity effect in normal metals on the Josephson effect are discussed. An interplay between the two effects drastically enhances the Josephson current and suppresses its fluctuations in a p_x wave symmetry.

We have studied the very high frequency response of high critical temperature Josephson junctions. High quality YBa₂Cu₃O_7-x epitaxial films were fabricated by pulsed laser deposition on tilted (vicinal) sapphire substrates with CeO₂ buffer layers. YBaCuO films have smaller tilt angles, from 1.0° up to 10.3°, compared to inclination angles of the substrates from 1.5° to 13.6°. X-ray diffraction shows only a single orientation of the films in the a-b plane, as well as an absence of a-axis particles and outgrowths. Critical temperatures as high as T_c=88.5–89.0 K and ΔT_c≤1.5 K were obtained in all films. The meandering of the artificial grain boundary in a tilted bicrystal film is three times less than in an in-plane (un-tilted) bicrystal. Josephson junctions of widths from 1.5 to 6 μm were tested at temperatures from 0.26 K to 77 K. I_cR_n products of up to 4.5 mV were observed at T=4.2 K. Shapiro steps were observed at voltages over 3 mV under 300 GHz irradiation. Josephson radiation was measured at frequencies up to 1.7 THz by a cryogenic bolometer. Suppressing the critical current with a magnetic field can separate Josephson radiation and thermal radiation. A parabolic dependence of the response on bias voltage for thermal radiation corresponds to an increase of junction temperature from 260 mK at zero bias to 3 K at 1 mV bias.

We report analysis of experimental tunneling spectra with a zero-bias conductance peak (ZBCP) of Bi₂Sr₂CaCu₂O_8+δ (Bi-2212) planar type junctions by using a simplified formula for the circuit theory based on the d-wave pairing symmetry. The circuit theory has been recently generalized from conventional superconductors to unconventional superconductors. The ZBCP frequently appears in tunneling spectra for this theory, in which the total resistance was constructed by resistances between a d-wave superconductor and a diffusive normal metal at a junction interface. The experimental tunneling spectra are consistent with those of recent studies on the circuit theory.

Transport properties of junctions of Ru and Sr₂RuO₄ were investigated in the eutectic system Sr₂RuO₄-Ru. We fabricated a device with electric contacts to individual Ru micro-inclusions in the eutectic system Sr₂RuO₄-Ru. This device enabled the conductance at the interface between a single Ru micro-inclusion and ruthenate to be measured. Zero bias conductance peaks (ZBCP) were observed in the voltage dependence of the differential conductance, suggesting that Andreev bound states were present at the interface. We investigated the magnetic field and temperature dependence of the onset of the ZBCP. The onset of the ZBCP is considerably smaller than the upper critical field H_c2 when the magnetic field is parallel to the ab-plane. Possible origins of the difference between the onset of the ZBCP and H_c2 are discussed on the basis of a prediction in a theory by Sigrist and Monien.

In this paper, we study macroscopic quantum tunneling (MQT) in d-wave superconductor Josephson junctions. By using the functional integral method and the instanton method we have obtained the MQT rate (the inverse lifetime of the metastable state) for the c-axis twist Josephson junctions. In the case of the zero twist angle, we find that the system shows the super-Ohmic dissipation due to the presence of the nodal quasiparticle tunneling. Therefore, the MQT rate is strongly suppressed in compared with the finite twist angle cases.

Spin polarized tunneling spectroscopy was applied to optimally doped YBa₂Cu₃O_7–δ (YBCO) in order to detect the quasiparticle properties of d-wave superconducting phase. YBCO/La_0.67Sr_0.33MnO₃ junctions were fabricated by PLD and photolithographic process and a Zeeman magnetic field was applied to the direction parallel to the ab-plane. Expected Zeeman splitting of conductance spectrum was not detected for the field up to 14T. Instead, unpredictably large gap suppression due to the applied field was observed. Since both of these responses are inconsistent with weak coupling BCS model which takes into account of d-wave symmetry, the present results reflect the anomalous quasiparticle states in high-T_c oxides.

