Continuous monitoring with jump operators forming a deformed unitary 1-design rigorously produces the Scrooge ensemble as the unique late-time equilibrium distribution of quantum trajectories for any target density matrix.
Cui , author T
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Derives improved mode-independent sample complexity bounds O(η log η) for fermionic classical shadows on particle-preserving operators and Slater determinant overlaps.
Random projections enable a tunable tradeoff between coherent quantum resources and sampling overhead for multi-copy estimation of multivariate traces like tr(ρ^K).
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.
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 multi-copy discriminability for pure states when N suffices, mixed states outperform beyond that, and quantum offers quadratic advantage over classical in Bayes capacity terms.
A parallelized amplitude estimation algorithm achieves near-Heisenberg query complexity with logarithmic circuit depth by combining a GHZ state with QSP-based phase shifters.
citing papers explorer
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Exact Hilbert-space ergodicity from continuous monitoring
Continuous monitoring with jump operators forming a deformed unitary 1-design rigorously produces the Scrooge ensemble as the unique late-time equilibrium distribution of quantum trajectories for any target density matrix.
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Particle-preserving fermionic shadows with mode-independent sample complexity
Derives improved mode-independent sample complexity bounds O(η log η) for fermionic classical shadows on particle-preserving operators and Slater determinant overlaps.
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Random Projections for Multi-Copy Quantum Algorithms
Random projections enable a tunable tradeoff between coherent quantum resources and sampling overhead for multi-copy estimation of multivariate traces like tr(ρ^K).
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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 multi-copy discriminability for pure states when N suffices, mixed states outperform beyond that, and quantum offers quadratic advantage over classical in Bayes capacity terms.
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Near-Heisenberg-limited parallel amplitude estimation with logarithmic depth circuit
A parallelized amplitude estimation algorithm achieves near-Heisenberg query complexity with logarithmic circuit depth by combining a GHZ state with QSP-based phase shifters.