Download Qubits based on electrons on helium The basic building block of a

Qubits based on electrons on helium
The basic building block of a quantum computer is called a qubit, and a large number of qubit
systems have been suggested. However, so far only relatively primitive systems with a limited
number of qubits have been tested. The most advanced demonstration so far is a seven qubit
implementation of Shor’s factoring algorithm. Qubit systems can be divided into three categories: i)
those which are based on microscopic systems, such as molecules, trapped atoms, or photons, ii)
those which are based on solid state systems, and iii) combined systems, where microscopic
systems are trapped on a chip using modern nano-technology. All categories have advantages and
disadvantages, especially the microscopic systems have long coherence times, but are hard to
integrate into systems with a larger number of qubits. For the solid state systems, the situation is the
opposite. So far the microscopic systems have demonstrated the most advanced state manipulation,
however it is generally believed that an operating quantum computer would have to be based on
qubits from category ii) or iii) due to the easier integration, and the possibility to couple the
manipulation and read-out systems with more conventional electronics.
In 1999, Platzman and Dykman [1] proposed that electrons on the surface of liquid helium
(EOH) could be used as qubits, and hence form the basis of a quantum computer. This proposal is in
between the atomic trap idea and a solid-state device. Indeed, electrons are localized in micro-traps.
One can even put neutral atoms, instead of electrons, there. On the other hand, fabrication and
operation is similar to those of solid-state devices. In fact, the principle of operation is very similar
to that of the quantum dot quantum computer. The main difference is that our “quantum dot” is
located in vacuum, isolated from the environment. Super-fluid helium provides an ideal surface for
forming two-dimensional arrays of electrons. It is free from impurities and atomically smooth.
Electrons above the surface are bound very weakly to it by their interaction with image charges in
the bulk helium, forming a hydrogen like atom. The lowest energy-state has a mean separation of
about 100Å from the surface. The 2D electrons, above a thick enough (0.5µm) helium film on a
dielectric substrate, can be trimmed by metallic electrostatic gates patterned using conventional
nanofabrication technique. This makes the system easily scalable.
a
b
Fig.3. a) A schematic drawing of the qubit, including confinement electrodes, and a SET read-out. The electron is
suspended over a liquid helium film, which is held by surface tension on a thick circular electrode. In the vertical
(perpendicular to the film) direction, the electron is held by attraction to its image charge on one hand and by large
potential barrier to enter helium on the other. In the plane the electron is localized by potential applied between the
circular electrode and the Single Electron Transistor (SET) located at its center and below the ring. This SET is also
used for the readout. The system is subjected to the microwave radiation.
b) The electron and its image form one dimensional pseudo-hydrogen atom with the first two excited levels
separated by 120-150 GHz depending on the electric field F.
The two-level system, necessary for a qubit, is formed by the electron in the lowest energystate, and the first excited state. The energy difference is 0.5 meV, corresponding to roughly 6K (i.e.
the first two Rydberg levels corresponding to the |0> and |1> qubit states). At low temperatures, the
vapor density is very low, and does not cause any electron scattering. The only degrees of freedom
the qubit can interact with, are surface waves, called ripplons. This coupling is quite small and can
be suppressed in moderately high magnetic fields. As a result, the electron mobility on a helium
surface is the highest ever achieved in any condensed matter system [2]. This indicates that long
enough coherence times of a two-level system could be reached; estimates give numbers
comparable to the ones in systems of atomic physics. If the spin degeneracy of the orbital states
turns out to degrade the performance, it is possible to lift it by applying magnetic field of the order
of 2 T, which will split the energy of the up and down spin states by ~2.5 K; similar field strength
has to be used to suppress effects caused by ripplon scattering. However, one can also use the spin
states of the electron as basic qubit states.
We have with a very limited amount of funding started a collaboration with the Kapitza
Institute where the electrons on helium have been studied for about 20 years. So far we have
fabricated the sample cell and made a layout for the first samples (see Fig. 3). We plan to use the
same cryostat as for the SCB measurements where the RF-SET set up is already installed. We thus
expect to get a quick start on this project.
b
a
c
Fig. 3. a). General view of the silicon chip with four qubit sites (in the middle of the chip) and
a structure for the monitoring the surface electron density (microchannel capacitor)3.
b). SET with the electrostatic gate. In this design the ring, confining electron has a reduced diameter
of 0.4 micrometers, enabling to capture the only electron in the trap (see also Fig.1a).
c).color dI/dV plot of the SET sensor taken at 16 mK.
