CBNE enables estimation of nonlinear quantum properties such as higher-order expectations from a single randomized measurement setting under sufficient system dimension or ancillary qubits.
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Typical trace-distance relaxation concentrates around a mean in open quantum systems, producing typical mixing times separated from worst-case by rare-state bottlenecks that scale logarithmically, linearly, or exponentially depending on the slow modes.
Two constructions yield strong unitary k-designs and pseudorandom unitaries on D-dimensional grids with provably optimal depth.
k-designs achieve maximal discriminability for pure states in multi-copy minimum-error discrimination; mixed states outperform for larger ensembles, with quantum offering quadratic advantage over classical.
A tunable parallel amplitude estimation algorithm achieves near-Heisenberg query scaling and logarithmic depth via GHZ states and quantum signal processing, with a near-optimality proof using the parallel quantum adversary method.
citing papers explorer
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Quantum Nonlinear Properties from a Single Measurement Setting
CBNE enables estimation of nonlinear quantum properties such as higher-order expectations from a single randomized measurement setting under sufficient system dimension or ancillary qubits.
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Typical Mixing and Rare-State Bottlenecks in Open Quantum Systems
Typical trace-distance relaxation concentrates around a mean in open quantum systems, producing typical mixing times separated from worst-case by rare-state bottlenecks that scale logarithmically, linearly, or exponentially depending on the slow modes.
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Arts & crafts: Strong random unitaries and geometric locality
Two constructions yield strong unitary k-designs and pseudorandom unitaries on D-dimensional grids with provably optimal depth.
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The most discriminable quantum states in the multicopy regime
k-designs achieve maximal discriminability for pure states in multi-copy minimum-error discrimination; mixed states outperform for larger ensembles, with quantum offering quadratic advantage over classical.
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Near-Heisenberg-limited parallel amplitude estimation with logarithmic depth circuit
A tunable parallel amplitude estimation algorithm achieves near-Heisenberg query scaling and logarithmic depth via GHZ states and quantum signal processing, with a near-optimality proof using the parallel quantum adversary method.