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Efficient Quantum Algorithm for Port-based Teleportation
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abstract
In this paper, we provide the first efficient algorithm for port-based teleportation, a unitarily equivariant version of teleportation useful for constructing programmable quantum processors and performing instantaneous nonlocal computation (NLQC). The latter connection is important in AdS/CFT, where bulk computations are realized as boundary NLQC. Our algorithm yields an exponential improvement to the known relationship between the amount of entanglement available and the complexity of the nonlocal part of any unitary that can be implemented using NLQC. Similarly, our algorithm provides the first nontrivial efficient algorithm for an approximate universal programmable quantum processor. The key to our approach is a generalization of Schur-Weyl duality we call twisted Schur-Weyl duality, as well as an efficient algorithm we develop for the twisted Schur transform, which transforms to a subgroup-reduced irrep basis of the partially transposed permutation algebra, whose dual is the $U^{\otimes n-k} \otimes (U^*)^{\otimes k}$ representation of the unitary group.
Forward citations
Cited by 4 Pith papers
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Optimal complex conjugation of unknown isometry channels
The optimal n-use fidelity for complex conjugating an unknown isometry C^d→C^D is derived in closed form, with parallel protocols proven optimal among all general quantum superchannels.
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Sequential quantum processes with group symmetries
A canonical streaming circuit decomposition for (G×H)-invariant quantum combs is derived, and numerical optimization suggests a deterministic 7-query transposition protocol for qutrits that is reported as exact.
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Quantum Simulation of Random Unitaries from Clebsch-Gordan Transforms
Clebsch-Gordan transforms give exact compressed oracles for Haar-random unitary group actions, with efficient circuits for U(d).
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Port-based telecloning of an unknown quantum state
A new port-based telecloning protocol, built from a partially symmetrized pretty good measurement, asymptotically achieves the optimal quantum cloning fidelity and outperforms clone-and-MPBT for small port numbers.
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