The past year saw important progress across all of the Centre's eleven experimental and seven theoretical research programs, with 100 papers published in, or accepted for, peer-reviewed journals in 2005, and a further 13 submitted. In the next few pages we bring together the key highlights for 2005 across the Centre.
Silicon-based Si:P Qubits via Ion Implantation
The development of spin-based qubits in the Si:P materials system is the key focus of the Centre's solid-state programs. As a stepping stone to spin-based qubits, a charge-based Si:P architecture has been proposed by Centre researchers - see Physical Review B 69, 113301 (2004) - for which fast single charge readout is accessible now, using rf-SET technology established within the Centre. Although a charge-based qubit will decohere faster that its spin-based counterparts, the readout signal generated during electron transfer is similar to that used for spin readout schemes and as such provides a critical test bed for the development of spin qubits.
In 2004 our teams at UM and UNSW refined the process of counted single ion implantation, allowing known numbers of P atoms to be implanted with nearly 100% confidence. During 2005 this process was developed further to allow mass-production of qubit test devices with a precise number of P atoms. During 2005 we performed the first experiments that address the relevant energy and time scales for Si:P charge qubits. In particular we performed microwave spectroscopy on few-atom devices and measured inelastic tunnelling rates between two phosphorus atoms. By studying the dynamical response between individual phosphorus donors or P-clusters using gate voltage pulses or imposing a GHz microwave field, we are able to gain information about the charge state relaxation time, and energy level spectrum, respectively. A key result comes from a device implanted with exactly two atoms, which showed an extremely stable charge transfer event. Dynamic measurements were performed by pulsing the gate voltage, yielding remarkably long charge state relaxation times of order 10 ms. A remarkable match to theoretical predictions for combined resonant and phonon assisted tunnelling was found - see Figure 1a. Evidence of oscillatory behaviour due to interference with acoustic phonons is confirmed by Fourier transformation (Figure 1b), which is consistent with the expected donor spacing of 50 nm. These results represent the first conclusive measurement of single electron transfer in an atomically-engineered Si:P device.
Figure 1 (a) Charge state relaxation times for a 2-P-atom device with a spacing of 50nm, deduced from pulsed gate measurements (red, blue), together with theoretical prediction for 50 nm donor separation (black line).
(b) Fourier transforms of bias dependence reveal peaks due to phonon interference on a length scale of ~ 50 nm.
To observe coherent or resonant microwave excitation in a Si:P device, a device with four implanted (and counted) P atoms was fabricated. Within a large gate voltage range only one charge transfer event was observed. Exposed to microwave radiation, this event showed a striking and complex sub-structure. We observed diamond-like features in the differentiated SET signal as a function of gate voltage and microwave frequency (Figure 2a). This data is indicative of microwave induced transitions between single particle levels and constitutes the first direct probe of energy scales in a Si:P few-atom system. In 2005 we continued our studies on ion-implanted phosphorus clusters. Single metallic clusters containing hundreds to thousands of P atoms were fabricated and we were able to control single electron tunnelling in these devices. This work ultimately led to demonstration of a basic cell of a quantum cellular automata (QCA) - see Figure 3. The devices comprised four P-implanted dots configured into two pairs. Electron tunnelling occurs between dots in each individual pair, but electrons cannot tunnel from pair to pair. SETs are used to monitor the number of electrons (m,n) on the two dots in each pair - see Figures 3b,c. To perform a QCA bit-flip, the gates are swept along the arrow eA in Figure 3b, driving an interdot tunnelling event in pair A. This in turn induces a reverse transfer in pair B, which is detected by SET B - see Figure 3d. While QCA architectures are of interest for single electron information processing in their own right, we are interested in these devices because their inter-pair Coulomb coupling provides important information on the charge coupling expected between pairs of Si:P qubits. In an important new initiative in 2005, we developed nanoscale Schottky contacts (Figure 4) that can be used as electron reservoirs to control the electron occupancy of individual P donors. Silicide electrodes are formed by thermal reaction that offers a nearly perfect interface with a well-defined Schottky barrier. Such nano-patterned PtSi electrodes were configured near implanted clusters of 20-600 P atoms, with charge detection via an rf-SET. All devices showed a sequence of charge transfer events that may be attributed to tunnelling between the reservoir and donors, or possibly within the cluster itself. This technology opens a pathway to the measurement of single electron spins on P donors and will be critical for the development of Si:P spin qubits.
Figure 2 (a) For a 4-P-atom device, the differentiated SET signal as a function of Vc and microwave frequency showsa complex pattern, indicative of a complex energy spectrum in this system.
