Abstract：Quantum process tomography (QPT) is one of the foundations of quantum information science research, but the required experimental resources during QPT grow exponentially with the number of qubits. Recently, a compressed sensing QPT (CSQPT) was proposed that significantly reduces the required resources and the post-processing time based on the sparseness of the process matrix. However, the quantum channel analysis needs to simultaneously identify a variety of quantum gates and there are always outliers during the QPT process. This paper describes a distributed compressed sensing quantum process tomography (DCSQPT) method to identify the multi quantum channel tomography while effectively attenuating outliers through collaborative sparse learning. Simulations show that this method is robust to outlier data and accurately reconstructs the process matrix compared to the compressed sensing QPT method while significantly improving the quantum process tomography identification speed.
Nielsen M A, Chuang I L. Quantum Computation and Quantum Information[M]. Cambridge:Cambridge University Press, 2010.
[2]
Kofman A G, Korotkov A N. Two-qubit decoherence mechanisms revealed via quantum process tomography[J]. Physical Review A, 2009, 80(4), 042103.
[3]
Mohseni M, Rezakhani A T, Lidar D A. Quantum-process tomography:Resource analysis of different strategies[J]. Physical Review A, 2008, 77(3), 032322.
[4]
Mohseni M, Rezakhani A T. Equation of motion for the process matrix:Hamiltonian identification and dynamical control of open quantum systems[J]. Physical Review A, 2009, 80(1), 010101.
[5]
Knill E, Leibfried D, Reichle R, et al. Randomized benchmarking of quantum gates[J]. Physical Review A, 2008, 77(1), 012307.
[6]
Flammia S T, Liu Y K. Direct fidelity estimation from few Pauli measurements[J]. Physical Review Letters, 2011, 106(23), 230501.
[7]
Kosut R L. Quantum process tomography via l1-norm minimization[J]. arXiv:0812.4323, 2008.
[8]
Shabani A, Kosut R L, Mohseni M, et al. Efficient measurement of quantum dynamics via compressive sensing[J]. Physical Review Letters, 2011, 106(10), 100401.
[9]
Donoho D. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4):1289-1306.
[10]
Cands E, Tao T. Near-optimal signal recovery from random projections:Universal encoding strategies?[J]. IEEE Transactions on Information Theory, 2006, 52(12):5406-5425.
[11]
Lustig M, Donoho D, Pauly J M. Sparse MRI:The application of compressed sensing for rapid MR imaging[J]. Magnetic Resonance in Medicine, 2007, 58(6):1182-1195.
[12]
MA Jianwei. Single-pixel remote sensing[J]. IEEE Transactions on Geoscience and Remote Sensing Letters, 2009, 6(2):199-203.
[13]
Hennenfent G, Herrmann F J. Simply denoise:Wavefield reconstruction via jittered under sampling[J]. Geophysics, 2008, 73(13):V19-V28.
[14]
Rodionov A V, Veitia A, Barends R, et al. Compressed sensing quantum process tomography for superconducting quantum gates[J]. Physical Review B, 2014, 90(14), 144504.
[15]
Prades-Nebot J, Ma Y, Huang T. Distributed video coding using compressive sampling[C]//Picture Coding Symposium. Chicago, IL, USA:IEEE, 2009:1-4.
[16]
Yang H, Huang L, Xu H, et al. Distributed compressed sensing in wireless local area networks[J]. International Journal of Communication Systems, 2014, 27(11):2723-2743.
[17]
Je?ek M, Fiurášek J, Hradil Z. Quantum inference of states and processes[J]. Physical Review A, 2003, 68(1), 012305.
[18]
Chow J M, Gambetta J M, Tornberg L, et al. Randomized benchmarking and process tomography for gate errors in a solid-state qubit[J]. Physical Review Letters, 2009, 102(9), 090502.
[19]
Berg E, Friedlander M P. Joint-sparse recovery from multiple measurements[J]. arXiv:0904.2051, 2009.
[20]
Liu H, Liu Y, Yu Y, et al. Simultaneous prototype selection and outlier isolation for traffic sign recognition:A collaborative sparse optimization method[C]//2014 IEEE International Conference on Robotics and Automation (ICRA). Hong Kong, China:IEEE, 2014:2138-2143.
[21]
Li K, Zhang H, Kuang S, et al. An improved robust ADMM algorithm for quantum state tomography[J]. Quantum Information Processing, 2016, 15(6):2343-2358.
[22]
Tropp J A, Gilbert A C, Strauss M J. Algorithms for simultaneous sparse approximation. Part I:Greedy pursuit[J]. Signal Processing, 2006, 86(3):572-588.
2017, Vol. 57 