RF-SET read-out
For several years we have at Chalmers developed and optimized the RF-SET [1] and
demonstrated very good sensitivity, 3.2 µe/vHz [3]. Combining the best experimental results on the
RF-SET with theoretical calculations by the theory group, we have recently shown that the RF-SET
should capable of single shot measurements [4,5]
We will continue to develop the RF-SET and optimize its performance aiming for single shot
measurement. In our best measurements, it is still the cold amplifier which limits the performance
of our RF-SET. In collaboration with John Clarke's group at Berkeley, we will add a microwave
SQUID amplifier [6] between our RF-SET and the present cold amplifier. This SQUID amplifier
has a noise temperature close to 50 mK which should be compared with our present HEMT
amplifier which has a noise temperature of ~5K. Adding the SQUID amplifier will substantially
improve our read-out system. It turn out that there will be several advantages of switching to a
transmission RF-SET [7] when implementing the SQUID amplifier, thus we will make this change
simultaneously.
In Platzman and Dykman proposal [1], read out would project the qubits onto the Rydberg
basis states, by ionizing the excited state electrons onto a multi-channel plate (MCP) detector. We
propose to use an RF-SET as the readout system also for this type of qubit. This means that we will
not lose the electron from the trap (which would be a real problem when we want to do error
corrections). As it was discussed in by Lea et al. [8], the difference between the induced charge in
the metallic electrode by the electron switching between the ground and excited states is fairly
small. The change is a few per cent of the electron charge, but it is feasible to detect by an RF-SET
in a single shot measurement. We will demonstrate trapping of a single electron on a surface and
demonstrate read-out of the EOH qubits using the RF-SET.
Manipulation of the qubits
Qubits can in principle be manipulated in two different ways. If the qubit has an avoided level
crossing controlled by an external variable, it is possible to manipulate the states in the qubit by
applying fast dc-pulses to that variable. A good example is the SCB where the gate voltage can be
used to switch between the two different charge states. Alternatively we can apply an rf-pulse which
is resonant with the level spacing of the two energy states. This is the method which has to be used
in systems where there is no anti level crossing. EOH belongs to that this category of qubits. The
dc-pulse method gives faster operations, but so far the longest decoherence times have been
reported for rf-pulsed systems.
Manipulation of the qubits based on electrons on helium
The energy state for electrons on helium does not have an anti-level crossing, and thus the states
cannot be addressed using dc-pulses. Instead we will use resonant microwave excitation at the
frequency fR, the single qubits can be manipulated in a manner very similar to NMR technique.
Individual qubits can be tuned by voltages on the underlying electrodes, through the linear Stark
effect, The energy difference corresponds to frequency of 120GHz and above. We intend to use a
frequency tripler to multiply the signal from an existing microwave generator in the range 40 to 50
GHz, such that we can cover the range 120-150 GHz. This signal will be introduced to the sample
via a wave guide. At a later stage of the project it can be replaced by superconducting flux-flow
oscillator nearby the qubit site. For a realistic estimate of the microwave field amplitude Fω ≈ 100
V/m the length of a π-pulse would be a few ns.
Expected milestones
Month 12
• Trapping and detection of a single electron on a Helium surface
• Microwave SQUID amplifier added to the RF-SET
Month 24
• Microwave power delivered to the qubit.
• Measurements of decoherence in a single qubit.
Month 36
• Preparation and detection of the states of the qubits, measuring the coherence times in the
qubits.
• Designing and testing two-qubit gates.
• Optimization of the decoherence time.
• Evaluation of the initialization problem
Month 48
• Implementation of controlled coupling by moving of electrons on helium (“flying qubits”)
• Two qubit operation demonstrated
People:
Sergey Kafanov, Alexander Ya. Parshin, Alexander F. Andreev, P.L. Kapitza Institute for Physical
Problems, Moscow, Russia,
Per Delsing, Sergey Kubatkin, Chalmers
References
1
P. M. Platzman and M. I. Dykman, Science 284, 1967 (1999).
2
K. Shirahama, S. Ito, H. Suto and K. Kono, J. of Low Temp. Phys. 101, 439 (1995).
3
P. Glasson, V. Dotsenko, P. Fozooni, M. J. Lea, W. Bailey, and G.Papageorgiou S. E. Andresen and A. Kristensen,
Phys. Rev. Lett. 87, 176802 (2001).
4
A. Aassime, G. Johansson, G. Wendin, R. J. Schoelkopf and P. Delsing, Phys. Rev. Lett. 86, 3376 (2001).
5
G. Johansson, A. Kack and G. Wendin, Phys. Rev. Lett. 88, 046802 (2002).
6
M. Mück, J. B. Kycia and J. Clarke, Appl. Phys. Lett. 78, 967 (2001).
7
T. Fujisawa and Y. Hirayama, Appl. Phys. Lett. 77, 543 (2000).
8
M. J. Lea, P. G. Frayne and Y. Mukharsky, Fortschr. Phys. 48, 1109 (2000).