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Learning stabilizer states by Bell sampling
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We show that measuring pairs of qubits in the Bell basis can be used to obtain a simple quantum algorithm for efficiently identifying an unknown stabilizer state of n qubits. The algorithm uses O(n) copies of the input state and fails with exponentially small probability.
Forward citations
Cited by 11 Pith papers
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Optimal Stabilizer Testing and Learning with Limited Quantum Memory
Stabilizer testing requires Θ(n-k) copies and non-adaptive learning Θ(n²/k) copies with k-qubit memory, removing the testing-learning separation.
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Complexity of detecting large coefficients in the Pauli basis
Detecting large Pauli coefficients in circuit-prepared quantum states (even pure) is QCMA-complete and not in BQP unless NP ⊆ BQP, resolving an open question on efficient tomography.
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Heisenberg-limited Hamiltonian learning without short-time control
Heisenberg-limited Hamiltonian learning is achievable with any constant minimum evolution time T per query, attaining optimal 1/ε total-time scaling for logarithmically sparse Hamiltonians.
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Cloning is as Hard as Learning for Stabilizer States
For n-qubit stabilizer states the optimal sample complexity of approximate cloning is Θ(n), matching the complexity of learning.
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Fermionic non-Gaussianity via Bell sampling: monotones and efficient quantum algorithms
Defines bridge degree monotone for fermionic non-Gaussianity from Bell-sampling eigenvalues of Lambda, shows non-increase under Gaussian protocols for stronger no-go theorems, and gives polynomial-sample tests for Gau...
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Single-copy stabilizer learning: average case and worst case
Log-depth circuits suffice for average-case single-copy stabilizer learning with t=O(log n), but worst-case adaptive single-copy learning requires exp(t) samples.
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Sector length distributions of recursively definable graph states through analytic combinatorics
Closed-form sector length distributions for recursively definable graph states (paths, cycles, stars, grids) via generating functions, yielding analytical concentratable entanglement, depolarizing fidelity bounds, and...
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Adaptive Stabilizer State Fidelity Certification
Adaptive gauge selection protocol for stabilizer state fidelity certification that reports full intervals with monotonic tightening and exact recovery on full coverage.
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Sample- and Hardware-Efficient Fidelity Estimation by Stripping Phase-Dominated Magic
Phase stripping reduces target-state magic to enable O(poly(n)) or O(1) sample fidelity estimation for phase-dominated states using a single fan-out gate plus nonlinear Pauli post-processing.
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Classical Simulations of Low Magic Quantum Dynamics
Classical simulation algorithms for low-magic adaptive quantum circuits with high Pauli measurement rates, demonstrated on all-to-all monitored circuits with sub-extensive T-gates to study measurement-induced phase tr...
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Optimal detection of dissipation in Lindbladian dynamics
A randomized algorithm detects dissipation of magnitude at least epsilon in unknown Lindbladian dynamics with optimal total evolution time O(epsilon^{-1}) under bounded strength and locality assumptions.
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