Universität Karlsruhe

Institut für Theoretische Festkörperphysik

Quantum computing

Stephan André, Jared Cole, Pei-Qing Jin, Michael Marthaler, Alessandro Romito, Gerd Schön
Ongoing collaboration with members of TKM: Alexander Shnirman, Clemens Müller
We also work closely with the experimental groups of A. Ustinov (Karlsruhe), J. Wrachtrup (Stuttgart)

Quantum computing, as an area of study, has grown enormously in the last 15 years, linking quantum physics with computer science, information theory and computer engineering. As the principles and models used to describe quantum information processing are found in many physical systems, the study of these processes tells us much about the fundamental rules and limitations of quantum theory. In the quantum computing subgroup of the Institut für Theoretische Festkörperphysik, we tackle many problems, including; the control and description of quantum coherent solid-state devices, the effects of decoherence, measurement theory in solid-state, and the application of these ideas beyond that of quantum information processing.

Quantum computing using solid-state devices

Quantum state engineering, i.e., active control over the coherent dynamics of suitable quantum mechanical systems, opens fascinating perspectives including the ideas of quantum computation. For this purpose a number of individual two-state quantum systems (qubits) should be manipulated in a controlled way. Nano-electronic devices appear particularly promising because they can be embedded in electronic circuits and scaled up to large numbers of qubits. Ultrasmall quantum dot systems with charge or spin degrees of freedom have been suggested. Low-capacitance Josephson junction devices with logical states differing by one Cooper-pair charge (Josephson charge qubit) or one flux quantum (flux qubit) futher exploit the phase coherence of the superconducting state to achieve long phase coherence times. We proposed a design, with controlled Josephson couplings, which is close to ideal. Single- and two-bit operations can be performed by applying a sequence of gate voltages and currents.

Design of a register of qubits controlled by gate voltages and fluxes, coupled by the oscillations in the LC oscillator

Quantum measurement theory and its application to quantum devices

The standard picture of a 'projective' measurement is only valid in some situations. Many modern experiments in quantum physics investigate a range of regimes and therefore rely on more sophisticated models of the measurement process. In such situations, concepts such as imperfect collapse, weak continuous measurement and weak values come into play. We consider these issues within a range of physical systems, including solid-state devices. While understanding the measurement process is central to the operation of a quantum computer, such considerations have increased our understanding of the interplay of measurement in quantum physics in general.
A practical example is superconducting devices, where, in addition to the controlled manipulation of the quantum state of the system the resulting state must be read out. This can be accomplished by coupling a single-electron transistor capacitively to the (quantum dot or Josephson) charge qubit or a SQUID to the flux qubit. We analyze the process by evaluating the time-evolution of the density matrix of the coupled system. The quantum measurement process is characterized by three time scales: a fast dephasing time, a longer time needed to read out the signal, and a third, even longer time scale when the measurement induced transitions destroy the information about the inital quantum state.

The theory of decoherence and the cross-over between the quantum and classical worlds

When considering the boundary between the quantum and classical descriptions of the world around us, decoherence plays a fundamental role. How a quantum system looses phase coherence, or how this process can be prevented, is the key to realising interesting quantum mechanical effects in practice. Motivated by recent experiments with Josephson-junction circuits we reconsidered decoherence effects in quantum two-level systems (TLS). On one hand, the experiments demonstrate the importance of 1/f noise, on the other hand, by operating at symmetry points one can suppress noise effects in linear order. We, therefore, analyzed noise sources with a variety of power spectra, with linear or quadratic coupling, which are longitudinal or transverse relative to the eigenbasis of the unperturbed Hamiltonian. Manipulations of the quantum state of the TLS define characteristic time scales. We discussed the consequences for relaxation and dephasing processes.

The application of quantum computing ideas in controllable quantum devices

Recently, an additional focus has been the application of some of the above ideas from quantum computing to the design of quantum devices. In this case, the power of superposition or entanglement is used in the operation of novel solid-state devices. Recent examples include, single-qubit lasing, Sisyphus heating and cooling, parameteric amplification, photon number squeezing and decoherence microscopy.

Some publications
  1. For an introduction see
    Qubits (fast) zum Anfassen
    G. Schön und A. Shnirman, Physik Journal 11/2005, p. 51-56

  2. Scanning Quantum Decoherence Microscopy
    J.H. Cole and L.C.L. Hollenberg
    Nanotechnology 20, 495401 (2009)
  3. Phase diffusion and locking in single qubit lasers
    S. André, V. Brosco, A. Shnirman, and G. Schön
    Phys. Rev. A 79, 053848 (2009)

  4. Modeling two-spin dynamics in a noisy environment
    M.J. Testolin, J.H. Cole, and L.C.L. Hollenberg
    Phys. Rev. A 80, 042326 (2009)

  5. Sensing of Fluctuating Nanoscale Magnetic Fields Using Nitrogen-Vacancy Centers in Diamond
    L.T. Hall, J. H. Cole, C.D. Hill, and L.C.L. Hollenberg
    Phys. Rev. Lett. 103, 220802 (2009)

  6. Sisyphus damping and amplification by a superconducting qubit
    M. Grajcar, S.H.W. van der Ploeg, A. Izmalkov, E. Il'ichev, H.-G. Meyer, A. Fedorov, A. Shnirman, and G. Schön
    Nature Physics 4, 612-616 (2008)

  7. Single-qubit lasing and cooling at the Rabi frequency
    J. Hauss, A. Fedorov, C. Hutter, A. Shnirman, and G. Schön
    Phys. Rev. Lett. 100, 037003 (2008)

  8. Photon-number squeezing in circuit quantum electrodynamics
    M. Marthaler, G. Schön, and A. Shnirman
    Phys. Rev. Lett. 101, 147001 (2008)

  9. Decoherence from ensembles of two-level fluctuators
    J. Schriefl, Yu. Makhlin, A. Shnirman, and G. Schön
    New Journal of Physics 8, 1 (2006).

  10. Decoherence in a superconducting quantum bit circuit
    G. Ithier, E. Collin, P. Joyez, P.J. Meeson, D. Vion, D. Esteve, F. Chiarello, A. Shnirman, Y. Makhlin, J. Schriefl, and G. Schön
    Phys. Rev. B 72, 134519 (2005)

  11. Low- and high-frequency noise from coherent two-level systems
    A. Shnirman, G. Schön, I. Martin, and Y. Makhlin
    Phys. Rev. Lett. 94 , 127002 (2005)

  12. Dephasing of solid-state qubits at optimal points
    Yu. Makhlin and A. Shnirman
    Phys. Rev. Lett. 92, 178301 (2004)

  13. Quantum State Engineering with Josephson-Junction Devices
    Yu. Makhlin, G. Schön, and A. Shnirman
    Rev. Mod. Phys. 73, 357-400 (2001)

  14. Josephson-Junction Qubits with Controlled Couplings
    Y. Makhlin, G. Schön, and A. Shnirman
    Nature 398, 305-307 (1999).

  15. Quantum Measurements Performed with a Single-Electron Transistor
    A. Shnirman and G. Schön
    Phys. Rev. B 57, 15400 (1998).

  16. Quantum Manipulations of Small Josephson Junctions
    A. Shnirman, G. Schön, and Z. Hermon
    Phys. Rev. Lett. 79, 2371 (1997).

Relevant grants and some links

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