### Google Quantum A.I. Lab Team

Shared publicly -**Computational multiqubit tunnelling in programmable quantum annealers**

The Google Quantum A.I. Lab Team, together with external collaborators, has recently published a paper (http://www.nature.com/ncomms/2016/160107/ncomms10327/abs/ncomms10327.html) in Nature Communications which studies computational multiqubit tunnelling in programmable quantum annealers. Quantum annealing (QA) is an optimization technique inspired by classical simulated annealing (SA). SA is a global optimization algorithm that mimics classical thermal activation at a high enough initial algorithmic “temperature” to escape false local minima of an optimization function. As the temperature is lowered to distinguish between local minima with small energy differences, SA can freeze. The idea behind QA is to use quantum tunneling to escape local minima even at low temperature. Quantum tunnelling is a phenomenon in which a quantum state traverses energy barriers higher than the energy of the state itself

Despite substantial academic and industrial interest in QA, computational multiqubit tunnelling had not yet been observed, and a theory of co-tunnelling under realistic noise models (including low-frequency noise) was lacking. In this paper we introduce a 16-qubit probe for tunnelling, a computational primitive where classical paths are trapped in a false minimum. To distinguish between tunnelling and thermal activation, we study the thermal dependence of the probability of success for the computational primitive. Thermal activation shows an increasing probability of success with increasing temperature, as expected. Multiqubit tunnelling, on the other hand, shows a decreasing probability of success with increasing temperature, both in theory and experiment.

We performed our experiments to observe computational multiqubit tunneling in a D-Wave Two quantum annealer. On the one hand, we obtain a good agreement with a standard quantum open system master equation (Redfield) and the new theory introduced in this paper (multiqubit NIBA). On the other hand, we observe the opposite dependence of temperature if we use a related numerical model, Spin Vector Monte Carlo (SVMC) (http://arxiv.org/abs/1401.7087), which aims to mimic quantum annealing but does not include entanglement.

The theory of multiqubit tunneling introduced in our paper (multiqubit NIBA) explains the effect of low frequency noise at the multiqubit freezing point. As the annealing progresses, the physical environment of the qubits, and the low frequency noise in particular, induces transitions in the physical system. These transitions tend to thermalize the system at the low physical temperature. At some point, the system freezes. If it did not, a quantum annealer would solve most optimization problems, simply because the energy of sub-optimal solutions is much higher than the very low physical temperature. Our theory shows that in the multiqubit setting this freezing is related to an energy shift introduced by the low frequency noise, which is linear in the number of qubits.

We applied the insights gained in this work to construct proof-of-principle optimization problems and programmed these into the D-Wave 2X quantum annealer (http://www.dwavesys.com/press-releases/d-wave-systems-announces-general-availability-1000-qubit-d-wave-2x-quantum-computer) that Google operates jointly with NASA. The problems were designed to demonstrate that quantum annealing can offer runtime advantages for hard optimization problems characterized by rugged energy landscapes. We found that for problem instances involving nearly 1000 binary variables, QA significantly outperforms SA: it is more than 10^8 times faster than SA running on a single core. You can see this benchmark in a more recent paper (http://arxiv.org/abs/1512.02206) and a related blogpost (http://googleresearch.blogspot.com/2015/12/when-can-quantum-annealing-win.html).

Sergio Boixo

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2 comments

At Milan I propose changing name POST EXPO to

QUANTUM MI LABS.I invite all companies to start Quantum MI LABS,also in Fashion,Design and Quantum Energy.But my Govern love fossil energy,

QUANTUM MI LABS.I invite all companies to start Quantum MI LABS,also in Fashion,Design and Quantum Energy.But my Govern love fossil energy,

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