Universal super-replication of unitary gates

TL;DR

This paper demonstrates that generic sequences of unitary gates can be deterministically replicated at nearly quadratic rates with minimal error, contrasting the no-cloning theorem for quantum states, and introduces efficient gate compression methods.

Contribution

It introduces a universal method for deterministic super-replication of unitary gates and a protocol for exponential compression of unknown gates, expanding quantum information processing capabilities.

Findings

Deterministic super-replication of unitary gates at nearly quadratic rates.

Exponential reduction in quantum communication for remote gate implementation.

Replication error vanishes on most inputs, with only exponentially small exceptions.

Abstract

Quantum states obey an asymptotic no-cloning theorem, stating that no deterministic machine can reliably replicate generic sequences of identically prepared pure states. In stark contrast, we show that generic sequences of unitary gates can be replicated deterministically at nearly quadratic rates, with an error vanishing on most inputs except for an exponentially small fraction. The result is not in contradiction with the no-cloning theorem, since the impossibility of deterministically transforming pure states into unitary gates prevents the application of the gate replication protocol to states. In addition to gate replication, we show that $N$ parallel uses of a completely unknown unitary gate can be compressed into a single gate acting on $O(\log N)$ qubits, leading to an exponential reduction of the amount of quantum communication needed to implement the gate remotely.