Learning stabilizer states by Bell sampling

Abstract

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.

2+eps pages; first presented at Coogee'13 workshop, Sydney, January 2013. v2: reference added

References in corpus (6)

• Improved Simulation of Stabilizer Circuits
• Efficient quantum state tomography
• The Clifford group, stabilizer states, and linear and quadratic operations over GF(2)
• Learning and Testing Algorithms for the Clifford Group
• Quantum algorithms to solve the hidden shift problem for quadratics and for functions of large Gowers norm
• Fast graph operations in quantum computation

Cited by in corpus (4)

• Schur-Weyl Duality for the Clifford Group with Applications: Property Testing, a Robust Hudson Theorem, and de Finetti Representations
• On quantum invariants and the graph isomorphism problem
• Quantum State Isomorphism
• Quantum algorithms for learning a hidden graph and beyond