Optimally combining dynamical decoupling and quantum error correction

Danny Lidar has said that he does not believe D-Wave Adiabatic quantum computer approach is scalable without error correction. He believes that the incorporation of error correction is a necessary condition in order to ever achieve a speedup with D-Wave’s machines. He does not believe D-Wave’s machines are any different from other types of quantum information processing in this regard. He hopes that in the future Dwave’s designs will allow more flexibility in the incorporation of error correction.

Here is a paper by Danny from this year on quantum error correction.

Journal of Scientific Reports – Optimally combining dynamical decoupling and quantum error correction by Danny Lidar and Gerardo A. Paz-Silva

ABSTRACT – Quantum control and fault-tolerant quantum computing (FTQC) are two of the cornerstones on which the hope of realizing a large-scale quantum computer is pinned, yet only preliminary steps have been taken towards formalizing the interplay between them. Here we explore this interplay using the powerful strategy of dynamical decoupling (DD), and show how it can be seamlessly and optimally integrated with FTQC. To this end we show how to find the optimal decoupling generator set (DGS) for various subspaces relevant to FTQC, and how to simultaneously decouple them. We focus on stabilizer codes, which represent the largest contribution to the size of the DGS, showing that the intuitive choice comprising the stabilizers and logical operators of the code is in fact optimal, i.e., minimizes a natural cost function associated with the length of DD sequences. Our work brings hybrid DD-FTQC schemes, and their potentially considerable advantages, closer to realization.

The nemesis of quantum information processing is decoherence, the outcome of the inevitable interaction of a quantum system with its environment, or bath. Several methods exist that are capable of mitigating this undesired effect. Of particular interest to us here are quantum error correction (QEC) and dynamical decoupling (DD). QEC is a closed-loop control scheme which encodes information and flushes entropy from the system via a continual supply of fresh ancilla qubits, which carry off error syndromes. DD is an open-loop control scheme that reduces the rate of entropy growth by means of pulses applied to the system, which stroboscopically decouple it from the environment. QEC and DD have complementary strengths and weaknesses. QEC is relatively resource-heavy, but can be extended into a fully fault-tolerant scheme, complete with an accuracy threshold theorem. DD demands significantly more modest resources, can theoretically achieve arbitrarily high decoherence suppression but cannot by itself be made fully fault-tolerant

Quantum Search Engine Ranking Paper

Adiabatic quantum algorithm for search engine ranking (Physical Review Letters)

We propose an adiabatic quantum algorithm for generating a quantum pure state encoding of the PageRank vector, the most widely used tool in ranking the relative importance of internet pages. We present extensive numerical simulations which provide evidence that this algorithm can prepare the quantum PageRank state in a time which, on average, scales polylogarithmically in the number of web pages. We argue that the main topological feature of the underlying web graph allowing for such a scaling is the out-degree distribution. The top-ranked log(n) entries of the quantum PageRank state can then be estimated with a polynomial quantum speed-up. Moreover, the quantum PageRank state can be used in “q-sampling” protocols for testing properties of distributions, which require exponentially fewer measurements than all classical schemes designed for the same task. This can be used to decide whether to run a classical update of the PageRank.

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