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IRC Connections
Introduction
This document, produced within the QIPIRC in Autumn 2005, brings out some common
scientific themes which have emerged from the first year or so of the IRC’s work. It is
not intended to be any kind of full progress report, a quality review of the projects, or a
list of scientific highlights; rather, it is a subset of the results recently reported by the IRC
(either in quarterly scientific progress reports to the management team, or in publications
and preprints) that, while interesting in themselves, relate to more than one of the IRC
projects or seem to have the potential to lead to further work in several different areas. It
was discussed at the recent IRC science meeting; two of the areas highlighted for their
developing connections were chosen for discussion symposia at that meeting. For each
topic we mention one or two names as contact points for those who are interested in the
work; this is not intended to be any kind of formal assignment of scientific credit, for
which the author lists of the papers referenced provide a better indication.
The present document was written by Andrew Fisher and the selection corresponds to his
own subjective choices. It has benefited from the input of others in the IRC, but the
responsibility for the selection and any remaining errors is entirely his – comments are
welcome (andrew.fisher@ucl.ac.uk)! If it is found to be useful we will update it
regularly and also produce versions for other audiences.
Producing and reading qubits
Reading out angular momentum states in an ion trap
The Oxford ion trap group, led by David Lucas and Andrew Steane, has developed an
elegant way of distinguishing between two quantum states which differ in their angular
momentum, but hardly at all in energy. The states are two spin states of the 2S1/2
electronic ground state of the 40Ca+ ion, which are exactly degenerate in zero external
magnetic field and have only a very small splitting (a few MHz) in the weak fields used
in the experiments. This energy separation is too small to use as a basis for
distinguishing the states. The Oxford group’s is a natural one for QIP because the state
of an isolated ion evolves only slowly in time, but it presents the significant challenge of
how to read out the state of a qubit; in practice this meant designing a sequence of
operations such that fluorescence was produced only from one spin state when it is
suitably illuminated by lasers.
This was done [1] by the technique of “coherent population trapping”: a combination of
two polarized lasers was used to drive one of the qubit states ( 2 S1/ 2 , mJ   1 ) into a
2
“dark” (i.e. non-fluorescing) combination of the original state and a particular excited
state ( 2 D3/ 2 , mJ   3 ) excited state via an intermediate energy level
2
2
P3/ 2 , mJ   1 . But this is only accomplished for one of the two qubit states, because
2
the conservation laws for angular momentum prevent the other qubit state from following
the same path; the other state therefore fluoresces when excited by the first laser. From
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the presence or absence of fluorescence, one therefore infers the orientation of the ion’s
original angular momentum vector relative to that of the incoming photons.
Given the immense difficulty of single-qubit readout in a whole range of systems, it is
very tempting to ask whether this general idea could be extended to solid-state schemes,
for example to single spins or to single quantum dots. The essential features of the
scheme are: (i) sufficient spin-orbit coupling to separate the energy levels of the same
spatial character but different angular momentum; and (ii) the existence of a strong
selection rule (angular momentum conservation) to allow the formation of the fluorescing
state only from one qubit state. The symmetry in a solid-state environment is much
lower, but the spin-orbit coupling can be strong and significant selection rules survive.
Challenges for the IRC therefore include: can we make use of these features for new
readout schemes in other contexts? Can we make use of the new-found ability to read out
optically information held in degenerate levels to perform further new demonstration
experiments, as the Oxford group have themselves recently done in joining the select
“club” of those leading groups who have demonstrated entangling interactions in ion
traps?
Producing degenerate levels for quantum-dot qubits
A somewhat similar issue has arisen in the production and optical characterization of
quantum dots. In general such a dot (although commonly described as an “artificial
atom”) is not truly spherically symmetric, and this results in energy splittings between the
exciton states (say
and  ) produced by different incident laser polarizations. To
use these exciton states as static qubits, it would be highly desirable to make the
polarizations degenerate, so that imprinting of an arbitrary quantum state 
 
on the dot could be performed with a single laser and no phase difference would
accumulate between the qubit states. No amount of care in the growth process will make
quantum dots perfectly isotropic, but the collaboration between the groups at Toshiba,
Cambridge (led by Andrew Shields) and Sheffield (led by Maurice Skolnick) has now
shown that the exciton splitting can be tuned to less than the homogeneous exciton
linewidth by changing the emission wavelength, either by tuning the growth conditions or
by annealing the dots after they have been produced [2]. In other words, the energies can
be made so similar (within 1μeV) that they cannot be distinguished within the dephasing
time of the system. Provided strong coupling of these dots to the photon field can be
achieved at the same time (as was previously demonstrated by the Würzburg group and
others), this opens the way to using the polarization degree of freedom of the dot as a
matter qubit that can interact strongly with the electromagnetic field.
