Efficient Measurement of Quantum Dynamics via Compressive Sensing

PHYSICAL    REVIEW    LETTERS    week ending PRL 106, 100401 (2011)    11 MARCH 2011
Efficient Measurement of Quantum Dynamics via Compressive Sensing
A. Shabani,1 R. L. Kosut,2 M. Mohseni,3 H. Rabitz,1 M. A. Broome,4 M. P. Almeida,4 A. Fedrizzi,4 and A. G. White4
1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA 2SC Solutions, Sunnyvale, California 94085, USA 3Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 4Center for Engineered Quantum Systems and Center for Quantum Computation and Communication Technology, School of Mathematics and Physics, The University of Queensland, QLD 4072, Australia (Received 5 November 2009; revised manuscript received 14 November 2010; published 7 March 2011)

First few lines of the paper:

The resources required to characterize the dynamics of engineered quantum systems—such as quantum computers and quantum sensors—grow exponentially with system size. Here we adapt techniques from compressive sensing to exponentially reduce the experimental configurations required for quantum process tomography. Our method is applicable to processes that are nearly sparse in a certain basis and can be implemented using only single-body preparations and measurements. We perform efficient, high- fidelity estimation of process matrices of a photonic two-qubit logic gate. The database is obtained under various decoherence strengths. Our technique is both accurate and noise robust, thus removing a key roadblock to the development and scaling of quantum technologies.

Understanding and controlling the world at the nanoscale—be it in biological, chemical or physical phenomena—requires quantum mechanics. It is therefore essential to characterize and monitor realistic complex quantum systems that inevitably interact with typically uncontrollable environments. One of the most general descriptions of the dynamics of an open quantum system is a quantum map—typically represented by a process matrix [1]. Methods to identify this matrix are collectively known as quantum process tomography (QPT) [1,2]. For a d-dimensional quantum system, they require Oðd4Þ experi- mental configurations: combinations of input states, on which the process acts, and a set of output observables. For a system of n qubits—two level quantum systems— d    1⁄4    2n .    The    required    physical    resources    hence    scale exponentially with system size. Recently, a number of alternative methods have been developed for efficient and selective estimation of quantum processes [3]. However, full characterization of quantum dynamics of comparably small systems, such as an 8-qubit ion trap [4], would still require over a billion experimental configurations, clearly impractical. So far, process tomography has therefore been limited by experimental and off-line computational resources, to systems of 2 and 3 qubits [5–7].
Here we adapt techniques from compressive sensing to develop an experimentally efficient method for QPT. ...

Compressive tomography techniques can also be applied to quantum metrology and Hamiltonian parameter estima- tion: for example, estimating selective properties of biological or chemical interest in molecular systems and nanostructures with typically sparse Hamiltonians [23]