Program: Measurement and Control for Quantum Computing

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Researchers in the Centre for Quantum Computer Technology (and related researchers) at Griffith University in 2003.

From left to right, David Pegg (Professor), Jay Gambetta (Ph.D.), Howard Wiseman (Assoc. Professor, Program Manager), Damian Pope (post-doc; not a member), Kurt Jacobs (post-doc), Josh Combes (Honours), Laura Thomsen (Ph.D), Daniel Atkins (Ph.D.), Neil Oxtoby (Ph.D),  Kenny Pregnell (Ph.D.), and Josh Garretson (Honours; not a member).


The Centre for Quantum Computer Technology was established as an Australian Research Council Centres of Excellence in 2003. It has research programs at six Australian Universities: New South Wales, Melbourne, Queensland, Macquarie, Griffith, and Sydney. Its primary aim is to build a prototype Silicon-based quantum computer (to be done at the University of New South Wales), but there are several other research directions, experimental and theoretical. The Griffith Program is Measurement and Control for Quantum Computing. It supports wide-ranging theoretical research in quantum measurement, control and information. For more information on the program, see below, or see the Program Page (under construction) on the CQCT website.

The Griffith Program: Measurement and Control for Quantum Computing.

1. Quantum Measurement Theory for Read-Out Devices

A crucial part of quantum computing is read-out. Schemes for reading out the state of a solid-state QC include a single-electron transistor, a quantum point contact, and a micromechanical cantilever. We plan both to develop more sophisticated theories for such schemes, and to investigate other schemes. The theory of quantum trajectories, as developed in quantum optics, has proven very useful for understanding continuous measurement in the solid state context. However, as traditionally formulated it is a highly idealized theory, assuming that individual quantum events (such as electrons tunnelling through a barrier) can be observed. In practice, the electronic noise and impedance of the external circuit will mask this. A generalization of the quantum trajectory approach to describe the effect of such read-out imperfections on the conditioned system state has recently been developed for photon detectors (Warszawski, Wiseman and Mabuchi, 2002). This technique is now being applied in the solid-state context.
 

2. Quantum Feedback Control

Applications for quantum feedback in quantum computers include quantum error correction for detected errors, testing read-out devices, state engineering, and measurement engineering. State engineering requires a general understanding of quantum control, which will be sought. Measurement engineering by feedback means adaptive measurements, which could be useful in linear optics quantum computing.
 

3. Quantum Information - Measurement Interface

Dissipation is the transfer of energy from the system to the environment. It is now well understood that what is more relevant for quantum computers is decoherence, the transfer of information from the system to the environment. This information is quantum information, but it can be turned into classical information by measuring the environment. This new perspective on quantum measurement theory is a fruitful field for investigation.
 

4. Quantum Computing - Measurement Interface

This part of the program will seek new schemes for quantum measurement as they may be useful for quantum computing. On the flip-side, quantum algorithms should also suggest new measurement schemes.

2003 Annual Report on the Research Program Measurement and Control in Quantum Computing.

Program Manager
A/Prof Howard Wiseman, GU

Measurement and Control Researchers
Students: Mr Neil Oxtoby (PhD), Mr Kenneth Pregnell (PhD), Ms Laura Thomsen (PhD), Mr Daniel Atkins (PhD), Mr Joshua Combes (Honours)
Staff: Prof David Pegg, Dr Kurt Jacobs, Mr Jay Gambetta, Dr He-Bi Sun (UQ)

Collaborating Centre Researchers
University of Queensland: Prof Gerard Milburn, A/Prof Tim Ralph

Other Collaborators
Macquarie University / University of Queensland: Dr Stephen Bartlett
University of Hertfordshire: Dr John Vaccaro
California Institute of Technology: A/Prof Hideo Mabuchi, Ms Charlene Ahn, Mr Asa Hopkins
Los Alamos National Laboratory: Dr Salman Habib, Dr Tanmoy Bhattacharya, Dr Daniel Steck
University of Maryland: Dr Keith Schwab

Program Description
The aim of this program is to understand the measurement and control of devices operating on a quantum scale and to apply this understanding to quantum information processing. The program has four sub-programs: Quantum Measurement Theory for Read-Out Devices; Quantum Feedback Control; Quantum Information -- Measurement Interface; Quantum Computing -- Measurement Interface.

