Universal super-replication of unitary gates

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.

5+8 pages, 2 figures

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• Models of reduced-noise, probabilistic linear amplifiers
• Quantum-enhanced learning of rotations about an unknown direction
• Universal construction of decoders from encoding black boxes
• Quantum Compression of Tensor Network States
• No-signaling bounds for quantum cloning and metrology
• Quantum superreplication of states and gates
• Fundamental limits on quantum cloning from the no-signalling principle
• Universal adjointation of isometry operations using conversion of quantum supermaps
• Experimental replication of single-qubit quantum phase gates
• Representation matching for delegated quantum computing
• Strongly non-quantitative classical information in quantum carriers
• Analytical Lower Bound on Query Complexity for Transformations of Unknown Unitary Operations
• Virtual Cloning of Quantum States