Understand
Quantum control requires full knowledge of the system many-body Hamiltonian.
- In many cases this information is not directly available due to restricted access to the system.
- Here we show how to indirectly estimate all the coupling strengths in a spin chain by measuring one spin at the end of the chain.
- We also discuss the efficiency of this "quantum inverse problem" and give a numerical example.
Built on
R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, Princeton, 1999)
1999
Earlier work this paper cites.
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)
2000
Earlier work this paper cites.
Similar
G. M. L. Gladwell, Inverse Problems in Vibration (Kluwer, Dordrecht, 2004)
2004
Cited alongside, same era.
H. L. Haselgrove, Phys. Rev. A 72
2005
Cited alongside, same era.
S. G. Schirmer, I. C. H. Pullen, P. J. Pemberton-Ross, arXiv:0801.0721
Cited in the paper.
D. Burgarth, S. Bose, C. Bruder, and V. Giovannetti, arXiv:0805.3975
Cited in the paper.
S. G. Schirmer, D. K.L. Oi, and S. J. Devitt, arXiv:0805.2725
Cited in the paper.
D. Burgarth and V. Giovannetti, arXiv:0710.0302
Cited in the paper.
For the specific Hamiltonians at hand, counting the qubits is indeed possible. The easiest approach is to count the number of peaks in the Fourier transform. However in the presence of localization or degeneracy there are better ways of doing this: introduce many excitations into the system by replacing the end qubit state with | 1 ⟩ , |1\rangle, until the spin chain state converged to | 111 … 1 ⟩ |111\dots 1\rangle [ 7 ] . Then, measure and reset the end qubit state to | 0 ⟩ |0\rangle , until the state of the chain converged to | 000 … 0 ⟩ . |000\ldots 0\rangle. The number of 1 ′ s 1^{\prime}s measured is equal to the number of qubits
Cited in the paper.
Then
C. K. Burrell and T. J. Osborne, Phys. Rev. Lett. 99
2007
Later among the works it cites.
D. D’Alessandro, Introduction to Quantum Control and Dynamics (Taylor and Francis, Boca Raton, 2008)
2008
Closest in time.
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