Quantum gate identification: error analysis, numerical results and optical experiment. (English) Zbl 1414.81079
Summary: The identification of an unknown quantum gate is a significant issue in quantum technology. In this paper, we propose a quantum gate identification method within the framework of quantum process tomography. In this method, a series of pure states are applied to the gate and then a fast state tomography on the output states is performed and the data are used to reconstruct the quantum gate. The algorithm has computational complexity \(O(d^3)\) with the system dimension \(d\). The identification approach is compared with the maximum likelihood estimation method for the running time, which shows an efficiency advantage of our method. An error upper bound is established for the identification algorithm and the robustness of the algorithm against impurities in the input states is also tested. We perform a quantum optical experiment on a single-qubit Hadamard gate to verify the effectiveness of the identification algorithm.
MSC:
| 81P68 | Quantum computation |
| 81P15 | Quantum measurement theory, state operations, state preparations |
| 68Q12 | Quantum algorithms and complexity in the theory of computing |
| 93B15 | Realizations from input-output data |
| 94B65 | Bounds on codes |
| 62F10 | Point estimation |
References:
| [1] | Baldwin, C. H.; Kalev, A.; Deutsch, I. H., Quantum process tomography of unitary and near-unitary maps, Physical Review A, 90, 012110 (2014) |
| [2] | Beterov, I. I.; Saffman, M.; Yakshina, E. A.; Tretyakov, D. B.; Entin, V. M.; Hamzina, G. N., Simulated quantum process tomography of quantum gates with Rydberg superatoms, Journal of Physics B: Atomic, Molecular & Optical Physics, 49, 114007 (2016) |
| [3] | Bhatia, R., Matrix analysis (1997), New York: Springer-Verlag |
| [4] | Blume-Kohout, R., Optimal, reliable estimation of quantum states, New Journal of Physics, 12, 4, 043034 (2010) · Zbl 1375.81065 |
| [5] | Bonnabel, S.; Mirrahimi, M.; Rouchon, P., Observer-based Hamiltonian identification for quantum systems, Automatica, 45, 5, 1144-1155 (2009) · Zbl 1162.93020 |
| [6] | Bris, C. Le.; Mirrahimi, M.; Rabitz, H.; Turinici, G., Hamiltonian identification for quantum systems: well-posedness and numerical approaches, ESAIM. Control, Optimisation and Calculus of Variations, 13, 2, 378-395 (2007) · Zbl 1123.93040 |
| [7] | Burgarth, D.; Yuasa, K., Quantum system identification, Physical Review Letters, 108, 8, 080502 (2012) |
| [8] | Burgarth, D.; Yuasa, K., Identifiability of open quantum systems, Physical Review A, 89, 3, 030302 (2014) |
| [9] | Chuang, I. L.; Nielsen, M. A., Prescription for experimental determination of the dynamics of a quantum black box, Journal of Modern Optics, 44, 11-12, 2455-2467 (1997) |
| [10] | Dong, D.; Petersen, I. R., Quantum control theory and applications: A survey, IET Control Theory & Applications, 4, 2651-2671 (2010) |
| [11] | Golub, G. H.; Van Loan, C. F., Matrix computation (2012), JHU Press |
| [12] | Guţă, M.; Yamamoto, N., System identification for passive linear quantum systems, IEEE Transactions on Automatic Control, 61, 4, 921-936 (2016) · Zbl 1359.93501 |
| [13] | Gutoski, G.; Johnston, N., Process tomography for unitary quantum channels, Journal of Mathematical Physics, 55, 032201 (2014) · Zbl 1404.81060 |
| [14] | Holzäpfel, M.; Baumgratz, T.; Cramer, M.; Plenio, M. B., Scalable reconstruction of unitary processes and Hamiltonians, Physical Review A, 91, 042129 (2015) |
| [15] | Hou, Z.; Zhong, H.-S.; Tian, Y.; Dong, D.; Qi, B.; Li, L., Full reconstruction of a 14-qubit state within four hours, New Journal of Physics, 18, 8, 083036 (2016) |
| [16] | Hradil, Z., Quantum-state estimation, Physical Review A, 55, 3, R1561 (1997) |
| [17] | Ježek, M.; Fiurášek, J.; Hradil, Z., Quantum inference of states and processes, Physical Review A, 68, 1, 012305 (2003) |
| [18] | Kato, Y.; Yamamoto, N., Structure identification and state initialization of spin networks with limited access, New Journal of Physics, 16, 2, 023024 (2014) |
| [19] | Kimmel, S.; Low, G. H.; Yoder, T. J., Robust calibration of a universal single-qubit gate set via robust phase estimation, Physical Review A, 92, 6, 062315 (2015) |
| [20] | Kimmel, S.; da Silva, M. P.; Ryan, C. A.; Johnson, B. R.; Ohki, T., Robust extraction of tomographic information via randomized benchmarking, Physical Review X, 4, 1, 011050 (2016) |