A new generation of microscopic ratchet systems is currently being developed for controlling the motion of electrons and fluxons, as well as for particle separation and electrophoresis. Virtually all of these use static spatially asymmetric potential energies to control transport properties. We have proposed ¹ completely new types of ratchet-like systems that do not require fixed spatially asymmetric potentials in the samples. As specific examples of this novel general class of ratchets, we proposed devices that control the motion of flux quanta in superconductors and could address a central problem in many superconducting devices; namely, the removal of trapped magnetic flux that produces noise. In layered superconductors there are two interpenetrating perpendicular vortex lattices consisting of Josephson vortices (JVs) and pancake vortices (PVs). We showed in ¹ that, owing to the JV-PV mutual interaction and asymmetric driving, the a.c. motion of JVs and/or PVs can provide a net d.c. vortex current. This controllable vortex motion can be used for making pumps, diodes and lenses of quantized magnetic flux. These proposed devices sculpt the microscopic magnetic flux profile by simply modifying the time dependence of the a.c. drive, without the need for samples with static pinning-for example, without lithography or irradiation.

We have revealed thermodynamically stable vortex-antivortex configurations in mesoscopic type I superconducting equilateral triangles. The revealed effect is explained by two factors: (i) vortex confinement in mesoscopic triangles and (ii) appearance of the vortex-antivortex repulsion in mesoscopic type I superconductor triangles in the vicinity of the dual point. The stability of the obtained solutions is examined as a function of material and external parameters – the Ginzburg-Landau parameter κ and temperature – as well as a function of a distortion of the sample’s shape. The vortex-antivortex “molecule” turns out to be stable in a wide range of the parameters that makes it possible its experimental visualization.

We calculate the Hofstadter butterfly diagram for a two-dimensional tight binding square lattice subjected to spatially varying flux patterns. Samples of superconducting wire network decorated with mesoscopic ferromagnet array exhibit characteristic Little-Parks oscillation patterns reminiscent of the edge shape of the corresponding Hofstadter spectra.

Responses of mesoscopic superconducting rings and disks to perpendicular magnetic fields are studied by using the multiple-small-tunnel-junction method, in which transport properties of several small tunnel junctions attached to the sample are measured simultaneously. This allows us for a direct experimental observation of the paramagnetic supercurrent, which is closely related to the paramagnetic Meissner effect. The results are compared with numerical results based on the nonlinear Ginzburg-Landau theory.

Controlled trapping and guided motion of vortices via special arrangements of micro-holes, so-called antidots, in YBa₂Cu₃O₇ films and devices is demonstrated. Resistive Hall-type measurements prove the presence of guided flux motion along rows of antidots. In contrast to conventional vortex motion due to vortex unpinning at currents exceeding the critical current, this motion is present down to zero current and low temperatures. It is characterized by a linear voltage-current dependence, i.e., ohmic behavior. The latter is indicative for a novel mechanism of flux propagation in superconducting systems that might be based upon (a) restricted vortex formation in mesoscopic superconductors or/and (b) flux nucleation within antidots due to the redistribution of screening currents. The combination of strategically trapping of vortices and guided vortex motion using isolated or rows of antidots, respectively, can be used for new devices concepts.

Special relativistic effects on quantum tunneling of a fluxon are investigated based on the Dirac equation. From a derived expression of tunneling probability, a relativistic feature different from non-relativistic cases has been revealed. An experimental strategy for observing such relativistic fluxon tunneling is also discussed.

We have derived explicit non-perturbative expression for decoherence of quantum oscillations in a qubit by low-frequency noise. Decoherence strength is controlled by the noise spectral density at zero frequency while the noise correlation time τ determines the time t of crossover from the to the exponential suppression of coherence. We also performed Monte Carlo simulations of qubit dynamics with noise which agree with the analytical results and show that most of the conclusions are valid for both Gaussian and non-Gaussian noise.