(b) Traces at fixed microwavefrequency show different signal shapes.
Figure 3 (a) SEM image of QCA device. (b) and (c) Hexagonal charging diagrams for cell A and B respectively.
(d) QCA response seen in SET B as cell A interdot tunnelling event occurs.
Figure 4 (a) Schematic of nano-Schottky device with P-atom between PtSi contact and SET island.
(b) SEM image of device layout.
(c) Compensated SET signal from a 20-atom cluster, Sawtooth signature due to sequence of single electron transfers.
Single Cooper pair transistors (SCPT) can be used as highly sensitive charge detectors for measurements of quantum systems. We have developed a method to minimise 'quasiparticle poisoning', an effect in which non-equilibrium quasiparticles tunnel onto the device island, suppressing the supercurrent. We reduce this by using different thickness Al films for the island and the leads of the SCPT, exploiting the fact that the superconducting gap significantly increases as film thickness is reduced. We thus create a barrier for quasiparticles which reduces the poisoning and allows us to observe for the first time a 2e-periodic supercurrent in a radio-frequency single electron transistor - see Figure 5. This has important implications for electrometry as it provides a low-noise, low-dissipation electrometer with advantages for measuring quantum systems. In the presence of microwave irradiation we observe photon assisted tunnelling (PAT) of Cooper pairs across both junctions in the transistor, in good agreement with theory. This is the first time it has been possible to investigate the interplay of PAT events across a two-junction system.
Figure 5 One of the 2e-periodic supercurrent peaks of the single Cooper pair transistor under microwave irradiation..
Silicon-based Si:P Qubits via Scanning Probe Microscopy
Following our success in developing a complete fabrication strategy to pattern dopants in silicon with atomic precision using scanning probe microscopy, the group has recently succeeded in fabricating three key components of the qubit architecture. First we demonstrate that we can form the narrowest wires in silicon that still conduct and exhibit ohmic behaviour. These wires will act as the source-drain leads for electrical transport measurements through quantum dot systems leading to both spin and charge detection. Four-terminal electrical measurements of these wires, measured at 4K, reveal ohmic behaviour with resistances ~ 50 kO for wire widths down to 27 nm. The resistance of these wires is nearly an order of magnitude lower than wires of similar dimensions produced by other technologies. Second, a key aspect of the STM fabrication route is the ability to form well-defined regions of high doping density separated by insulating regions that have no stray dopants or charge traps. To characterise the quality of the barrier between two highly doped regions we have fabricated tunnel junction devices. Figure 6 shows an image of an STM patterned region for one such planar tunnel junction with a gap of 50 nm. Electronic transport measurements of this device showed a non-ohmic behaviour across the tunnel junction with a resistance of ~1 MO. Importantly the junction characteristics are extremely clean with no evidence of oscillatory behaviour due to charge traps or stray dopants.
Figure 6 (a) STM image of a 50 nm tunnel junction device. (b) Differential conductance (black) and I-V characteristics (red) of the tunnel junction at 4K.
Third we have developed a fabrication strategy to realize few atom dot devices, with the ultimate goal of fabricating few and single P atoms between source-drain leads to investigate the control of individual quantum mechanical charge and spin states. Figure 7 highlights how STM lithography has been used to define an island 10nm in diameter situated with a gap of 20nm between highly conducting source and drain leads. For this particular structure the island contains ~100 P atoms, highlighting how STM can be used to determine both the location and number of P atoms in the device. Figure 8 shows electrical results from a device consisting of an 80 nm diameter dot with source-drain leads separated by a gap of ~20nm. By substrate patterning we have demonstrated that we can fabricate the active component of the device on one atomic plane of the silicon substrate STM. Electrical transport measurements at 4K through the device in Figure 8(c) show a highly reproducible blockade region between source-drain voltages of �700 mV. In addition there is a clear peak in the differential conductance, shown in Figure 8(d) corresponding to charge transfer across the island. These results are extremely promising with work underway to reduce the size of the island towards the few electron level, where it is anticipated that discrete quantum levels will be observed.
Figure 7 STM images of a planar dot with source drain leads.
(a) STM lithography of a 10nm dot with 20nm separation.
(b) The same surface after PH3 dosing and annealing showing ~100 P atoms in the dot.
(c) After STM removal of H-resist showing dot integrity is maintained.
Figure 8 Electrical characterisation of 80nm dot device.
(a) Cross section schematic.
(b) STM image of 80nm dot defined between source and drain leads on one atomic terrace of the Si(100) surface.
