Environmentally decoupled sds -wave Josephson junctions for quantum computing

Abstract

Unconventional superconductors exhibit an order parameter symmetry lower than the symmetry of the underlying crystal lattice. Recent phase sensitive experiments on YBa2Cu3O7 single crystals have established the d-wave nature of the cuprate materials, thus identifying unambiguously the first unconventional superconductor [1,2]. The sign change in the order parameter can be exploited to construct a new type of s-wave-d-wave-s-wave Josephson junction exhibiting a degenerate ground state and a double-periodic current-phase characteristic. Here we discuss how to make use of these special junction characteristics in the construction of a quantum computer. Combining such junctions together with a usual s-wave link into a SQUID loop we obtain what we call a 'quiet' qubit -a solid state implementation of a quantum bit which remains optimally isolated from its environment.PACS numbers: 85.25. Cp, 85.25.Hv, 89.80.+h Quantum computers take advantage of the inherent parallelism of the quantum state propagation, allowing them to outperform classical computers in a qualitative manner. Although the concept of quantum computation has been introduced quite a while ago [3], wide spread interest has developed only recently when specific algorithms exploiting the character of coherent state propagation have been proposed [4]. Here we deal with the device aspect of quantum computers, which is florishing in the wake of the recent successes achieved on the algorithmic side. Two conflicting difficulties have to be faced by all hardware implementations of quantum computation: while the computer must be scalable and controllable, the device should be almost completely detached from the environment during operation in order to minimize phase decoherence. The most advanced propositions are based on trapped ions [5,6], photons in cavities [7], NMR spectroscopy of molecules [8], and various solid state implementations based on electrons trapped in quantum dots [9], the Coulomb blockade in superconducting junction arrays [10,11], or the flux dynamics in Superconducting Quantum Interference Devices (SQUIDs) [12]. Nanostructured solid state quantum gates offer the attractive feature of large scale integrability, once the limitations due to decoherence can be overcome [13].Here we propose a new device concept for a (quantum) logic gate exploiting the unusual symmetry properties of unconventional superconductors. The basic idea is sketched in Fig. 1: connecting the positive (100) and negative (010) lobes of a d-wave superconductor with a s-wave material produces the famous π-loop with a current carrying ground state characteristic of d-wave symmetry [1]. Here we make use of an alternative geometry and match the s-wave superconductors (S) to the (110) boundaries of the d-wave (D) material. As a consequence, the usual Josephson coupling ∝ (1 − cos φ) vanishes due to symmetry reasons and we arrive at a bistable device, where the leading term in the coupling takes the form E d cos 2φ with minima at φ = ±π/2 (here, φ denotes the gauge invariant phas...

Quantum Computation and Spin Electronics

“…The flux models come in a number of varieties [37,38]; the approach favored by the experimentalists [39] involves a low-Tc (Al or Nb) SQUID circuit which, classically, has two degenerate low energy states which differ slightly in their flux configuration; from the quantum point of view, this is a double-well potential problem with two nearly degenerate ground states, which functions as the qubit. The observation of single-qubit control is then equivalent to the "MQC" phenomenon which has been sought in these structures for many years.…”

Detection of geometric phases in superconducting nanocircuits

“…The quest for large scale integrability has stimulated an increasing interest in superconducting nanocircuits [11][12][13][14][15][16] as possible candidates for the implementation of a quantum computer. Mesoscopic Josephson junctions can be prepared in a controlled superposition of charge states [17,18] and the coherent time evolution in a Josephson charge qubit has been recently observed [5].…”

Topologically protected quantum bits using Josephson junction arrays

“…Proposals based on quantum optics naturally emphasize the aspect of optimal isolation [1][2][3], while those following the solid state route exploit the variability and scalability of modern nanoscale fabrication techniques [4][5][6][7][8]. Recently, various designs using superconducting structures have been successfully tested for quantum coherent operation [9][10][11], however, the ultimate goal of reaching coherent evolution over thousands of elementary operations remains a formidable task.…”

“…Individual qubit operations are carried out as described above. The implementation of a non-trivial two-qubit operation again involves a superconducting strip: biasing the strip connecting two qubits lifts the energy of the states |e o and |o e with respect to the states |e e and |o o and combining this two-qubit 'phase shifter' with a suitable set of single qubit operations allows for the construction of the controlled-NOT operation [8].…”