Abstract
Many quantum computational tasks have inherent symmetries, suggesting a path to enhancing their efficiency and performance. Exploiting this observation, we propose representation matching, a generic probabilistic protocol for reducing the cost of quantum computation in a quantum network. We show that the representation matching protocol is capable of reducing the communication or memory cost to almost minimum in various tasks, including remote execution of unitary gate arrays, permutation gates and unitary conjugation, as well as the storage and retrieval of unitary gates.
Highlights
The past few years have witnessed tremendous progress in quantum computing and quantum communication
We prove a general lower bound on the communication cost of such a setting for remote quantum computing
We prove a lower bound on the communication cost of remote quantum computing, where one party performs a computation Utgarget for a state held by another faraway party
Summary
The past few years have witnessed tremendous progress in quantum computing and quantum communication. In discussing the classification of quantum complexity classes, e.g., the nondeterministic quantum polynomial-time complexity class, protocols with a small success probability play an important role In a network setting, the remote parties can communicate the desired computation using probabilistic protocols such as gate teleportation [15,16]. It may still be beneficial to employ a probabilistic protocol even if its expected communication cost, i.e., the expected amount of communication required until the protocol succeeds, is higher than that of deterministic protocols Another less explored observation is that many quantum computational tasks are associated with inherent symmetry. We prove a general lower bound on the communication cost of such a setting for remote quantum computing. IX, we conclude the paper with some discussions on future directions for research
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