(c) I-V characteristics through the dot for four different contact configurations at 4K.
(d) Differential conductance across the device, showing large blockade region and resonant tunnelling on and off the island.
Linear Optical Quantum Computing (LOQC)
The Centre's LOQC programs aim to construct the basic building blocks of an optical quantum processor and develop the foundations of a scaleable architecture based on the protocols introduced by Knill, Laflamme and Milburn (KLM). A key requirement for a quantum computer is error encoding and error correction. In the KLM scheme one of the main sources of error is the accidental measurement of a qubit when one of the teleportation steps fails. This year our experimental team at UQ demonstrated high-fidelity encoding against this kind of error - see Physical Review A 71(R), 060303 (2005). A controlled-NOT gate was used to implement parity encoding, where one logical qubit is encoded using two physical qubits. A measurement on either of the physical qubits of the encoded state collapses it to an unencoded qubit, but preserves the superposition. A measurement result "0" returns the original unencoded state. If the measurement result is "1" a bit-flipped version of the unencoded qubit results, but the qubit can be recovered with feed-forward operations.
We encoded a wide variety of input states, by using the to-be-encoded qubit as the target input for the CNOT gate and an equal superposition state as the control. The average fidelity between the output states and the ideal encoded states is 88%. When the decoded states were characterised by quantum state tomography an average fidelity of 96% was obtained.
This parity encoding is a key tool in the scale up strategy for optical circuits. This year our theory program UQ looked at improvements to the original KLM strategy. We showed that by using parity encoding, but re-encoding via the "fusion" technique, we obtain a major reduction in overheads, similar to that achieved for "cluster states".
We also showed how efficient codes can be designed, based on the parity state approach, that are fault tolerant to loss - see Physical Review Letters 95, 100501 (2005). Although loss is present in all the elements, i.e. inefficient detectors, sources and optical memories, the coding prevents the loss from propagating and destroying the computation. The threshold value for the greatest amount of loss tolerable (in all elements) was found to be �17%; a level much higher than those previously obtained and thought to be optimal.
For scale-up of optical qubit gates and optimal performance fidelity it is desirable to find the simplest possible gate realisations. Entangling gates are particularly important
- they lie at the heart of QC protocols, and are used in Bell state analysis, as required for quantum teleportation. This year our experimental team at UQ have demonstrated a version of the maximally-entangling CNOT
- see Physical Review Letters 95, 210504 (2005), that is significantly simpler than our previous demonstration published in Nature 426, 264 (2003). This simplified gate (the controlled-z or CZ gate, Figure 9) does not require interferometric stability and requires only one optical mode-matching condition. This will be important for production of circuits in large numbers or in micro-or integrated-optics realisations.
Figure 9 (a) Interferometric CZ gate. Operation is enabled by transforming each qubit from polarisation to spatial encoding, and back again, requiring high interferometric stability and spatio-temporal mode-matching.
(b) Partially-polarising beam splitter (PPBS) gate. The qubits can remain polarisation-encoded, since the vertically-polarised modes are completely reflected by the first PPBS, and do not interact.
The new CZ gate is the simplest entangling (or dis-entangling) linear optics gate yet realized, requiring only three partially-polarising beam splitters, two half-wave plates, no classical interferometers, and no ancilla photons. Quantum process tomography was used to completely characterize the new gate � see Figure 10. After compensation for additional single-qubit rotations, the average gate fidelity for a pulsed photon source (important for scaleability) was 89.3�0.1%. The operation is thus very high-fidelity, and is believed to be limited primarily by the quality of the non-classical interference. This simpleentangling gate is promising for micro-optics or guided optics implementations, where extremely good non-classical interference is realisable.
Figure 10 Quantum process tomography of the CZ gate. Real components of the c matrix for the:
(a) ideal and (b) pulsed CZ gate. The imaginary components of the experimental matrices are not shown.
Typically LOQC models assume that all input photons are completely indistinguishable. However photons have a spatio-temporal �structure� that can introduce a degree of distinguishability between them and as a result can compromise LOQC algorithms. This year we theoretically investigated which spatio-temporal structure is most resilient to small �distinguishability producing� imperfections (i.e. mode-mismatch) in the optical circuits. We found that Gaussian distributed photons with large bandwidth were optimal. The result is general and holds for arbitrary linear optical circuits � see Physical Review A 72, 052332 (2005).
