Quantum Information

Raussendorf introduced a powerful model of fault tolerant measurement based quantum computation, which can be understood as a layering (or “foliation”) of a multiplicity of Kitaev’s toric code.  I will discuss our generalisation of Raussendorf’s construction to an arbitrary CSS code.  We call this a Foliated Quantum Code.  Decoding this foliated construction is not necessarily straightforward, so I will discuss an example in which we foliate a family of finite-rate quantum turbo codes, and present the results of numerical simulations of the decoder performance.

If I have time, I will discuss some ongoing work (with Gavin Brennan) on relational time applied to topological quantum field theories, in particular, how anyonic systems with essentially trivial dynamics can still exhibit correlations that track “time".

In this talk I will introduce recent research into quantum clocks of finite dimension, with the focus on their accuracy, as determined by their dimension, coherence, and power consumption.

I will present arguments to bound the synchronization time of any quantum clock as a function of its dimension. In addition, quantum coherence appears to be necessary to saturate these bounds, as the synchronization time of incoherent clocks is seen to have a worse bound. In addition, I will review simple proposals for autonomous clocks built out of thermal machines, and demonstrate that the power consumption of thermal clocks determines the limit of their accuracy. Finally, I will introduce an example of a finite quantum clock that is able to control any quantum operation up to a calculable accuracy, and discuss whether it represents a best case scenario for quantum clocks.

We give a new theoretical solution to a leading-edge experimental challenge, namely to the verification of quantum computations in the regime of high computational complexity. Our results are given in the language of quantum interactive proof systems. Specifically, we show that any language in BQP has a quantum interactive proof system with a polynomial-time classical verifier (who can also prepare random single-qubit pure states), and a quantum polynomial-time prover. Here, soundness is unconditional---i.e it holds even for computationally unbounded provers. Compared to prior work achieving similar results, our technique does not require the encoding of the input or of the computation; instead, we rely on encryption of the input (together with a method to perform computations on encrypted inputs), and show that the random choice between three types of input (defining a "computational run", versus two types of "test runs") suffice. As a proof technique, we use a reduction to an entanglement-based protocol; this enables a relatively simple analysis for a situation that has previously remained ambiguous in the literature.