Efficient quantum state tomography

Abstract

Quantum state tomography, the ability to deduce the state of a quantum system from measured data, is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger systems it becomes infeasible because the number of quantum measurements and the amount of computation required to process them grows exponentially in the system size. Here we show that we can do exponentially better than direct state tomography for a wide range of quantum states, in particular those that are well approximated by a matrix product state ansatz. We present two schemes for tomography in 1-D quantum systems and touch on generalizations. One scheme requires unitary operations on a constant number of subsystems, while the other requires only local measurements together with more elaborate post-processing. Both schemes rely only on a linear number of experimental operations and classical postprocessing that is polynomial in the system size. A further strength of the methods is that the accuracy of the reconstructed states can be rigorously certified without any a priori assumptions.

9 pages, 4 figures. Combines many of the results in arXiv:1002.3780, arXiv:1002.3839, and arXiv:1002.4632 into one unified exposition

References in corpus (7)

• Many-Body Physics with Ultracold Gases
• Scalable multi-particle entanglement of trapped ions
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Sequential Generation of Matrix-Product States in Cavity QED
• Simulation of time evolution with the MERA
• Exact Matrix Completion via Convex Optimization
• Quantum Process Tomography via L1-norm Minimization

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• Direct estimation of decoherence rates