Quantum computing with an electron spin ensemble

Quantum computing with an electron spin ensemble
J.H. Wesenberg,1 A. Ardavan,2 G.A.D. Briggs,1 J.J.L. Morton,1, 2 R.J. Schoelkopf,3 D.I. Schuster,3 and K. Mlmer4
1Department of Materials, University of Oxford, OX1 3PH, United Kingdom
2Clarendon Laboratory, Department of Physics, University of Oxford, OX1 3PH, United Kingdom
3Department of Applied Physics, Yale University, Connecticut 06520
4Lundbeck Foundation Theoretical Center for Quantum System Research,
Department of Physics and Astronomy, University of Aarhus, 8000 Aarhus C, Denmark
(Dated: March 20, 2009)
We propose to encode a register of quantum bits in di erent collective electron spin wave excitations
in a solid medium. Coupling to spins is enabled by locating them in the vicinity of a
superconducting transmission line cavity, and making use of their strong collective coupling to the
quantized radiation eld. The transformation between di erent spin waves is achieved by applying
gradient magnetic elds across the sample, while a Cooper Pair Box, resonant with the cavity eld,
may be used to carry out one- and two-qubit gate operations.
PACS numbers: 03.67.Lx, 33.90.+h, 85.25.Cp, 42.70.Ln
The construction of a large quantum computer is a
challenge for current research. The overarching problem
is to develop physical systems which can reliably store
thousands of qubits and which allow addressability of in-
dividual bits and pairs of bits in gate operations. Propos-
als in which single trapped ions or atoms encode qubits
in their internal state have successfully demonstrated the
building blocks for few-bit devices, while scaling of these
systems to larger register sizes is believed to require in-
terconnects, e.g., with optical transmission. A novel col-
lective encoding scheme for qubits proposes to use many
identical quantum systems to encode each qubit, either
in the collective population of di erent internal states
[1, 2, 3] or in di erent spatial modes of excitation of the
entire system [4, 5].
In this Letter we propose a hybrid approach to quan-
tum computing making use of an ensemble of 1010..1012
electron spins coupled to a superconducting transmission
line cavity. We will describe how a large number of spa-
tial modes can be addressed in the spin ensemble, and
how a transmon Cooper Pair Box (CPB) [6], integrated
in the cavity can provide one- and two-bit gates for quan-
tum computing in the spin ensemble [7, 8]. Our scheme
enables materials for which large spin coherence times
have been demonstrated in ensemble measurements to be
incorporated into a solid state device. In this way, with-
out requiring single spin measurement or strong coupling
to a cavity, full use can be made of the sophisticated tech-
niques which are no w well established for control of large
numbers of spins.



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