The challenge for the IRC is: can it find ways of profiting from this unexpected discovery
to simplify or accelerate demonstration experiments on quantum information transfer
between photons and quantum dots?
High-Q cavities for single-photon production and detection
Quantum dots also feature in an exchange of samples and expertise between the formerly
separate fields of solid-state and optical physics, with the production of samples by the
Sheffield group for use by John Rarity and his colleagues in Bristol. Here the
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requirements are for the highest possible Q of optical cavity, with the smallest possible
mode volume: these requirements are very similar for the IRC’s cavity QED project, and
for single-photon production and readout, which is needed both for true single-photon
quantum cryptography and for linear-optical quantum information processing using the
KLM scheme or its variants. The opportunity for the IRC is that very similar growth and
fabrication developments are required for success in two of its different projects.
Progress with SAW fabrication and readout
The use of the electron as a flying qubit is a characteristic of the surface acoustic wave
(SAW) schemes being pursued by Crispin Barnes and his collaborators in Cambridge.
The qubit is embodied in a single electron spin; as always with solid-state spin-based
schemes, a significant challenge is the readout step. In this scheme, readout would be
done by polarized single-photon detection from the recombination step as electrons
trapped in the surface acoustic wave recombine with a hole gas at the end of the network
of one-dimensional channels that form the quantum gates. The challenge for the IRC now
is an experimental one: can it implement the models that the IRC group has set up [3] for
the readout process, and hence definitively demonstrate the proposed single-qubit
operations using the SAW architecture? The basic fabrication and lithography steps have
been demonstrated during the first year of the IRC, and the experiments to observe the
recombination luminescence are beginning. The challenge will be to combine the very
sensitive single-photon optics required with demanding solid-state experiments; the
Cambridge group already has strong links with the Toshiba Laboratory (with its own
experience of single-photon production and detection). Can other expertise within the
IRC (for example, from the Sheffield activity on single quantum-dot optics, or the SAW
work based at Malvern) contribute? Can we pass the test (which will have to be faced in
many of our condensed-matter studies) of transforming our work from getting the
materials science of the system right to studying its coherent quantum dynamics?
NV centres in diamond
A class of qubits that was not envisaged at the beginning of the IRC and consequently
does not appear in the original project workplans, but which is now under very active
investigation, is the NV centre in diamond (a defect complex consisting of a
substitutional N impurity plus a neighbouring vacancy). It has been shown in several
laboratories that these defects provide a very good system in which to prepare pure states,
produce coherent evolution and perform single-centre readout (see [4] for a review).
Now several new lines of investigation are under way involving personnel within the
IRC.
The first is the possible use of arrays of NV centres for the imprinting of quantum
information to form the quantum memories in the joint Cambridge/Oxford project led by
Ian Walmsley: here the ground and excited states of the NV centre would replace the
states of quantum dots or molecular systems originally envisaged for this project.
Second, the NV centres may be candidate systems for the production of cluster states by
induced optical interactions between them (see below). Third, it may be possible to
produce more conventional two-qubit entangling gates by interacting two NV centres
optically. All this is proceeding in collaboration with some of the established groups in
the NV centre field, notably that in Melbourne (on the supply of samples).
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Among the challenges for the IRC in this area are:
 Can it compete in the very demanding area of single-defect measurements?
 Can we quantify the advantages and disadvantages of defect-based systems, with
the attendant difficulties in addressing, as compared to mesoscopic systems such
as quantum dots which carry a significant fabrication overhead?
Producing and characterizing entanglement
Cluster states
There is a clutch of new results from the IRC in the area of the practical production of
cluster states. A cluster state is a highly entangled quantum state of N subsystems, whose
strong correlations lend themselves particularly well to exploitation. If the subsystems
are spin-1/2 objects, the cluster state is prepared) selected projective measurements are
made locally on the cluster; no coherently operating gates are required. So, one would
like ways of producing cluster states as efficiently as possible in the presence of the
inevitable dissipation and errors arising in a real experiment, and by a procedure that is as
nearly as possible deterministic.
There have already been several significant steps forward in this direction from within
the IRC. Dan Browne and Terry Rudolph [5] showed how linear optical elements
(specifically polarizing beamsplitters) could be used to combine systematically pairs of
entangled photons into a single cluster state of arbitrary complexity; the significance of
this is that the production of the cluster state, and subsequent QIP by single-photon
measurements, can be performed much more efficiently than in the original KLM linear
optics schemes.
