The silicon-based quantum computer proposal has been one of the actively pursued ideas during the past three years. Here we calculate the donor electron exchange in silicon and germanium, and demonstrate an atomic-scale challenge for quantum computing in Si (and Ge), as the six (four) conduction band minima in Si (Ge) lead to inter-valley electronic interference, generating strong oscillations in the exchange splitting of two-donor two-electron states. Donor positioning with atomic scale precision within the unit cell thus becomes a decisive factor in determining the strength of the exchange coupling-a fundamental ingredient for two-qubit operations in a silicon-based quantum computer.PACS numbers: 03.67. Lx, 71.55.Cn, Following the seminal proposal [1] by Kane there has been a great deal of activity [2][3][4] in efforts to develop a silicon-based quantum computer (QC) architecture. The basic ideas of the Kane proposal are simple and attractive: to use donor nuclear spins as quantum bits (qubits), and to utilize the vast infrastructure and technology associated with the Si industry to fabricate precisely controlled Si nanostructures, where exchange effects between electrons and nuclei in neighboring donor impurities (e.g. 31 P in Si) could serve as the two-qubit gates, similar to the electron-spin-based QC proposal by Loss and DiVincenzo [5]. The motivation for a Si quantum computer is obvious: Once the basic one-qubit and two-qubit operations have been demonstrated using donor impurities in Si nanostructures, computer chip fabrication technology associated with the existing and dominant Si industry will easily enable the scale-up of information processing involving large number of donor nuclear spin qubits. Indeed, one of the formidable stumbling blocks in developing working quantum computer hardwares has been the scale-up problem, as the demonstrated qubits in trapped ion and liquid state NMR techniques are not readily scalable in any significant manner [6].A great deal of experimental work is currently being aimed at developing suitable qubits in Si nanostructures with precisely introduced dopant impurities, using both a "top-down" approach with ion-implantation, and a "bottom-up" approach with MBE growth and scanning tunneling microscopy [4]. In the Si QC model [1,2], donor electrons act as shuttles between different nuclear spins. For two-qubit operations, which are required for a universal QC, both electron-electron exchange and electronnucleus hyperfine interaction need to be precisely controlled. These are unquestionably formidable experimental problems. In the original proposal, Kane used the Herring-Flicker exchange formula [7] for two hydrogenic centers to obtain an order of magnitude estimate of the electron exchange among donors in Si [1]. However, as he also pointed out, donor exchange in Si is not hydrogenic.In this Letter we show that exchange effects in proposed donor nuclei based Si QC architectures are actually very subtle due to quantum interference effects inherent in the complicated Si band...
We propose a quantum dot qubit architecture that has an attractive combination of speed and fabrication simplicity. It consists of a double quantum dot with one electron in one dot and two electrons in the other. The qubit itself is a set of two states with total spin quantum numbers S(2)=3/4 (S=1/2) and S(z)=-1/2, with the two different states being singlet and triplet in the doubly occupied dot. Gate operations can be implemented electrically and the qubit is highly tunable, enabling fast implementation of one- and two-qubit gates in a simpler geometry and with fewer operations than in other proposed quantum dot qubit architectures with fast operations. Moreover, the system has potentially long decoherence times. These are all extremely attractive properties for use in quantum information processing devices.
We study theoretically a double quantum dot hydrogen molecule in the GaAs conduction band as the basic elementary gate for a quantum computer with the electron spins in the dots serving as qubits. Such a two-dot system provides the necessary two-qubit entanglement required for quantum computation. We determine the excitation spectrum of two horizontally coupled quantum dots with two confined electrons, and study its dependence on an external magnetic field. In particular, we focus on the splitting of the lowest singlet and triplet states, the double occupation probability of the lowest states, and the relative energy scales of these states. We point out that at zero magnetic field it is difficult to have both a vanishing double occupation probability for a small error rate and a sizable exchange coupling for fast gating. On the other hand, finite magnetic fields may provide finite exchange coupling for quantum computer operations with small errors. We critically discuss the applicability of the envelope function approach in the current scheme and also the merits of various quantum chemical approaches in dealing with few-electron problems in quantum dots, such as the Hartree-Fock self-consistent field method, the molecular orbital method, the Heisenberg model, and the Hubbard model. We also discuss a number of relevant issues in quantum dot quantum computing in the context of our calculations, such as the required design tolerance, spin decoherence, adiabatic transitions, magnetic field control, and error correction. I. BACKGROUNDIn recent years there has been a great deal of (as well as a growing) interest throughout the physics community in quantum computation and quantum computers (QC) [1], in which microscopic degrees of freedom such as atomic levels and electron spins play the role of quantum bits (qubits). Because of the inherent entanglement and superposition during the unitary evolution of multiple qubits, QCs can perform certain tasks such as factoring large integers [2] exponentially faster than classical computers. They also have significant advantages over classical computers in tasks such as searching [3] and simulating quantum mechanical systems [4,5]. Moreover, quantum error correction codes have been discovered [6], which further bolster the hope for a practical quantum computer. Various QC architectures have been proposed in the literature. The basic ingredients for a QC are two-level elements serving as qubits, controlled single-and two-qubit unitary operations, exponentially large and precisely defined (i.e., no mixing with other states) Hilbert space, weak decoherence, and single qubit measurements [7]. One of the earliest QC proposals uses electronic energy levels of ions in a linear trap ("ion trap" QC) as qubits [8,9]. Optical pulses perform single-qubit operations, while two-qubit operations are provided by multiple optical pulses with the lowest vibrational mode of the ion chain as an intermediary. In another proposed QC architecture, the cavity QED QC [10,11], photon polarization provid...
