Universal Quantum Computation

Richard L. Amoroso

Zhu Cao

Universal quantum computation is usually associated with interaction among two-level quantum subsystems, as this interaction is commonly viewed as a necessity to achieve universal quantum computation. In this work we show that, contrary to this intuition, universal quantum computation can be achieved without interaction among initially independent two-level quantum subsystems. We call it counterfactual universal quantum computation. As special cases, we show how to achieve counterfactual communication of quantum states, counterfactual quantum swapping, and counterfactual quantum erasure codes. To ease practical implementation, we analyze counterfactual universal quantum computation with realistic devices, including the effects of finite execution time, photon loss, and atom missing. Besides the theoretical interest of illustrating the mysterious and counterintuitive nature of quantum physics, our work has practical applications to color imaging of ancient arts, upon which light is forbidden to shine.

Michel Le Bellac

Jiawei Ji

Quantum circuits based only on matchgates are able to perform non-trivial (but not universal) quantum algorithms. Because matchgates can be mapped to non-interacting fermions, these circuits can be efficiently simulated on a classical computer. One can perform universal quantum computation by adding any non-matchgate parity-preserving gate, implying that interacting fermions are natural candidates for universal quantum computation. Most work to date has focused on Majorana fermions, which are difficult to realize and manipulate in the laboratory, despite the advantage of topologically protecting quantum information. We instead show that universal quantum computation can be implemented using interacting spinless (spin-polarized) fermions and further propose a scheme for achieving universal quantum computation with the Hubbard model, which may be realized in the laboratory based on current experimental techniques.

Y. Yamamoto, Fumiko Yamaguchi

Xiaoqin Gao, Zhengwei Liu

We use one photon to simulate an n-qubit quantum system for the first time. We propose a new scheme to realize universal quantum computation in polynomial time O(n^5). A generating set of gates can be realized with high accuracy in the lab. We conclude that photonic quantum computation is one of the promising approaches to universal quantum computation.