Abstract
A universal programmable quantum processor uses program quantum states to apply an arbitrary quantum channel to an input state. We generalize the concept of a finite-dimensional programmable quantum processor to infinite dimension assuming an energy constraint on the input and output of the target quantum channels. By proving reductions to and from finite-dimensional processors, we obtain upper and lower bounds on the program dimension required to approximately implement energy-limited quantum channels. In particular, we consider the implementation of Gaussian channels. Due to their practical relevance, we investigate the resource requirements for gauge-covariant Gaussian channels. Additionally, we give upper and lower bounds on the program dimension of a processor implementing all Gaussian unitary channels. These lower bounds rely on a direct information-theoretic argument, based on the generalization from finite to infinite dimension of a certain replication lemma for unitaries.
Highlights
A programmable quantum processor takes an input state and applies a quantum channel to it, controlled by a program state that contains all relevant information for the implementation
Since infinite-dimensional systems are fundamental in quantum theory, and are gaining more and more attention in quantum communication [3,4], quantum cryptography [5,6], and quantum computing [7,8,9], here we investigate programmable quantum processors for continuous-variable systems
We achieve this by relating the performance of infinite-dimensional approximate programmable quantum processors to that of their finite-dimensional counterparts in Theorems 9 and 10
Summary
A programmable quantum processor takes an input state and applies a quantum channel to it, controlled by a program state that contains all relevant information for the implementation. This concept, introduced by Nielsen and Chuang [1], is inspired by the von Neumann architecture of classical computers and universal Turing machines, which postulate a single device operating on data using a “program,” which is just another kind of data. Yang et al [2] closed the gap for the universal implementation of unitaries, providing essentially the optimal scaling of the program dimension and the accuracy for a given finite-dimensional Hilbert space on which the unitaries act. Since infinite-dimensional ( known as continuousvariable) systems are fundamental in quantum theory, and are gaining more and more attention in quantum communication [3,4], quantum cryptography [5,6], and quantum computing [7,8,9], here we investigate programmable quantum processors for continuous-variable systems
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