Quantum control methods for three-level systems have become recently an important direction of research in quantum information science and technology. Here we present numerical simulations using realistic experimental parameters for quantum process tomography in STIRAP (stimulated Raman adiabatic passage) and saSTIRAP (superadiabatic STIRAP). Specifically, we identify a suitable basis in the operator space as the identity operator together with the 8 Gell-Mann operators, and we calculate the corresponding process matrices, which have 9 × 9=81 elements. We discuss these results for the ideal decoherence-free case, as well as for the experimentally-relevant case with decoherence included.
REFERENCES
1.
M. A.
Nielsen
and I. L.
Chuang
, Quantum Computation and Quantum Information, quantum information, quantum computation,cryptography
(Cambridge University Press
, Cambridge UK
, 2000
).2.
A.
Kandala
, K.
Temme
, A. D.
Córcoles
, A.
Mezzacapo
, J. M.
Chow
, and J. M.
Gambetta
, “Error mitigation extends the computational reach of a noisy quantum processor
,” Nature
567
, 491
–495
(2019
).3.
S. J.
Devitt
, “Performing quantum computing experiments in the cloud
,” Phys. Rev. A
94
, 032329
(2016
).4.
M. R.
Perelshtein
, A. I.
Pakhomchik
, A. A.
Melnikov
, A. A.
Novikov
, A.
Glatz
, G. S.
Paraoanu
, V. M.
Vinokur
, and G. B.
Lesovik
, “Advanced quantum supremacy using a hybrid algo ritho for linear systems of equations
,” arXiv:2003.12770 (2020
).5.
G.
García-Pérez
, M. A. C.
Rossi
, and S.
Maniscalco
, “Ibm q experience as a versatile experimental testbed for simulating open quantum systems
,” npj Quant. Inf.
6
, 1
(2020
).6.
A.
Kandala
, A.
Mezzacapo
, K.
Temme
, M.
Takita
, M.
Brink
, J. M.
Chow
, and J. M.
Gambetta
, “Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets
,” Nature
549
, 242
–246
(2017
).7.
R.
Harper
and S. T.
Flammia
, “Fault-tolerant logical gates in the ibm quantum experience
,” Phys. Rev. Lett.
122
, 080504
(2019
).8.
E.
Huffman
and A.
Mizel
, “Violation of noninvasive macrorealism by a superconducting qubit: Implementation of a leggett-garg test that addresses the clumsiness loophole
,” Phys. Rev. A
95
, 032131
(2017
).9.
D.
Alsina
and J. I.
Latorre
, “Experimental test of mermin inequalities on a five-qubit quantum computer
,” Phys. Rev. A
94
, 012314
(2016
).10.
G.
Paraoanu
, “Non-local parity measurements and the quantum pigeonhole effect
,” Entropy
20
, 606
(2018
).11.
N. N.
Hegade
, A.
Das
, S.
Seth
, and P. K.
Panigrahi
, “Investigation of quantum pigeonhole effect in ibm quantum computer
,” arXiv:1904.12187.12.
A.
Shukla
, M.
Sisodia
, and A.
Pathak
, “Complete characterization of the directly implementable quantum gates used in the ibm quantum processors
,” Physics Letters A
384
, 126387
(2020
).13.
I. L.
Chuang
and M. A.
Nielsen
, “Prescription for experimental determination of the dynamics of a quantum black box
,” J. Mod. Opt.
44
, 2455
–2467
(1997
).14.
M.
Howard
, J.
Twamley
, C.
Wittmann
, T.
Gaebel
, F.
Jelezko
, and J.
Wrachtrup
, “Quantum process tomography and linblad estimation of a solid-state qubit
,” New Journal of Physics
8
, 33
–33
(2006
).15.
R. C.
Bialczak
, M.
Ansmann
, M.
Hofheinz
, E.
Lucero
, M.
Neeley
, A. D.
O’Connell
, D.
Sank
, H.
Wang
, J.
Wenner
, M.
Steffen
, A. N.
Cleland
, and J. M.
Martinis
, “Quantum process tomography of a universal entangling gate implemented with josephson phase qubits
,” Nature Physics
6
, 409
–413
(2010
).16.
A. M.
Palmieri
, E.
Kovlakov
, F.
Bianchi
, D.
Yudin
, S.
Straupe
, J. D.
Biamonte
, and S.
Kulik
, “Experimental neural network enhanced quantum tomography
,” npj Quantum Information
6
(2020
), .17.
A.
Shukla
and T. S.
Mahesh
, “Single-scan quantum process tomography
,” Phys. Rev. A
90
, 052301
(2014
).18.
A.
Gaikwad
, D.
Rehal
, A.
Singh
, Arvind
, and K.
Dorai
, “Experimental demonstration of selective quantum process tomography on an nmr quantum information processor
,” Phys. Rev. A
97
, 022311
(2018
).19.
A.
Bendersky
, F.
Pastawski
, and J. P.
Paz
, “Selective and efficient estimation of parameters for quantum process tomography
,” Phys. Rev. Lett.
100
, 190403
(2008
).20.
L. C. G.
Govia
, G. J.
Ribeill
, D.
Ristè
, M.
Ware
, and H.
Krovi
, “Bootstrapping quantum process tomography via a perturbative ansatz
,” Nat. Commns.
11
, 1084
(2020
).21.
B. P.
Lanyon
, M.
Barbieri
, M. P.
Almeida
, T.
Jennewein
, T. C.
Ralph
, K. J.
Resch
, G. J.
Pryde
, J. L.
O’Brien
, A.
Gilchrist
, and A. G.
White
, “Simplifying quantum logic using higher-dimensional hilbert spaces
,” Nat Phys
5
, 134
–140
(2009
).22.