We examine the effect of multilevels on decoherence and dephasing properties of a quantum system consisting of a non-ideal two level subspace, identified as the qubit and a finite set of higher energy levels above this qubit subspace. The whole system is under interaction with an environmental bath through a Caldeira-Leggett type coupling. The model that we use is an rf-SQUID under macroscopic quantum coherence and coupled inductively to a flux noise characterized by an environmental spectrum. The model interaction can generate dipole couplings which can be appreciable for a number of high levels. The decoherence properties of the qubit subspace is examined numerically using the master equation formalism of the system’s reduced density matrix. We numerically examine the relaxation and dephasing times as the environmental frequency spectrum, and the multilevel system parameters are varied at zero temperature. We observe that, these time scales receive contribution from all available energies in the noise spectrum (even well above the system’s energy scales) stressing the dominant role played by the non-resonant (virtual) transitions. The relaxation and dephasing times calculated, strongly depend on the number of levels within the range of levels for which appreciable couplings are produced. Under the influence of these effects, we remark that the validity of the two level approximation is restricted not by the temperature but by these dipole couplings as well as the availability of the environmental modes at low temperatures.

We show that one-dimensional Josephson junction arrays can behave as quantum channels and can be used to transfer quantum information between distant sites. In particular, we discuss simple protocols to realize, without external control, state transfer with high fidelity in Josephson chains. The channels do not require complicate gating but use the natural dynamics of a properly designed array. We analyze the influence of disorder both in the Josephson energies and in the background gate charges, and we propose an experiment, realizable with present-day technology, that may allow to implement these protocols.

Because they are scalable and can be addressed with electric signals, solid state devices are particularly attractive to implement quantum bits (qubits), which are the building blocks of quantum processors. However, their quantum coherence time is usually too short for that purpose. In the quantronium circuit, a built-in decoupling of the qubit from its environment allows one to circumvent this limitation. For this device, qubit states are prepared by applying resonant microwave pulses, and the read-out is performed by monitoring the switching of a large Josephson junction. The phenomena that limit quantum coherence, and strategies to fight them, are discussed.

A pulse-and-hold technique is used to measure the switching of small critical current Josephson junctions. This technique allows one to achieve a good binary detection and therefore measure switching probabilities. The technique overcomes limitations on simple square pulses and allows for the measurement of junctions with critical currents of the order of 10nA with bias pulses of the order of 100ns. A correlation analysis of the switching events is performed to show how the switching probability depends on the wait time between repeated bias pulses.

We present a scheme of experiment to observe entangled states in coupled flux qubits. The results of simulation are shown for the energy levels, magnetic flux detected by a DC-SQUID and transition matrix elements as the flux bias is applied asymmetrically. Near the degeneracy point the ground state and the first excited state of the system are dominantly the symmetric and antisymmetric combination of —01¿ and —10¿ states, respectively. The simulation shows that the use of asymmetric flux bias is suited for the observation of the energy spectrum with resonant microwaves.

We study solid state implementations of entanglement and communication protocols using an interconnection scheme among mesoscopic sub-circuits, suitable for quantum communication. The building block is a superconducting qubit coupled with a solid-state resonator. We study decoherence, discuss rules for environment engineering and analyze working conditions where a high degree of protection from phase errors is achieved. We review some of the protocols which have been recently proposed for studying entanglement in the solid state.

We investigate quantum coherence of electron spin transported through a semiconductor spintronic device, where spins are envisaged to be controlled by electrical means via spin-orbit interactions. To quantify the degree of spin coherence, which can be diminished by an intrinsic mechanism where spin and orbital degrees of freedom become entangled in the course of transport involving spin-orbit interaction and scattering, we study the decay of the off-diagonal elements of the spin density matrix extracted directly from the Landauer transmission matrix of quantum transport. This technique is applied to understand how to preserve quantum interference effects of fragile superpositions of spin states in ballistic and non-ballistic multichannel semiconductor spintronic devices.

We study decoherence due to random telegraph and 1/f noise in Josephson qubits. We illustrate differences between gaussian and non gaussian effects at different working points and for different protocols. Features of the intrinsically non-gaussian and non-Markovian low-frequency noise may explain the rich physics observed in the spectroscopy and the dynamics of charge based devices.