Then came two, initially independent, developments. Almut Beige and her colleagues at
Imperial and Cambridge [6] introduced a “repeat-until-success” approach, in which a
protocol not guaranteed to succeed at once can nevertheless be repeated until successive
atoms trapped in electromagnetic cavities have been added to the cluster. In the scheme
from Pieter Kok and his colleagues at Hewlett-Packard [7], matter qubits that can be
strongly coupled to the radiation field (for example, trapped atoms or quantum dots) are
once again intimately involved. Matter qubits in separate electromagnetic cavities are
first prepared in separable states which are separately allowed to interact with radiation;
the photons from the two cavities are then combined using a beam-splitter. Conditional
on the detection of a photon in the output channel, one prepares an entangled state of the
matter qubits; this entanglement can be transferred to the electromagnetic field by
appropriate projective measurements on the matter degrees of freedom. These two IRC
teams have subsequently joined forces in a follow-up paper combining their two schemes
[8].
Another recent development has seen the groups from H-P, Imperial and Oxford are now
working together to find further efficient ways of generating the cluster state
deterministically, with a recent proposal from Simon Benjamin and his colleagues [9] to
use optical interactions among three-level matter qubits for this purpose.
Among the challenges this poses for the rest of the IRC are:
 Are these the best ways to use the available combinations of matter and radiation
qubits to generate graph states? Can we find better protocols and can we start
taking them towards physical realisation? (A pioneering experiment in Vienna
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
recently generated four-qubit cluster states, setting the international benchmark.)
Can we devise practically implementable demonstration experiments in a
reasonable timescale that make use of the combination of expertise within the
IRC? What resources might these require?
Should the IRC change its direction to concentrate explicitly on the generation
and use of cluster states, rather than on gate-based quantum information
processing?
Ground-state entanglement in field theories
As well as producing entanglement, characterising what is already present in the ground
state of a quantum system is very important in determining what quantum resources are
available in any given system. In relation to the IRC’s goals of transferring quantum
information between static and propagating forms, some of the most interesting systems
to study are those that have propagating excitations – notably quantum field theories,
which can be thought of as a continuum limit of a set of coupled, quantized, oscillators.
Martin Plenio and his collaborators [10] have succeeded in proving a long-conjectured
result: that in the ground state of such a scalar field, the entanglement of a finite region of
space with the rest is proportional to the area of the region’s surface. Specifically, they
find that for a d-dimensional lattice of locally coupled oscillators (effectively a quantum
field theory with a particular well defined ultraviolet cutoff), the entanglement of a finite
“lump” of oscillators of dimension m in each direction with the rest of the system is
proportional to its neighbours, and En,m is the von Neumann entropy of the “lump’s”
density matrix.
Challenges for the IRC arising from this work are: can we find ways of confirming the
existence of this entanglement experimentally, or even exploiting it? What connections
are there (theoretically or experimentally) to the entanglement present in the ground
states of other systems, for example spin systems or degenerate quantum gases?
Propagating and Communicating Entanglement
Spin-carrying impurities in fullerenes and nanotubes
One of the IRC’s major projects is in the use of novel molecular materials, including
nanotubes and endohedral fullerenes, for QIP. Single-electron qubits play a key role in
the proposed experiments, but such single-spin experiments are very difficult, and the
emphasis so far within the IRC has been on the very delicate materials science that needs
be done to characterize the systems [11], measuring and modelling the spin properties of
endohedral fullerene materials [12], and the adaptation of composite pulse sequences
from the NMR community to carry out (in ensembles) the very high-accuracy singlequbit manipulations that would be required for true QIP [13, 14]. There is also
theoretical work in preparation for the possibility of single-qubit experiments, in
particular to study the extent to which it will be feasible to entangle static and
propagating qubits using exchange interactions [15], with by-products that might also be
useful in classical information processing (for example, spin filtering [16]). At present
these are model calculations: they rely on parameters that are much less well known than
(for example) the corresponding coupling constants between matter qubits and photons.
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Combining these studies with the experimental programme poses several challenges for
the IRC:
 Can the studies be made quantitative, to the extent that the parameters involved
can be related to those to be expected in a real measurement?
 How could a successful demonstration of such an effect be made, i.e. can we
formulate a full experimental protocol, including some sort of detection step,
preferably one that falls short of a local projective spin measurement in a
condensed-matter structure?
 Can this work be connected with the other progress that has been made on onedimensional spin systems that have direct exchange interactions between
localised spins (see below)?
 The theories generally treat the scattering of one or two electrons – yet in the
majority of real experiments there will be many. Can we either generalize the
models to many-electron scattering, or develop experimental protocols that have
a reasonable chance of scattering single electrons?