G. S.
Paraoanu
, “Recent progress in quantum simulation using superconducting circuits
,” J. Low Temp. Phys.
175
, 633
–654
(2014
).23.
J. Q.
You
and F.
Nori
, “Atomic physics and quantum optics usingsuperconducting circuits
,” Nature
474
, 589
(2011
).24.
H.-S.
Chang
, Y. P.
Zhong
, A.
Bienfait
, M.-H.
Chou
, C. R.
Conner
, E.
Dumur
, G.
Grebel
, G.
Peairs
, R. G.
Povey
, K. J.
Satzinger
, and A. N.
Cleland
, “Remote entanglement via adiabatic passage using a tunably-dissipative quantum communication system
,” arXiv:2005.12334v1 (2020
).25.
A. R.
Shlyakhov
, V. V.
Zemlyanov
, M. V.
Suslov
, A. V.
Lebedev
, G. S.
Paraoanu
, G. B.
Lesovik
, and G.
Blatter
, “Quantum metrology with a transmon qutrit
,” Physical Review A
97
(2018
), .26.
S.
Danilin
, A. V.
Lebedev
, A.
Vepsäläinen
, G. B.
Lesovik
, G.
Blatter
, and G. S.
Paraoanu
, “Quantum-enhanced magnetometry by phase estimation algorithms with a single artificial atom
,” npj Quantum Information
4
(2018
), .27.
M. S.
Blok
, V. V.
Ramasesh
, T.
Schuster
, K.
O’Brien
, J. M.
Kreikebaum
, D.
Dahlen
, A.
Morvan
, N. Y.
Yoshida
, B. amd
Yao
, and S. I., “Quantum information scrambling in a superconducting qutrit processor
,” arXiv:2003.03307 (2020
).28.
G.
Falci
, A.
Ridolfo
, P. G.
Di Stefano
, and E.
Paladino
, “Ultrastrong coupling probed by coherent population transfer
,” Scientific Reports
, 9249
(2019
).29.
K.
Bergmann
, H.-C.
Nägerl
, C.
Panda
, G.
Gabrielse
, E.
Miloglyadov
, M.
Quack
, G.
Seyfang
, G.
Wichmann
, S.
Ospelkaus
, A.
Kuhn
, S.
Longhi
, A.
Szameit
, P.
Pirro
, B.
Hillebrands
, X.-F.
Zhu
, J.
Zhu
, M.
Drewsen
, W. K.
Hensinger
, S.
Weidt
, T.
Halfmann
, H.-L.
Wang
, G. S.
Paraoanu
, N. V.
Vitanov
, J.
Mompart
, T.
Busch
, T. J.
Barnum
, D. D.
Grimes
, R. W.
Field
, M. G.
Raizen
, E.
Narevicius
, M.
Auzinsh
, D.
Budker
, A.
Pálffy
, and C. H.
Keitel
, “Roadmap on STIRAP applications
,” J. Phys. B
52
, 202001
(2019
).30.
K. S.
Kumar
, A.
Vepsäläinen
, S.
Danilin
, and G. S.
Paraoanu
, “Stimulated raman adiabatic passage in a three-level superconducting circuit
,” Nat. Commun.
7
(2016
).31.
E.
Torrontegui
, S.
Ibáñez
, S.
Martínez-Garaot
, M.
Modugno
, A.
del Campo
, D.
Guéry-Odelin
, A.
Ruschhaupt
, X.
Chen
, and J. G.
Muga
, “Chapter 2 - shortcuts to adiabaticity
,” in Advances in Atomic, Molecular, and Optical Physics
, Advances In Atomic, Molecular, and Optical Physics
, Vol. 62
, edited by P. R. B. Ennio
Arimondo
and C. C.
Lin
(Academic Press
, 2013
) pp. 117
–169
.32.
A.
Vepsäläinen
, S.
Danilin
, and G. S.
Paraoanu
, “Superadiabatic population transfer in a three-level superconducting circuit
,” Sci. Adv.
5
(2019
).33.
A.
Vepsäläinen
, S.
Danilin
, and G. S.
Paraoanu
, “Optimal superadiabatic population transfer and gates by dynamical phase corrections
,” Quantum Sci. Technol.
3
, 024006
(2018
).34.
A.
Vepsäläinen
, S.
Danilin
, E.
Paladino
, G.
Falci
, and G. S.
Paraoanu
, “Quantum control in qutrit systems using hybrid rabi-stirap pulses
,” Photonics
3
(2016
), .35.
S.
Dogra
, A.
Vepsäläinen
, and G. S.
Paraoanu
, “Majorana representation of adiabatic and superadiabatic processes in three-level systems
,” Phys. Rev. Research
2
, 043079
(2020
).36.
K.
Kraus
, “General state changes in quantum theory
,” Annals of Physics
64
, 311
–335
(1971
).37.
J.
Stolze
and D.
Suter
, Quantum Computing: A Short Course from Theory to Experiment
(John Wiley & Sons
, 2004
).38.
G.
Falci
, P. G.
Di Stefano
, A.
Ridolfo
, A.
D’Arrigo
, G. S.
Paraoanu
, and E.
Paladino
, “Advances in quantum control of three-level supercon-ducting circuit architectures
,” Fortschritte der Phys.
65
, 1600077
(2017
).39.
A.
Vepsäläinen
, S.
Danilin
, and G. S.
Paraoanu
, “Simulating spin chains using a superconducting circuit: Gauge invariance, superadiabatic transport, and broken time-reversal symmetry
,” Adv. Quantum Technol.
3
, 1900121
(2020
).
This content is only available via PDF.
© 2021 Author(s).
2021
Author(s)