| [21] | Leghtas, Z.; Turinici, G.; Rabitz, H.; Rouchon, P., Hamiltonian identification through enhanced observability utilizing quantum control, IEEE Transactions on Automatic Control, 57, 10, 2679-2683 (2012) · Zbl 1369.93161 |
| [22] | Levitt, M.; Guţă, M., Identification of single-input-single-output quantum linear systems, Physical Rrview A, 95, 3, 033825 (2017) |
| [23] | Mičuda, M.; Miková, M.; Straka, I.; Sedlák, M.; Dušek, M.; Ježek, M., Tomographic characterization of a linear optical quantum Toffoli gate, Physical Review A, 92, 032312 (2015) |
| [24] | Nielsen, M. A.; Chuang, I. L., Quantum computation and quantum information (10th ed.) (2010), Cambridge University Press · Zbl 1288.81001 |
| [25] | O’Brien, J. L.; Pryde, G. J.; Gilchrist, A.; James, D. F.V.; Langford, N. K.; Ralph, T. C., Quantum process tomography of a controlled-NOT gate, Physical Review Letters, 93, 080502 (2004) |
| [26] | Paris, M.; Řeháček, J., Quantum state estimation (2004), Berlin: Springer · Zbl 1084.81004 |
| [27] | Poyatos, J. F.; Cirac, J. I.; Zoller, P., Complete characterization of a quantum process: the two-bit quantum gate, Physical Review Letters, 78, 2, 390 (1997) |
| [28] | Qi, B.; Hou, Z.; Li, L.; Dong, D.; Xiang, G.-Y.; Guo, G.-C., Quantum state tomography via linear regression estimation, Scientific Reports, 3, 3496 (2013) |
| [29] | Qi, B.; Hou, Z.; Wang, Y.; Dong, D.; Zhong, H.-S.; Li, L., Adaptive quantum state tomography via linear regression estimation: Theory and two-qubit experiment, npj Quantum Information, 3, 19 (2017) |
| [30] | Rodionov, A. V.; Veitia, A.; Barends, R.; Kelly, J.; Sank, D.; Wenner, J., Compressed sensing quantum process tomography for superconducting quantum gates, Physical Review B, 90, 144504 (2014) |
| [31] | Shabani, A.; Kosut, R. L.; Mohseni, M.; Rabitz, H.; Broome, M. A.; Almeida, M. P., Efficient measurement of quantum dynamics via compressive sensing, Physical Review Letters, 106, 10, 100401 (2011) |
| [32] | Shu, C. C.; Yuan, K. J.; Dong, D.; Petersen, I. R.; Bandrauk, A. D., Identifying strong-field effects in indirect photofragmentation reactions, The Journal of Physical Chemistry Letters, 8, 1-6 (2017) |
| [33] | Sone, A.; Cappellaro, P., Hamiltonian identifiability assisted by single-probe measurement, Physical Review A, 95, 2, 022335 (2017) |
| [34] | Sone, A.; Cappellaro, P., Exact dimension estimation of interacting qubit systems assisted by a single quantum probe, Physical Review A, 96, 6, 062334 (2017) |
| [35] | Teklu, B.; Olivares, S.; Paris, M. G., Bayesian estimation of one-parameter qubit gates, Journal of Physics B: Atomic, Molecular & Optical Physics, 42, 3, 035502 (2009) |
| [36] | Wang, Y.; Dong, D.; Petersen, I. R., An approximate quantum Hamiltonian identification algorithm using a Taylor expansion of the matrix exponential function, (Proceedings of the 56th IEEE conference on decision and control (2017)) |
| [37] | Wang, Y.; Dong, D.; Qi, B.; Zhang, J.; Petersen, I. R.; Yonezawa, H., A quantum Hamiltonian identification algorithm: computational complexity and error analysis, IEEE Transactions on Automatic Control, 63, 5, 1388-1403 (2018) · Zbl 1395.81092 |
| [38] | Wang, Y.; Yin, Q.; Dong, D.; Qi, B.; Petersen, I. R.; Hou, Z.; Yonezawa, H.; Xiang, G.-Y., Efficient identification of unitary quantum processes, (Proceedings of the 2017 Australian and New Zealand control conference (2017)) |
| [39] | Wang, H. Y.; Zheng, W. Q.; Yu, N. K.; Li, K. R.; Lu, D. W.; Xin, T., Quantum state and process tomography via adaptive measurements, Science in China, 59, 10, 100313 (2016) |
| [40] | Zhang, J.; Sarovar, M., Quantum Hamiltonian identification from measurement time traces, Physical Review Letters, 113, 8, 080401 (2014) |
| [41] | Zorzi, M.; Ticozzi, F.; Ferrante, A., Estimation of quantum channels: Identifiability and ML methods, (Proceedings of the 51st IEEE conference on decision and control (2012)) |
| [42] | Zorzi, M.; Ticozzi, F.; Ferrante, A., Minimal resources identifiability and estimation of quantum channels, Quantum Information Processing, 13, 3, 683-707 (2014) · Zbl 1291.81083 |
| [43] | Zorzi, M.; Ticozzi, F.; Ferrante, A., Minimum relative entropy for quantum estimation: Feasibility and general solution, IEEE Transactions on Information Theory, 60, 1, 357-367 (2014) · Zbl 1364.81074 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
