Physics (Internal)

Finite-Size Scaling in Quantum Annealing with Decoherence

This event is part of the PhD Final Oral Exams.

Examining Committee: Anders Sandvik, Anatoli Polkovnikov, Shyam Erramilli, Alex Sushkov, David Campbell

Abstract:

Quantum annealing represents an essential milestone towards the goal of universal quantum computing. While quantum annealing likely may not be as powerful as universal quantum computing, it may be better than classical algorithms. One important quantity that is useful for predicting the scaling of a quantum annealing calculation is the scaling of the minimum gap with problem size or the dynamic exponent. We show how one can use imaginary time dynamics combined with finite-size scaling to extract the dynamic exponent. Since one can calculate imaginary time evolution using methods like quantum Monte Carlo or matrix- and tensor-product states, one can calculate the dynamic exponent accurately.

In physical realizations of quantum annealing, there are still questions as to the role of quantum fluctuations in the operation of a device given the short coherence times of the individual qubits. These questions have consistently posed a challenge to theoretical physics, making it challenging to interpret experiments. We propose using dynamic finite-size scaling to understand the nature of the fluctuations in a device. By performing a systematic study comparing simulated classical and quantum annealing of the 2D Ising model, we find a difference in the scaling exponents between the two types of fluctuations. We then study the behavior when performing quantum annealing with decoherence observed in a physical device as a small amount of noise in the transverse-field of each qubit. We compare the model to a system of manufactured qubits produced by D-wave Systems. We extend the dynamic finite-size scaling to capture the competition between quantum fluctuations of the transverse-field and bit-flip errors from the noise. We argue that the weak noise model is more consistent with the device. These results imply that at the very least, the diagonal probabilities in the density matrix of the system are more robust against noise compared to an isolated qubit. Using this finite-size scaling, one can diagnose sources of noise in the system. Hopefully, in the near future, these devices will not only be realizing coherent quantum annealing but will likely be useful as another example of synthetic quantum matter.