Entanglement propagation and processing in quantum chains
The idea of propagating entanglement over long distances through interacting spin
systems, rather than through propagating electromagnetic modes, has been very actively
investigated over the last couple of years. Some recent developments in the IRC have
included the proof that “perfect” entanglement transmission can be performed with a
single spin chain provided that Alice and Bob both have interactions with it that are
sufficiently distributed in space [17], and the discovery that arrays of spin chains coupled
in parallel in various ways can also yield perfect entanglement [18]. These concepts have
been extended to other systems such as harmonic lattices [19, 20], raising the possibility
of more general types of “quantum data bus”. Challenges for future work in the IRC now
include: can these results be used by the experimental programmes, for example those
focused on spin-containing fullerene nanostructures? How are the entanglementtransmission properties of these spin or lattice systems, and indeed of the photon field,
related to the ground-state entanglement they contain in equilibrium? How does the
entanglement transmission behave in a real system as a function of temperature or of the
coupling to incoherent reservoirs?
References
1. High-Efficiency Detection of a Single Quantum of Angular Momentum by
Suppression of Optical Pumping. M. J. McDonnell, J.-P. Stacey, S. C.Webster,
J. P. Home, A. Ramos, D.M. Lucas, D. N. Stacey, and A.M. Steane, Phys. Rev.
Lett. 93 153601 (2004).
2. Inversion of exciton level splitting in quantum dots . R.J. Young et al. Phys. Rev.
B 72 113305 (2005)
3. Single-qubit gates and measurements in the surface acoustic wave quantum
computer. Furuta S, Barnes CHW, Doran CJL, Phys. Rev. B 70 205320 (2004)
4. Read-out of single spins by optical spectroscopy. F Jelezko et al J. Phys.:
Condens. Matter 16 R1089-R1104 (2004).
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5. Resource-efficient linear optical quantum computation. D.E. Browne and T.
Rudoph, Phys. Rev. Lett. 95 010501 (2005).
6. Repeat-Until-Success Linear Optics Distributed Quantum Computing. Y.L. Lim,
A. Beige and L.C. Kwek Phys. Rev. Lett. 95 030505 (2005)
7. Efficient high-fidelity quantum computation using matter qubits and linear optics.
Pieter Kok and Sean D. Barrett, Phys. Rev. A 71 060310(R) (2005)
8. Repeat-Until-Success quantum computing using stationary and flying qubits.
Y.L. Lim et al. quant-ph/0508218.
9. Optical generation of matter qubit graph states. S.C. Benjamin, J. Eisert and T.M.
Stace, quant-ph/0506110.
10. Entropy, entanglement, and area: analytical results for harmonic lattice systems
M.B. Plenio J. Eisert, J. Dreissig, M. Cramer , quant-ph/0405142 and Phys. Rev.
Lett. 94 (2005) 060503; An entanglement-area law for general bosonic harmonic
lattice systems. M. Cramer, J. Eisert, M.B. Plenio, J. Dreissig, quant-ph/0505092.
11. Observation of ordered phases of buckminsterfullerene in double-wall carbon
nanotubes. A.N. Khlobystov et al., Phys. Rev. Lett. 92 245507 (2004).
12. Hyperfine structure of Sc@C82 from ESR and DFT. G.W. Morley et al.
Nanotechnology 16, 2469-2473 (2005).
13. High fidelity single qubit operations using pulsed electron paramagnetic
resonance. J.J.L. Morton, A.M. Tyryshkin, A. Ardavan, K. Porfyrakis, S.A. Lyon
and G.A.D. Briggs. Phys. Rev. Lett. 95, 200501 (2005), quant-ph/0502119.
14. Bang-bang control of fullerene qubits using ultra-fast phase gates. J.J.L. Morton,
A.M. Tyryshkin, A. Ardavan, S.C. Benjamin, K. Porfyrakis, S.A. Lyon and
G.A.D. Briggs. Nature Physics (2005, in press).
15. Entanglement of Two Impurities through Electron Scattering. A. T. Costa Jr, S.
Bose, Y. Omar, quant-ph/0503183
16. Zener Quantum Dot Spin Filter in a Carbon Nanotube. D. Gunlycke, J.H.
Jefferson, S.W.D. Bailey, C.J. Lambert, D.G. Pettifor, and G.A.D. Briggs,
cond-mat/0412406.
17. The Propagation of Quantum Information Through a Spin System. Tobias J.
Osborne and Noah Linden, quant-ph/0312141.
18. Perfect quantum state transfer with randomly coupled quantum chains. Daniel
Burgarth andSougato Bose, quant-ph/0502186 and New J. Phys. 7 135 (2005)
19. High-efficiency transfer of quantum information and multi-particle entanglement
generation in translation invariant quantum chains. Martin B Plenio and Fernando
L Semiao, New J. Phys. 7 73 (2005) and quant-ph/0407034.
20. Dynamics and manipulation of entanglement in coupled harmonic systems with
many degrees of freedom. M.B. Plenio, J. Hartley, J. Eisert, New J. Phys. 6 36
(2004) and quant-ph/0402004.