1. Quantum Measurement Theory for Read-Out Devices

mcfqcp_fig1The aim of this sub-program is to develop methods for determining the state of a qubit (or register) conditioned on the results of monitoring the qubit using a realistic read-out device. That is, for example, the measurement record is filtered and has noise added by the external circuit containing the detector that couples to the qubit [Oxtoby et al, J. Phys. C 15, 8055-64 (2003)]. The main outcome for this year [Oxtoby et al, submitted] is that we have formulated a rigorous method for deriving a quantum trajectory (that is, the stochastic evolution for the conditioned system state) for a large class of solid-state detectors in a simplified external circuit, as shown in Figure 1. We have also investigated realistic detection in a cavity QED context, to see its effect on estimating an unknown parameter (the position of the atom) from the detection record [Warszawski et al, submitted]. This is relevant for quantum computing in that domain.

Figure 1. Circuit diagram for a "realistic" read-out device. The read-out on which the state of the CQD (coupled quantum dots) qubit is conditioned is the current through the Ammeter A. This represents the output of a Current Amplifier which adds noise as it amplifies. The bias voltage also contains noise. The Detector could be a DC SET (Single Electron Transistor) or a QPC (Quantum Point Contact). 


2. Quantum Feedback Controlmcfqcp_fig2

The aim of this sub-program is to investigate feedback control of quantum systems useful for quantum information processing, such as error correction of quantum registers, or cooling a system down to its lowest two quantum states. This year we have published a paper establishing a protocol to protect a quantum register against detected errors using only a single additional qubit [Ahn et al, Physical Review A 67, 052310 (2003)]. Work is underway to generalize this for more than one type of detected error per qubit.  In addition, we have considered motional cooling to close to the ground state in both a cavity QED system [Steck et al, submitted] and a nanomechanical system (see Figure 2) [Hopkins et al, SPIE 5276 (2003)].

Figure 2. Diagram for the cooling of a nanomechanical resonator close to its ground state using feedback based on continuous monitoring by an SET. This device is currently being built at the Laboratory for Physical Sciences, University of Maryland.

3. Quantum Information -- Measurement Interface

mcfqcp_fig3The aim of this sub-program is to study questions at the interface of quantum information and quantum measurement. The main outcome for this year has been (i) to generalize the concept of super-selection rules (SSRs) to describe a large class of restrictions on measurements and other quantum operations and (ii) to calculate the entanglement two parties can distill from a state they share, given a restriction in this class. This work [Wiseman and Vaccaro, Physical Review Letters 91, 097902 (2003); Bartlett and Wiseman, Physical Review Letters 91, 097903 (2003)] is significant for quantum information processing (QIP) in systems subject to SSRs, such as Bose-Einstein condensation, or NMR ensemble quantum computing.  Another outcome has been to derive fundamental inequalities relating to information extraction and the purification of conditioned states in measurements on a quantum system drawn randomly from an ensemble [Jacobs, Physical Review A 68, 054302 (2003)]. Thirdly, we have examined the question of the validity of optical continuous variable quantum teleportation, and concluded that a laser should be regarded as a clock, not a quantum channel [Wiseman, J. Opt. B (to be published)]. Finally, we have investigated the preparation of spin-squeezed states for the purposes of interferometric measurement of phase shifts [Combes et al, unpublished]. We find that the maximally spin squeezed state (shown in Figure 3) is not the optimal state for this purpose, and we identify a simple scheme to produce the optimal state.


Figure 3. Wigner function for the maximally spin squeezed state of an ensemble of 20 atoms, plotted as a function of polar co-ordinates for the spin direction. Note the "ripples" (positive and negative fluctuations) in the tails of the distribution. These make this state sub-optimal for single-shot measurement of the shift in the phase f (which could be produced by a magnetic field, for example)


4. Quantum Information -- Computing Interfacemcfqcp_fig4

The aim of this sub-program is to study questions at the interface of quantum information and quantum computing. The main outcome for this year has been the discovery of a general scheme to retrodict quantum states in optics using only coherent states and beam splitters [Pregnell and Pegg, J. Mod. Opt. (to be published)]. That is, it is possible to engineer an optical device such that one particular measurement result corresponds to a given (arbitrary) element in a positive operator measure (POM).  We have also discovered a simpler scheme for the specific problem where the POM is that arising from measurement of the Pegg-Barnett phase operator [Pregnell and Pegg, Physical Review A 67, 063814 (2003)]. This scheme (shown in Figure 4) requires a binomial input state as a reference field, but we show that this can be approximated by a squeezed state for low photon numbers.

Figure 4. Eight-port interferometer for measuring the canonical phase distribution of weak fields. The field to be measured is in the input port labeled In 0, the reference field in state is in input port In 1, and vacuum state fields are in In 2 and In 3. A photodetector is in each output port. The rectangles are phase shifters.


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