Optimal quantum controls robust against detuning error
Abstract: Precise control of quantum systems is one of the most important milestones for achieving practical quantum technologies, such as computation, sensing, and communication. Several factors deteriorate the control precision and thus their suppression is strongly demanded. One of the dominant factors is systematic errors, which are caused by discord between an expected parameter in control and its actual value. Error-robust control sequences, known as composite pulses, have been invented in the field of nuclear magnetic resonance (NMR). These sequences mainly focus on the suppression of errors in one-qubit control. The one-qubit control, which is the most fundamental in a wide range of quantum technologies, often suffers from detuning error. As there are many possible control sequences robust against the detuning error, it will practically be important to find ``optimal" robust controls with respect to several cost functions such as time required for operation, and pulse-area during the operation, which corresponds to the energy necessary for control. In this paper, we utilize the Pontryagin's maximum principle (PMP), a tool for solving optimization problems under inequality constraints, to solve the time and pulse-area optimization problems. We analytically obtain pulse-area optimal controls robust against the detuning error. Moreover, we found that short-CORPSE, which is the shortest known composite pulse so far, is a probable candidate of the time optimal solution according to the PMP. We evaluate the performance of the pulse-area optimal robust control and the short-CORPSE, comparing with that of the direct operation.
- A. K. Ekert, Quantum cryptography based on bell’s theorem, Physical review letters 67, 661 (1991).
- N. Gisin and R. Thew, Quantum communication, Nature photonics 1, 165 (2007).
- C. W. Helstrom, Quantum detection and estimation theory, Mathematics in Science and Engeneering, Vol. 123 (Academic press New York, 1976).
- C. M. Caves, Quantum-mechanical noise in an interferometer, Physical Review D 23, 1693 (1981).
- A. S. Holevo, Probabilistic and statistical aspects of quantum theory, Vol. 1 (Springer Science & Business Media, 2011).
- M. Nielsen and I. Chuang, Quantum Computation and Quantum Information, Cambridge Series on Information and the Natural Sciences (Cambridge University Press, 2000).
- M. Nakahara, Quantum computing: from linear algebra to physical realizations (CRC press, 2008).
- J. Preskill, Quantum computing in the nisq era and beyond, Quantum 2, 79 (2018).
- L. M. K. Vandersypen and I. L. Chuang, NMR techniques for quantum control and computation, Rev. Mod. Phys. 76, 1037 (2005).
- Y.-C. Yang, S. Coppersmith, and M. Friesen, Achieving high-fidelity single-qubit gates in a strongly driven charge qubit with 1/f charge noise, npj Quantum Information 5, 12 (2019).
- C. Counsell, M. Levitt, and R. Ernst, Analytical theory of composite pulses, Journal of Magnetic Resonance (1969) 63, 133 (1985).
- M. H. Levitt, Composite pulses, Progress in Nuclear Magnetic Resonance Spectroscopy 18, 61 (1986).
- T. D. Claridge, High-resolution NMR techniques in organic chemistry, Tetrahedron Organic Chemistry, Vol. 27 (Elsevier, 2016).
- R. Said and J. Twamley, Robust control of entanglement in a nitrogen-vacancy center coupled to a c 13 nuclear spin in diamond, Physical Review A 80, 032303 (2009).
- B. T. Torosov and N. V. Vitanov, Experimental demonstration of composite pulses on ibm’s quantum computer, Phys. Rev. Appl. 18, 034062 (2022).
- K. R. Brown, A. W. Harrow, and I. L. Chuang, Arbitrarily accurate composite pulse sequences, Physical Review A 70, 052318 (2004).
- H. K. Cummins, G. Llewellyn, and J. A. Jones, Tackling systematic errors in quantum logic gates with composite rotations, Physical Review A 67, 042308 (2003).
- H. Cummins and J. Jones, Use of composite rotations to correct systematic errors in nmr quantum computation, New Journal of Physics 2, 6 (2000).
- C. A. Ryan, J. S. Hodges, and D. G. Cory, Robust decoupling techniques to extend quantum coherence in diamond, Physical Review Letters 105, 200402 (2010).
- J. A. Jones, Designing short robust not gates for quantum computation, Physical Review A 87, 052317 (2013).
- S. Kukita, H. Kiya, and Y. Kondo, Short composite quantum gate robust against two common systematic errors, Journal of the Physical Society of Japan 91, 104001 (2022a).
- J. Ruths and J.-S. Li, Optimal control of inhomogeneous ensembles, IEEE Transactions on Automatic Control 57, 2021 (2012).
- X. Laforgue, X. Chen, and S. Guérin, Robust stimulated raman exact passage using shaped pulses, Phys. Rev. A 100, 023415 (2019).
- G. Dridi, K. Liu, and S. Guérin, Optimal robust quantum control by inverse geometric optimization, Phys. Rev. Lett. 125, 250403 (2020).
- Q. Ansel, S. J. Glaser, and D. Sugny, Selective and robust time-optimal rotations of spin systems, Journal of Physics A: Mathematical and Theoretical 54, 085204 (2021).
- X. Laforgue, G. Dridi, and S. Guérin, Optimal quantum control robust against pulse inhomogeneities: Analytic solutions, Phys. Rev. A 106, 052608 (2022).
- S. Kukita, H. Kiya, and Y. Kondo, Geometric property of off resonance error robust composite pulse, Scientific Reports 12, 9574 (2022b).
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