Quantum computing and single-qubit measurements using the spin filter effect

Many things will have to go right for quantum computation to become a reality in the lab. For any of the presently-proposed approaches involving spin states in solids, an essential requirement is that these spins should be measured at the single-Bohr-magneton level. Fortunately, quantum computing provides a suggestion for a new approach to this seemingly almost impossible task: convert the magnetization into a charge, and measure the charge. I show how this might be done by exploiting the spin filter effect provided by ferromagnetic tunnel barriers, used in conjunction with one-electron quantum dots.Comment: 11 pages, LaTeX, 1 figure. To be published in J. Appl. Phys., paper given at the 43rd Annual MMM Conferenc

Noise-Protected Gate for Six-Electron Double-Dot Qubits

Singlet-triplet spin qubits in six-electron double quantum dots, in moderate magnetic fields, can show superior immunity to charge noise. This immunity results from the symmetry of orbitals in the second energy shell of circular quantum dots: singlet and triplet states in this shell have identical charge distributions. Our phase-gate simulations, which include $1/f$ charge noise from fluctuating traps, show that this symmetry is most effectively exploited if the gate operation switches rapidly between sweet spots deep in the (3,3) and (4,2) charge stability regions; fidelities very close to one are predicted if subnanosecond switching can be performed.Comment: 7 pages, 3 figure

Inverted Singlet-Triplet Qubit Coded on a Two-Electron Double Quantum Dot

The $s_z=0$ spin configuration of two electrons confined at a double quantum dot (DQD) encodes the singlet-triplet qubit (STQ). We introduce the inverted STQ (ISTQ) that emerges from the setup of two quantum dots (QDs) differing significantly in size and out-of-plane magnetic fields. The strongly confined QD has a two-electron singlet ground state, but the weakly confined QD has a two-electron triplet ground state in the $s_z=0$ subspace. Spin-orbit interactions act nontrivially on the $s_z=0$ subspace and provide universal control of the ISTQ together with electrostatic manipulations of the charge configuration. GaAs and InAs DQDs can be operated as ISTQs under realistic noise conditions.Comment: 10 pages, 4 figure

Simple operation sequences to couple and interchange quantum information between spin qubits of different kinds

Efficient operation sequences to couple and interchange quantum information between quantum dot spin qubits of different kinds are derived using exchange interactions. In the qubit encoding of a single-spin qubit, a singlet-triplet qubit, and an exchange-only (triple-dot) qubit, some of the single-qubit interactions remain on during the entangling operation; this greatly simplifies the operation sequences that construct entangling operations. In the ideal setup, the gate operations use the intra-qubit exchange interactions only once. The limitations of the entangling sequences are discussed, and it is shown how quantum information can be converted between different kinds of quantum dot spin qubits.Comment: 9 pages, 4 figure

Hall Effect Gyrators and Circulators

The electronic circulator, and its close relative the gyrator, are invaluable tools for noise management and signal routing in the current generation of low-temperature microwave systems for the implementation of new quantum technologies. The current implementation of these devices using the Faraday effect is satisfactory, but requires a bulky structure whose physical dimension is close to the microwave wavelength employed. The Hall effect is an alternative non-reciprocal effect that can also be used to produce desired device functionality. We review earlier efforts to use an ohmically-contacted four-terminal Hall bar, explaining why this approach leads to unacceptably high device loss. We find that capacitive coupling to such a Hall conductor has much greater promise for achieving good circulator and gyrator functionality. We formulate a classical Ohm-Hall analysis for calculating the properties of such a device, and show how this classical theory simplifies remarkably in the limiting case of the Hall angle approaching 90 degrees. In this limit we find that either a four-terminal or a three-terminal capacitive device can give excellent circulator behavior, with device dimensions far smaller than the a.c. wavelength. An experiment is proposed to achieve GHz-band gyration in millimetre (and smaller) scale structures employing either semiconductor heterostructure or graphene Hall conductors. An inductively coupled scheme for realising a Hall gyrator is also analysed.Comment: 18 pages, 15 figures, ~5 MB. V3: sections V-VIII revisited plus other minor changes, Fig 2 added. Submitted to PR

Noise Analysis of Qubits Implemented in Triple Quantum Dot Systems in a Davies Master Equation Approach

We analyze the influence of noise for qubits implemented using a triple quantum dot spin system. We give a detailed description of the physical realization and develop error models for the dominant external noise sources. We use a Davies master equation approach to describe their influence on the qubit. The triple dot system contains two meaningful realizations of a qubit: We consider a subspace and a subsystem of the full Hilbert space to implement the qubit. We test the robustness of these two implementations with respect to the qubit stability. When performing the noise analysis, we extract the initial time evolution of the qubit using a Nakajima-Zwanzig approach. We find that the initial time evolution, which is essential for qubit applications, decouples from the long time dynamics of the system. We extract probabilities for the qubit errors of dephasing, relaxation and leakage. Using the Davies model to describe the environment simplifies the noise analysis. It allows us to construct simple toy models, which closely describe the error probabilities.Comment: 30 pages, 18 figure

Transmission lines and resonators based on quantum Hall plasmonics: electromagnetic field, attenuation and coupling to qubits

Quantum Hall edge states have some characteristic features that can prove useful to measure and control solid state qubits. For example, their high voltage to current ratio and their dissipationless nature can be exploited to manufacture low-loss microwave transmission lines and resonators with a characteristic impedance of the order of the quantum of resistance $h/e^2\sim 25\mathrm{k\Omega}$. The high value of the impedance guarantees that the voltage per photon is high and for this reason high impedance resonators can be exploited to obtain larger values of coupling to systems with a small charge dipole, e.g. spin qubits. In this paper, we provide a microscopic analysis of the physics of quantum Hall effect devices capacitively coupled to external electrodes. The electrical current in these devices is carried by edge magnetoplasmonic excitations and by using a semiclassical model, valid for a wide range of quantum Hall materials, we discuss the spatial profile of the electromagnetic field in a variety of situations of interest. Also, we perform a numerical analysis to estimate the lifetime of these excitations and, from the numerics, we extrapolate a simple fitting formula which quantifies the $Q$ factor in quantum Hall resonators. We then explore the possibility of reaching the strong photon-qubit coupling regime, where the strength of the interaction is higher than the losses in the system. We compute the Coulomb coupling strength between the edge magnetoplasmons and singlet-triplet qubits, and we obtain values of the coupling parameter of the order $100\mathrm{MHz}$; comparing these values to the estimated attenuation in the resonator, we find that for realistic qubit designs the coupling can indeed be strong

Blackbox Quantization of Superconducting Circuits using exact Impedance Synthesis

We propose a new quantization method for superconducting electronic circuits involving a Josephson junction device coupled to a linear microwave environment. The method is based on an exact impedance synthesis of the microwave environment considered as a blackbox with impedance function Z(s). The synthesized circuit captures dissipative dynamics of the system with resistors coupled to the reactive part of the circuit in a non-trivial way. We quantize the circuit and compute relaxation rates following previous formalisms for lumped element circuit quantization. Up to the errors in the fit our method gives an exact description of the system and its losses