Despite the mathematical decisive argument on the seperability of mixed states in NMR at room temperature, NMR experiment has been extensively used for demonstrations of even non-local quantum algorithms. The corresponding inconsistency between the mathematical argument and the NMR quantum processing is studied and an experimental approach is proposed for detecting the existence of entanglement by implementing the superdense coding algorithm, whereas no pseudo-purification is used in this approach.

We observed multiphoton absorptions accompanied by the transition between our superconducting flux-qubit states, those are the superposition of two macroscopically distinct states. We also report a systematic view on the switching current behavior of the readout dc-SQUID, depending on the sample parameters of the qubit and the SQUID.

The study of quantum query complexities for black-box functions (oracles) plays a central role for design methods of efficient quantum algorithms. We consider a general framework called the oracle identification problem (OIP) for black-box oracles and analyze the quantum query complexity. The OIP is, given a set S of M Boolean black-box oracles out of 2^N ones, to determine which oracle in S is the current black-box oracle. We can exploit the information that candidates of the current oracle is restricted to S. The OIP contains several concrete problems such as the Grover search problem and the Bernstein-Vazirani problem. Our interest is in the quantum query complexity, for which we present several upper bounds. They are quite general and almost optimal: (i) The upper bound of query complexity of OIP is for any S such that M = |S| > N, which is better than the obvious bound N if M < 2^{N / log3 N} and the lower bound is . Thus, the bounds are tight up to a logarithmic factor. (ii) It is for any S if |S| = N, which includes the upper bound for the Grover search as a special case. One can see that this bound is tight by the well-known lower bound of the Grover search problem, which needs queries by any quantum algorithms. (iii) For a wide range of oracles (|S| = N) such as random oracles and balanced oracles, the query complexity is , where K is a simple parameter determined by S. This is a joint work with Andris Ambainis, Akinori Kawachi, Hiroyuki Masuda, Raymond H. Putra, and Shigeru Yamashita.

We present a method to construct a non stabilizer Clifford code which encodes a single qupit, i.e. a state described as a vector in p-dimensional Hilbert space, to a pair of a single qupit and a single qubit, for any odd prime p. Thus obtaining infinite non stabilizer Clifford codes.

Golovkins introduced the quantum counterpart of pushdown automata (quantum pushdown automata, QPAs), including unitary criteria, in 2000. Golovkins showed that QPAs can recognize some non-context-free languages probabilistically, which indicates that QPAs might be more powerful than the classical counterpart in a bounded error scenario, namely than probabilistic pushdown automata. In this paper, we show that QPAs might be more powerful even in a deterministic case. That is, we show that there exists a QPA that deterministically solves a certain problem which might not be solved by deterministic pushdown automata.

Modular exponentiation is the most expensive portion of Shor’s algorithm. We show that it is possible to reduce the number of quantum modular multiplications necessary by a factor of w, at a cost of adding temporary storage space and associated machinery for a table of 2^w entries, and performing 2^w times as many classical modular multiplications. The storage space may be a quantum-addressable classical memory, or pure quantum memory. With classical computation as much as 10¹³ times as fast as quantum computation, values of w from 2 to 30 seem attractive; physically feasible values depend on the implementation of the memory.

We study the intractability of finding an optimal initial arrangement of input data on qubits when the qubits are arranged on the vertices of a d-dimensional grid (d is constant) and we can perform quantum operations only between nearest-neighbor qubits. The problem is called the d-IAP (d-dimensional initial arrangement problem) in this paper. We prove that the intractability of the d-IAP is equivalent to that of the weighted d-dimensional arrangement. Thus, there is no deterministic polynomial-time algorithm for finding an optimal initial arrangement of 1-IAP if P≠NP.