Our experimental team at the Australian Defence Force Academy (Canberra) is focused on the development of LOQC techniques in the frequency basis, whereby a qubit is encoded across a pair of frequency modes. An essential requirement for this research is the ability to probe the number of photons at optical sideband frequencies. For sufficiently small photon flux the individual photons might be resolved and counted using a number of standard techniques such as avalanche photodiodes, photomultipliers and superconducting bolometers. In the absence of sharp spectral filtering, however, such detection techniques fail to provide the required frequency selectivity.
In 2005 we illustrated the use of homodyne detection whereby an optical mode may be probed by first interfering it with a strong reference field � a local oscillator � before detecting its intensity. The intensity detection is performed by linear photodiodes that cannot resolve individual photons but instead allow measurement of the continuous spectrum of the signals� conjugate amplitude quadratures. In this case, frequency resolution is achieved via electronic (as opposed to optical) filtering, allowing for comparatively superior frequency domain selectivity. We have shown that the mean number of photons at a specific sideband frequency may be inferred from such a measurement � see Physical Review A 73, 033808(2006). Implementation of the detector is experimentally straightforward and hence easy to incorporate into subsequent experiments of frequency-basis LOQC.
Our data also permits a direct comparison between semi-classical and quantum mechanical optical vacuum noise models. Our results quantitatively support the quantum mechanical description of the vacuum over the semiclassical stochastic electrodynamic model as determined by comparison of the weighted mean square errors between the predicted and observed data. Given the absence of experimental free parameters, the quantum mechanical noise model permits close agreement between inferred and actual values of experimental photon flux (see Figure 11). To our knowledge this is the first time such a direct comparison has been made.
Figure 11 Comparison between single photon detector and homodyne measurements over four orders
of magnitude of photon flux. The green line indicates the ideal 1:1 relationship.
Figure 12 Protocol to deterministically entangle two atom-cavity qubits in a positive or negative Bell state
Our Measurement & Control program aims to understand better how the measurement and control of devices operating in the quantum regime differs from devices operating classically. This will lead to more efficient initialisation, operation and read-out of qubits. In 2005 we theoretically studied the use of a single-electron transistor (SET) operating in the strongly coupled mode. Unlike the standard weakly-coupled senario, we find a mathematically well-posed description whose output can give useful information about the measured qubit. We also used feedback technologies to study �single-rail� Linear Optical Quantum Computation (LOQC), which had previously been considered to be too inefficient in resource use. It was found to be as efficient as more typical �dual rail� encoding systems.
Our Device Modelling program aims to develop realistic and comprehensive theoretical descriptions of Si:P charge and spin qubits. It covers a wide range of activities ranging from fundamental condensed matter physics through to new paradigms of QC. In 2005 we developed a new investigative technique to characterise the operation of a single or two-qubit device Hamiltonian in the presence of noise. The testing of quantum systems is fast becoming a daunting task which must be tackled and this work has yielded a novel and useful approach to this problem. We also extended previous results on adiabatic transport through an unexcited bus, to theoretically propose a complete QC architecture. This architecture allows, via the unexcited bus, the preparation of multi-qubit entangled states, including GHZ and cluster states as well as full-blown QC. A natural physical implementation is via the optical coupling of spatially separated atomic qubits (either in solids or traps).
Our Quantum Information Theory program aims to understand general aspects of quantum information, with a particular emphasis on condensed matter systems. In 2005 we developed new protocols for transmitting quantum information along a qubit chain using measurement and teleportation. This could be useful for Si:P qubits provided the single qubit readout is highly efficient. We also examined how quantum entanglement could be dynamically engineered using feedback. A novel manner of performing a continuous quantum error correction was discovered which requires no active intervention. As a first step towards applying this to circuit quantum electrodynamics (QED), a method was found, using feedback, to generate entanglement using a single electron transistor.
Our Quantum Algorithms program aims to develop new, inherently quantum applications for quantum processors. Recent developments include the discovery of a quantum algorithm which can efficiently deduce an unknown rational function given partial data, and a construction for a new type of optimally-efficient quantum estimator, known as symmetrically complete positive operator valued measures (SC-POVMS). We also discovered a new QC architecture that primarily uses �global operations�, for qubit transport and computing. Use of global operations should reduce the need for technically challenging local addressing. We have also discovered efficient algorithms for the quantum simulation of sparse Hamiltonians, with a cost nearly linear in evolution time. The use of a quantum computer as a generic tool with which to simulate other quantum systems is generally considered to be one of the primary uses for a small-medium sized processor.
Figure 13 Depiction of the entanglement generating capability of two-qubit gates.
Figure 14 Schematic of a globally addressed quantum wire.