Global control, perpetual coupling and the like Easing the experimental burden Simon Benjamin, Oxford. EPSRC. DTI, Royal Soc.

Overview Motivation for looking at alternative architectures. Global Control of a Quantum Computer: Leaving interactions “always on”: Combining ideas Basic idea, Two Minimal Examples, Issues... Basic idea, different approaches, Issues... - All the benefits, all the issues.

An Orthodox Architecture All manipulations (inc. read, reset) are localised to specific qubits. Interactions are switched ‘on’ and ‘off’. (Kane, Nature ‘98) Great if you can build it!

The difficulty of implementing local control elements.....or in molecular scale structures, physical impossibility! Problem of decoherence caused by local electrodes, surface proximity. Global Control: Motivation

Ability to perform QC strictly under the constraint of sending ‘control signals’ to the entire structure. Way to achieve this depends on the physical model, especially the dimension of the system. Here I will discuss only one-dimensional systems (not interesting for classical comp.) What is Global Control?

Quick glimpse of 2D Case

First: ABCABC + asymmetric Ising interaction. Seth Lloyd, Science 261, 1569 (1993). ABABAB + symmetric Ising interaction. S. C. Benjamin, PRA 61, (2000). ABABAB + collectively switched Heisenberg. S. C. Benjamin, PRL 88, (2002). Quantum computation in optical lattices via global laser addressing Alastair Kay and Jiannis K. Pachos, quant- ph/ Some 1D GC References

Example: Heisenberg Chain One dimensional ABAB chain with non- diagonal switchable interaction. We’ll consider a system a two of minimal models: systems with just enough complexity to support universal QC.

Encoding Universality Essential idea is to introduce a “software read/write head” called the Control Unit (CU). One qubit gate by this method:

One qubit gate process: Schematics

Two-qubit gate process:

Example 2: Ising Chain Hamiltonian now contains constant interaction: Electrodes don’t constrain geometry! Simplest structure is ABAB..

However, we need to work hard to get enough control in such a minimal system... From symmetry, we see need for multi-spin encoding In fact we need 4 spins per qubit, and a gap of 4 => 8 in total.

Error correction and FT Adel Bririd, SCB, Alastair Kay, preprint quant- ph/

Size cost: multiple physical (pseudo-) spins required for each logical qubit. Factor varies with the specific scheme, 1:2 to 1:8. [Zeno] Time Cost: multiple global signals to implement single one-qubit gate (not too bad). Parallelism Cost: a device which is inherently highly parallel has been made effectively serial. - A fairly high degree of parallelism can be recovered, at and additional cost (e.g. x2 size). QC is not without cost!

But.... What if there is an “always-on” interaction that is not diagonal, and we can’t use any direct switching? Can we keep things under control? How?

A geometric solution X. Zhou et al., Phys. Rev. Lett. 89, (2002). Qubits become isolated: interaction free subspace. Switching during preparation, multi-step gates.

A Zeeman tuning solution S. C. Benjamin & S. Bose, PRL 90, (2003). S. C. Benjamin & S. Bose, PRA -current- (2004).

Or we can do almost everything via Zeeman tuning on one ‘type’ in an ABCABC... chain. cf DiVincenzo et al pure Heisenberg switching model (Nature 2000 etc)

Procedure for 2-qubit gate, now a phase accumulator: What if our fixed interaction strengths are irregular? -Still OK, can numerically search for the right tuning parameters. See Chiu Fan Lee, Neil F. Johnson, quant-ph ‘04.

Also works in 2 and 3 D, better ratio. ( S. C. Benjamin, NJP 2004)

Avoid Zeeman tuning? Good candidate for replacing the static tuning with dynamical cycling, since we can attack the barrier, not the qubits. S. C. Benjamin, B. Lovett, J. Reina, quant-ph/

Good performance even with strong decay. Works with pulsed laser too.

Removes the need for, eg, gating electrodes. Several different physical models have now been investigated. Should work well for few qubit QC. For large scale QC, questions remain regarding QEC (leakage, correlated errors). Summary for “Always On” Interactions

Combine all these ideas? Rather straightforward to combine the concepts of global control and always-on interactions: But then all the unknowns are combined too!

The End Visit