Modular squaring is not bijection map. Hence, in principal, we cannot construct a unitary operation U such that U|x〉 = |x² mod N〉, where N is a modulus. In general, we usually use a unitary operation U such that U|x〉 |0〉 = |x〉 |x² mod N〉. However, this construction uses too much qubits. In this paper, we show how to reduce the necessary number of qubits in attaining the reversibility of modular squaring operation for two cases. One is for prime modulus case and the other is for Blum integer modulus case. We clarify how many qubits we need and what kind of operation we should construct to attain the reversibility. Since modular squaring can be used in modular exponentiation, our proposed method leads to the efficient circuits for Shor’s factoring algorithm.

Tunneling spectra via Andreev bound states between a normal metal (N) / d_x²-y²-wave superconductor (S) (in the presence of a subdominant s-wave pair potential) junction are investigated. In the present work, in order to study the role of proximity effect, we employ quasiclassical Green’s function methods. This merit is that we can determine the spatial variation of the pair potentials self-consistently, where the leaking of pair potentials into the N side is involved. In the N/S junction with orientational angle θ = π/4, we can regard as the isolated d-wave superconductor, where attractive interaction in the N side is negligible. On the other hand, in the case of a high transparent contact to the d-wave superconductor (θ = 0), the pair potential penetrates into the inside of the N due to the proximity effect, where the is-wave is not indued at all. Then, the tunneling spectra has a very sharp zero-energy peak (ZEP). This ZEP originates from the fact that quasiparticles feel different sign of the pair potentials between normal metals and d-wave superconductors through Andreev reflections. We show that the spatial dependence of pair potentials is significantly sensitive to the transparency of the junction.

Triplet-pairing superconductors with broken time-reversal symmetry such as ruthenates, Sr₂RuO₄, have potential application as a basis for quantum computing (QC). The prerequisite here is the requirement of achieving superconductivity in single domain mesoscopic samples. One possible fabrication approach is application of thin film technologies. Initially some attempts were made by other groups to achieve epitaxial Sr₂RuO₄ films by pulsed laser deposition, but they failed. We propose an alternative method that makes small pieces of the material from larger crystals without destroying the crystal Meanwhile, experimental demonstration of quantum dynamics of triplet superconductors, such as Sr₂RuO₄, requires small structures on the order of the size of a single domain. QC done using triplet state superconductivity is potentially advantageous because the qubit is only a tiny piece of metal, yet a complete QC system can be implemented building upon this kind of qubit as the foundation. The supporting technology for initiation, entanglement and readout is described. Some of it involves application of ferromagnetic components, used in gate mechanisms. Ultimately, the approach presented here brings together triplet superconductivity in mesoscopic structures with ferromagnetic techniques.

We review our recent work on spin excitations in low-dimensional electron gases studied using far-infrared photoconductivity technique, which allows us to measure the spin-orbit coupling parameter α via spectroscopy and study the many-body aspects for spin excitations.

Mobile potentials created by surface acoustic waves in GaAs quantum wells provide a convenient way of manipulating photogenerated electron-hole pairs and spins. In this contribution, we use photoluminescence spectroscopy to demonstrate the unique ability of these mobile potentials to store and transport charge and spin excitations in the quantum well plane.

An uniqueness of lead telluride PbTe relies on combination of excellent semiconducting properties, like high electron mobility and tunable carrier concentration, with paraelectric behavior leading to huge dielectric constant at low temperatures. The present article is a review of our experimental works performed on PbTe nanostructures. The main result is observation of one-dimensional quantization of the electron motion at much impure conditions than in any other system studied so far. We explain this in terms of dielectric screening of Coulomb potentials produced by charged defects. Furthermore, in an external magnetic field, the conductance quantization steps show very pronounced spin splitting, already visible at several kilogauss. This indicates that PbTe nanostructures have a potential as local spin filtering devices.

Electron g-factor in an InAs-inserted-channel In_0.53Ga_0.47As/In_0.52Al_0.48As heterostructure is studied by measuring angle dependence of magnetotranport properties. The gate voltage dependence of g-factor is obtained from the coincidence method. The obtained g-factor values are surprisingly smaller than the g-factor value of bulk InAs, and it is close to the bare g-factor value of In_0.53Ga_0.47As. The large change in g-factor is observed by applying the gate voltage. The obtained gate voltage dependence is not simply explained by the energy dependence of g-factor.

