Adiabatic evolution under quantum control

Mária Kieferová, Nathan Wiebe

A major challenge facing adiabatic quantum computing is that algorithm design and error correction can be difficult for adiabatic quantum computing. Recent work has considered addressing his challenge by using coherently controlled adiabatic evolutions in the place of classically controlled evolution. An important question remains: what is the relative power of controlled adiabatic evolution to traditional adiabatic evolutions? We address this by showing that coherent control and measurement provides a way to average different adiabatic evolutions in ways that cause their diabatic errors to cancel, allowing for adiabatic evolutions to combine the best characteristics of existing adiabatic optimizations strategies that are mutually exclusive in conventional adiabatic QIP. This result shows that coherent control and measurement can provide advantages for adiabatic state preparation. We also provide upper bounds on the complexity of simulating such evolutions on a circuit based quantum computer and provide sufficiency conditions for the equivalence of controlled adiabatic evolutions to adiabatic quantum computing.

Alain Joye, Charles‐Edouard Pfister

Jie Liu, Sheng-Chang Li, Libin Fu +1 more

Mária Kieferová, Nathan Wiebe

We provide a new approach to adiabatic state preparation that uses coherent control and measurement to average different adiabatic evolutions in ways that cause their diabatic errors to cancel, allowing highly accurate state preparations using less time than conventional approaches. We show that this new model for adiabatic state preparation is polynomially equivalent to conventional adiabatic quantum computation by providing upper bounds on the cost of simulating such evolutions on a circuit-based quantum computer. Finally, we show that this approach is robust to small errors in the quantum control register and that the system remains protected against noise on the adiabatic register by the spectral gap.

Jie Liu, Sheng-Chang Li, Libin Fu +1 more

Abdelrahman A. H. Abdelrahim, Gharib S. Mahmoud, Sherzod Turaev +1 more

Quantum gates are the basic building blocks in the quantum circuits model. These gates can be implemented using adiabatic or non adiabatic processes. Adiabatic models can be controlled using auxiliary qubits, whereas non adiabatic models can be simplified by using one single-shot implementation. In this paper, the controlled adiabatic evolutions is combined with the single-shot implementation to obtain quantum gates with controlled non adiabatic evolutions. This is an important improvement which can speed the implementation of quantum gates and reduce the errors due to the long run in the adiabatic model. The robustness of our scheme to different types of errors is also investigated.