Implementing quantum walks with a single qubit
- URL: http://arxiv.org/abs/2206.03642v1
- Date: Wed, 8 Jun 2022 02:04:44 GMT
- Title: Implementing quantum walks with a single qubit
- Authors: Qi-Ping Su, Shi-Chao Wang, Yan Chi, Yong-Nan Sun, Li Yu, Zhe Sun,
Franco Nori and Chui-Ping Yang
- Abstract summary: We propose a novel method to implement discrete-time quantum walks (DTQWs) using only a single qubit.
We experimentally implement one-particle and two-particle DTQWs with seven steps using single photons.
- Score: 7.136104608099681
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum walks have wide applications in quantum information, such as
universal quantum computation, so it is important to explore properties of
quantum walks thoroughly. We propose a novel method to implement discrete-time
quantum walks (DTQWs) using only a single qubit, in which both coin and walker
are encoded in the two-dimensional state space of a single qubit, operations
are realized using single-qubit gates only, and high-dimensional final states
of DTQWs can be obtained naturally. With this "one-qubit" approach, DTQW
experiments can be realized much more easily, compared with previous methods,
in most quantum systems and all properties based on quantum states of DTQWs
(such as quantum correlation and coherence) can be investigated. By this
approach, we experimentally implement one-particle and two-particle DTQWs with
seven steps using single photons. Furthermore, we systematically investigate
quantum correlations and coherence (based on the full state of the coin and
walker) of the DTQW systems with different initial states of the coin, which
have not been obtained and studied in DTQW experiments. As an application, we
also study the assisted distillation of quantum coherence using the full state
of the two-particle DTQW from the experiment. The maximal increase in
distillable coherence for high-dimensional mixed states is investigated for the
first time by obtaining its upper and lower bounds. Our work opens a new door
to implement DTQW experiments and to better explore properties of quantum
walks.
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