The spin Hall effect is a phenomenon of inducing spin current by an external electric field. We recently proposed that this effect can occur in p-type semiconductors without relying upon any disorder scattering [S. Murakami et al., Science 301, 1348 (2003)]. This intrinsic effect is due to the “Berry phase in momentum space”, representing topological structure of the Bloch band structure. We explain how the Berry phase brings about the spin Hall effect, and review several interesting aspects of this effect.

We observed the suppression of the superconductivity in a mesoscopic superconducting Al wire in proximity contact with an overlaid ferromagnetic Co wire. Finite voltages over a certain length of Al wire occurred as evidence for the suppression of the superconductivity while the spin-polarized currents were injected through the Co/Al interfaces and the spin diffusion length in the superconductor, estimated from the finite voltages, turned out to be related to the pair-condensing relaxation of quasiparticles through opposite spin channels.

Magnetic bicrystal grain boundary junctions can be used as model systems for magnetic tunnel junctions. We demonstrate how the magnetization reversal process indirectly can be found from dc magnetoresistance measurements in manganite bicrystal junctions. The results are discussed in terms of a micromagnetic energy balance. We find that the magnetization reversal strongly depends on the direction of the magnetic field. With the field applied parallel to the grain boundary the magnetization hysteresis is determined by a Barkhausen-like reversal process. In the perpendicular configuration the hysteresis can be modelled as a Stoner-Wohlfart rotation.

We report finding of giant (two orders of magnitude at 0.05T) magnetoconductance (MC) at the interface between a two-dimensional hole system (2DHS) and a magnetic semiconductor (Ga,Mn) As. The MC, on one hand, clearly due to the ferromagnetism in (Ga,Mn) As, but also is a consequence of the elongation of the coherence length in 2DHS. A surprising property of the MC is the dependence on the sweep rate of the magnetic field, in other words, it has a finite decay time.

We have discussed the localization mechanism in the transport property in the randomly distributed system of the hole-induced magnetic solitons with the alloy potential fluctuations in diluted magnetic semiconductors, by using the effective Lagrangian of diffusion modes.

Spin polarized current in a three-terminal system in the presence of spin-orbit interaction is numerically studied. The third invasive voltage probe is attached. Our results show that the invasive voltage probe induces not only the dephasing effect but also the polarization of the current. By changing the height of the potential barrier located at the interface between the system and the invasive voltage probe, the polarization can be controlled. The polarization survives even in the presence of impurities.

We discuss theoretically the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and the Kondo effect in semiconductor quantum dots (QDs). The RKKY interaction between QDs is modulated by changing the Fermi energy, and the magnitude or even the sign of the exchange interaction can be tuned. We also consider electron transport along a single-mode channel that is in contact, via tunnel junctions in its walls, with two quantum dots. This two-dot device geometry offers the possibility of studying the crossover between fully screened and under-screened Kondo impurities.

We study the Kondo effect in a quantum dot (QD) coupled to ferromagnetic leads, and analyze its properties. The main goal of our work is to investigate how ferromagnetic leads influence the Kondo effect. The new key questions, which emerge are: (i) does the Kondo effect survive and how does the spin-asymmetry affect the effect, (ii) how are the transport properties modified, and (iii) what is the ground state of the system? We analyzed these and related questions using scaling arguments, the nonequilibrium equation of motion technique, and numerical renormalization group (NRG) approach.

Though the p-d exchange interaction of Ga_1−xMn_xAs is antiferromagnetic, early magnetoreflectivity experiments by Szczytko et al. [Solid State Comm. 99, 927 (1996)] indicated a sign reversal; in contrast to II-VI-based diluted magnetic semiconductors (DMS), the σ⁺ exciton appeared to have a higher energy than the σ⁻ exciton. In order to explain the sign reversal, we have theoretically investigated the difference in the optical band edge between II-VI- and III-V-based DMS, applying the dynamical coherent approximation (dynamical CPA) to a simple model. The present study reveals that in the low dilution of Ga_1−xMn_xAs, the optical band edge exists not at the band edge of the impurity band but lies near the bottom of the host band. The optical band edge behaves as if the exchange interaction is ferromagnetic although the antiferromagnetic exchange interaction actually operates at the Mn site.

