Efficient Generation of Quantum 2-Designs Under U(1) and SU(d) Symmetries Using Local Quantum Circuits
This paper constructs computationally efficient local quantum circuits that can generate approximate unitary 2-designs under U(1) and SU(d) symmetries, overcoming previous limitations and opening doors for applications in quantum error correction, quantum information, and simulations of physical systems.
On the (Im)possibility of Quantum Pseudorandomness in the (Inverseless) Haar Random Oracle Model
This paper explores the feasibility of constructing quantum pseudorandom primitives, specifically pseudorandom unitaries (PRUs) and pseudorandom state generators (PRSGs), in the idealized setting of the (inverseless) Haar Random Oracle Model ((i)QHROM).
Efficient Quantum Pseudorandomness from Hamiltonian Phase States: A Potential Foundation for Fully Quantum Cryptography
This research paper introduces Hamiltonian Phase States (HPS) as a novel and efficient approach to generating quantum pseudorandomness, potentially paving the way for fully quantum cryptography and offering practical applications in various quantum information tasks.
Constructing and Separating Quantum Pseudorandomness from a Single Haar Random State
A single Haar random quantum state can be used to construct single-copy pseudorandom states (1PRS), which are computationally indistinguishable from a Haar random state for a single copy. However, this single Haar random state is not sufficient to construct the stronger notion of (multi-copy) pseudorandom states (PRS).
Pseudorandom Unitaries: Limits and Insights
Pseudorandom unitaries require imaginarity, establishing fundamental limits on property testing and quantum pseudorandomness.
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