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Physica Scripta

Ca+quantum bits for quantum information processing

Jan Benhelm, Gerhard Kirchmair, R. Gerritsma, F. Zähringer, Thomas Monz, Philipp Schindler, Michael Chwalla, W. Hänsel, Markus Hennrich, Christian F. Roos, R. Blatt

Published Dec 1, 2009• 6 citations
Publisher

Abstract

With trapped ions quantum information can be encoded in various two-level systems or quantum bits (qubits). Here, we present an overview on qubit encoding with Ca + and several state-of-the-art operations involving two and three qubits. The use of decoherence-free subspaces and encoding logical qubits using two physical qubits may offer an advantageous route towards implementing scalable quantum information processing.

DOI
10.1088/0031-8949/2009/t137/014008

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With trapped ions quantum information can be encoded in various two-level systems or quantum bits (qubits). Here, we present an overview on qubit encoding with Ca + and several state-of-the-art operations involving two and three qubits. The use of decoherence-free subspaces and encoding logical qubits using two physical qubits may offer an advantageous route towards implementing scalable quantum information processing.
Quantum information processing is performed with single trapped Ca(+) ions, stored in a linear Paul trap and laser-cooled to the ground state of their harmonic quantum motion. Composite laser-pulse sequences were used to implement SWAP gate, phase gate and controlled-NOT gate operations. Stark shifts on the quantum-bit transitions were precisely measured and compensated. For a demonstration of quantum information processing, a Deutsch-Jozsa algorithm has been implemented using two quantum bits encoded on a single ion.
Decoherence-free subspaces protect quantum information from the effects of noise that is correlated across the physical qubits used to implement them. Given the ability to impose suitable Hamiltonians upon such a multi-qubit system, one can also implement a set of logical gates which enables universal computation on this information without compromising this protection. Real physical systems, however, seldom come with the correct Hamiltonians built-in, let alone the ability to turn them off and on at will. In the course of our development of quantum information processing devices based on liquid-state NMR, we have found the task of operating on quantum information encoded in decoherence-free subspaces rather more challenging than is commonly assumed. This contribution presents an overview of these challenges and the methods we have developed for overcoming them in practice. These methods promise to be broadly applicable to many of the physical systems proposed for the implementation of quantum information processing devices.
The state-of-the-art of the Innsbruck trapped-ion quantum computer [1] is briefly reviewed. We present an overview on the available quantum toolbox and discuss the scalability of the approach. With up to 50 fully controlled ion qubits we perform quantum simulations investigating quantum transport [2] and emerging hydrodynamics features [3]. Employing the quantum toolbox for entanglement-enhanced Ramsey interferometry, we find optimal parameters for quantum metrology [4]. Quantum computers can be protected from noise by encoding the logical quantum information redundantly into multiple qubits using error-correcting codes. Manipulating logical quantum states by imperfect operations requires that all operations on the quantum register obey a fault-tolerant circuit design to avoid spreading uncontrolled errors. We demonstrate a fault-tolerant universal set of gates on two logical qubits in the trapped-ion quantum computer [5].
We demonstrate a decoherence-free quantum memory of one qubit. By encoding the qubit into the decoherence-free subspace (DFS) of a pair of trapped 9Be+ ions, we protect the qubit from environment-induced dephasing that limits the storage time of a qubit composed of a single ion. We measured the storage time under ambient conditions and under interaction with an engineered noisy environment and observed that encoding into the DFS increases the storage time by up to an order of magnitude. The encoding reversibly transfers an arbitrary qubit stored in a single ion to the DFS of two ions.