A flux qubit can have a relatively long decoherence time at the degeneracy point, but away from this point the decoherence time is greatly reduced by dephasing. This limits the practical applications of flux qubits. Here we propose a new qubit design modified from the commonly used flux qubit by introducing an additional capacitor shunted in parallel to the smaller Josephson junction (JJ) in the loop. Our results show that the effects of noise can be considerably suppressed, particularly away from the degeneracy point, by both reducing the coupling energy of the JJ and increasing the shunt capacitance. This shunt capacitance provides a novel way to improve the qubit.Superconducting quantum circuits based on Josephson junctions (JJs) are promising candidates of qubits for scalable quantum computing (see, e.g., [1]). Like other types of superconducting qubits, flux qubits have been shown to have quantum coherent properties (see, e.g., [2, 3, 4, 5, 6, 7, 8]). A recent experiment [7] showed that this qubit has a long decoherence time T 2 (∼ 120 ns) at the degeneracy point; this T 2 can become as long as ∼ 4 µs by means of spin-echo techniques. However, even slightly away from the degeneracy point, the decoherence time is drastically reduced. This sensitivity to flux bias considerably limits the applications both for flux qubits for quantum computing, and also when performing quantum-optics and atomic-physics experiments on microelectronic chips with the qubit as an artificial atom.Typically, JJ circuits have two energy scales: the charging energy E c of the JJ, and the Josephson coupling energy E J of the junction. Ordinarily, a flux qubit works in the phase regime with E J /E c ≫ 1, where its decoherence is dominated by flux fluctuations. For the widely used three-junction flux qubit design [2,3,4,5,6], in addition to two identical JJs with coupling energy E J and charging energy E c , a third JJ, which has an area smaller by a factor α ∼ 0.7, is employed to properly adjust the qubit spectrum. Charge fluctuations can affect the decoherence of this flux qubit via the smaller junction.Here we search for an improved design for flux qubits. We show that reducing the ratio E J /E c suppresses the effects of flux noise, although charge noise becomes increasingly important. Reducing α further suppresses the effects of flux noise and considerably improves the decoherence properties away from the degeneracy point. As the effect of flux noise has been largely suppressed, charge noise would now be the dominant source of decoherence. It mainly comes from the charge fluctuations on the two islands separated by the smaller JJ and affects the qubit mainly through relaxation. We thus propose an improved flux qubit by introducing a large capacitor that shunts in parallel to the smaller JJ. This shunt capacitance suppresses the effects of the dominant charge noise in the two islands separated by the smaller JJ by reducing the charging energy. Our results reveal that using a larger shunt capacitor allows reducing both E J /E c and α ...
Proposed Silicon-based quantum computer architectures have attracted attention because of their promise for scalability and their potential for synergetically utilizing the available resources associated with the existing infrastructure of the powerful Si technology. Quantitative understanding of and precise physical control over donor (e.g. Phosphorus) exchange are crucial elements in the physics underlying the proposed Si-based quantum computer hardware. An important potential problem in this context is that inter-valley interference originating from the degeneracy in the Si conduction band edge causes fast oscillations in donor exchange coupling, which imposes significant constraints on the Si quantum computer architecture. In this paper we consider the effect of external strain on Si donor exchange in the context of quantum computer hardware. We study donor electron exchange in uniaxially strained Si, since strain partially lifts the valley degeneracy in the bulk. In particular, we focus on the effects of donor displacements among lattice sites on the exchange coupling, investigating whether inter-valley interference poses less of a problem to exchange coupling of donors in strained Si. We show, using the Kohn-Luttinger envelope function approach, that fast oscillations in exchange coupling indeed disappear for donor pairs that satisfy certain conditions for their relative positions, while in other situations the donor exchange coupling remains oscillatory, with periods close to interatomic spacing. We also comment on the possible role of controlled external strain in the design and fabrication of Si quantum computer architecture.
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