Quantum Computing

In contrast to the "standard" Divincenzo paradigm, in which a sequence of one- and two-bit unitary operations evolves a collection of qubits from a known initial state to a state that encodes the output, an adiabatic quantum computer maintains a system of qubits in the ground state of a slowly varying Hamiltonian and is less prone to decoherence. The initial (unfrustrated) Hamiltonian has a simple ground state, while the final Hamiltonian, which encodes the problem, has a complex ground state that encodes the solution.

In "standard" quantum computing the solution is encoded in an entangled superposition of states of a multiqubit system, which is fragile with respect to decoherence. This constitutes the main obstacle for a realization of standard quantum computing in the near future.

In adiabatic quantum computing, the solution is encoded in the ground state of the system evolving under an adiabatically slow change of a control parameter, b, from an easily accessible initial state (Fig. 1). The main advantages of adiabatic quantum computing are the following:

• The precise time-dependent control over specific qubits, which is necessary (but hardly realizable) for the standard scheme, is no longer an issue for adiabatic quantum computing.
• Staying in the ground state automatically protects the system against relaxation and dephasing.
• Any standard quantum algorithm can be realized by an adiabatic quantum computer with a local Hamiltonian (which is extremely important for any quantum computing realization).
• Thus, in contrast to standard quantum computing requiring very large number of qubits, some adiabatic quantum computing schemes can be realized with a modest number of physical qubits.

Therefore a solid state-based implementation of an adiabatic quantum computer is feasible.

Research in this area ranges from the principles of adiabatic quantum computing to Josephson-based quantum computing architectures. The predictions on such architectures are being tested in the experimental groups of Ilichev (Jena) and Clark (Berkeley).

The Quantum Information seminar series is designed to communicate these and related ideas to a wider audience.

Fig 1. Schematics of adiabatic quantum computing: starting (b=0) from a ground state of the energy spectrum with well-separated levels, the system adiabatically evolves to a final (b=1) complex ground state (along the red line) whose wave function or energy represents the result of quantum simulations.
Fig 2. Energy eigenvalues of the Hamiltonian of two coupled SQUIDs as a function of the external bias fluxes	Fig 3. Wigner function for an excited state of a SQUID ring

In the news

Qubit twist - nanotubes as mechanical qubits (Scientific American April 2005)

Some recent and current PhD theses

• Dmitry R Gulevich,Tunneling and Switching phenomena in Superconducting Quantum Dots and Josephson Junctions, 2006 (supervisor: Kusmartsev)
• Maria Silvia Garelli, Buckyball Quantum Computer: Practical realization of quantum gates, 2006 (supervisor: Kusmartsev)
• Neil Lindsey, Path integral calculation of Wigner functions, in preparation (supervisor: Samson)

Contacts

• Boris Chesca
• Mark Everitt
• Dmitry Gulevich
• Kliment Kugel
• Feodor Kusmartsev
• John Samson
• Sergey Savel'ev
• Alexandre Zagoskin

For further information

O. Astafiev, A. M. Zagoskin, A. A. Abdumalikov, et al, Resonance Fluorescence of a Single Artificial Atom, Science 327 840 (2010)

Rakhmanov AL, Zagoskin AM, Savel'ev S, et al, Quantum metamaterials: Electromagnetic waves in a Josephson qubit line, Phys Rev B 77 144507 (2008)

Zagoskin AM, Il'ichev E, McCutcheon MW, et al., Controlled Generation of Squeezed States of Microwave Radiation in a Superconducting Resonant Circuit , Phys Rev Lett 101 253602 (2008)

M J Everitt, T D Clark, P B Stiffell, R J Prance, H Prance, A Vourdas and J F Ralph, Superconducting analogues of quantum optical phenomena: Macroscopic quantum superpositions and squeezing in a superconducting quantum-interference device ring, Phys Rev A 69 043804 (2004)

A M Zagoskin, S Savel'ev and F Nori, Modeling an Adiabatic Quantum Computer via an Exact Map to a Gas of Particles, Phys Rev Lett 98 120503 (2007)

A Zagoskin and A Blais, Superconducting Qubits, Physics in Canada 63 215–227 (2007)

M J Everitt, S Khalil and A M Zagoskin, On “non-Hermitian Quantum Mechanics”

A O'Hare, F Kusmartsev, K Kugel and M S Laad, Two-dimensional Ising model with competing interactions and its application to clusters and arrays of rings and adiabatic quantum computing, Phys Rev, 76 064528 (2007)

A O'Hare, F Kusmartsev, K Kugel and M S Laad, Evidence of superstructures at low temperatures in frustrated spin systems, Physica C: Superconductivity, 437-438, 230-233 (2006)

R T Giles and F Kusmartsev, Novel Phenomena in the Josephson Ladder: Roto-breathers, Chaotic Transients and Application to Quantum Computing, review article in Studies of High Temperature Superconductors , Narlikar, A. (ed.), Nova Science, New York , 2002, pp. 103-153, ISBN: 1-56033-204-0

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