We study spin-polarized transport phenomena through double quantum dots coupled to ferromagnetic leads. By using the slave-boson mean-field approximation, we calculate the conductance in the Kondo regime for different setups: we change the configuration of the dots continuously from “series” to “parallel”. We find that transport properties, which are sensitive to the arrangement of the dots, exhibit characteristic dependence on the polarization of two ferromagnetic leads. These properties are explained in terms of the Kondo resonances appearing in the local density of states and the transmission probability through the system.

We examine theoretically the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two quantum dots (QDs) with odd numbers of electrons in the Coulomb blockade regime. We consider an Aharonov-Bohm (AB) ring embedded with a QD in each arm. We find the flux dependent RKKY interaction, which dominates the conductance. For antiferromagnetic coupling, the phase of AB oscillations is shifted by π. For ferromagnetic coupling, the amplitude of AB oscillations is enhanced by Kondo correlations.

We study few-electron GaAs quantum dot devices designed for generating a local AC magnetic field (~mT) in order to realize single-electron spin resonance. The AC magnetic field is induced by an AC current driven through a metal line in the vicinity of the dot. The Landé g-factor in the quantum dot is derived from the large (~T) in-plane magnetic field evolution of the Zeeman splitting observed in both Coulomb peak spacings and Coulomb diamonds. The obtained g-factor (|g| = 0.23) is significantly smaller than that for bulk GaAs. We measure electron transport through the dot for various AC currents and find evidence for the presence of an AC electric field in the form of photon assisted tunneling and current rectification. So far, we cannot confirm any effect of the AC magnetic field.

Kondo effect is theoretically studied in quantum dots with two orbitals and spin 1/2. We evaluate the Kondo temperature T_K as a function of energy difference Δ between the orbitals using the scaling method. We find that T_K is maximal around the degeneracy point (Δ = 0) and decreases with increasing |Δ| by a power law. This behavior of T_K is understood as a crossover from SU(4) to SU(2) Kondo effect. The calculated results agree with recent experimental results.

We propose a novel method for the investigation of the edge channels by utilizing circular polarized photoluminescence in the integer-quantum-Hall-effect regime. Single-particle energies and optical transition probabilities are calculated within the local-spin-density approximation formalism for the edge states at v = 3. Calculated spectrum explains the splittings and the polarization of the observed photoluminescence spectrum.

We describe calculations of the electronic structure of artificial molecular hydrogen. Double quantum dots, each containing a single electron, are analyzed within a molecular configuration calculation where basis states are calculated self-consistently, employing the full faithful geometry of realistic structures, using density functional theory. Results of the inter-dot exchange coupling and the exchange matrix element as a function of magnetic field are presented.

The photoluminescence spectra of a two-dimensional electron system induced in a Be-δ-doped GaAs/AlGaAs quantum well with a back gate are reported. The electron density is controlled from 1×10⁹cm⁻² to 2.5 × 10¹¹cm⁻² by changing the back gate voltage. Our sample is found to be especially advantageous in studying the properties of two-dimensional electron systems in the dilute electron density regime by photoluminescence measurements.

We report on the ²⁹Si nuclear spin decoherence process at room temperature for a pure (99.99999%, 7N) and carrier-less (p-type, doping level of 10¹⁵cm⁻³) silicon in which ²⁹Si nuclei are naturally abundant (4.7%). In spite of the extremely long spin-lattice relaxation time T₁ (of the order of 10⁴ s), we have succeeded in direct observation of the nuclear-spin decoherence process. We found that the decoherence process is well-reproduced by a bi-exponential function with the shorter T₂^S = 15±5 ms and the longer T₂^L = 200±20 ms.

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