A Multi-Qubit Quantum Gate Using the Zeno Effect

Philippe Lewalle1,2, Leigh S. Martin1,3, Emmanuel Flurin1,3, Song Zhang2, Eliya Blumenthal4, Shay Hacohen-Gourgy4, Daniel Burgarth5, and K. Birgitta Whaley1,2

1Berkeley Center for Quantum Information and Computation, Berkeley, California 94720 USA
2Department of Chemistry, University of California, Berkeley, California 94720 USA
3Department of Physics, University of California, Berkeley, California 94720 USA
4Department of Physics, Technion - Israel Institute of Technology, Haifa 32000 Israel
5Center for Engineered Quantum Systems, Macquarie University, 2109 NSW, Australia

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

The Zeno effect, in which repeated observation freezes the dynamics of a quantum system, stands as an iconic oddity of quantum mechanics. When a measurement is unable to distinguish between states in a subspace, the dynamics within that subspace can be profoundly altered, leading to non-trivial behavior. Here we show that such a measurement can turn a non-interacting system with only single-qubit control into a two- or multi-qubit entangling gate, which we call a Zeno gate. The gate works by imparting a geometric phase on the system, conditioned on it lying within a particular nonlocal subspace. We derive simple closed-form expressions for the gate fidelity under a number of non-idealities and show that the gate is viable for implementation in circuit and cavity QED systems. More specifically, we illustrate the functioning of the gate via dispersive readout in both the Markovian and non-Markovian readout regimes, and derive conditions for longitudinal readout to ideally realize the gate.

In gate-based quantum computation, algorithms are assembled from sequences of discrete single- and multi-qubit operations. Quantum systems are, by definition, so isolated from external influences that quantum measurements are necessarily an invasive process that alters the physics. The Quantum Zeno Effect refers to a particular manifestation of this principle: Repeated strong quantum measurements will tend to freeze a quantum system in a particular state, inhibiting the dynamics that the system would have undergone unobserved. While quantum gates are most often engineered using the unitary (isolated) dynamics, we here propose a method to realize multi-qubit quantum gates using (open system) Zeno dynamics instead.

In particular, we here propose a family of “Zeno gates'' that realize the dynamics of a conditional phase gate across multiple qubits. Our scheme relies on a local unitary operation using an auxiliary level of one system (one qutrit). The non-local (entangling) aspect of the gate is however realized via the Zeno effect: By engineering a measurement that Zeno blocks transition to the highest joint excitation level of the multi-qubit system, we transform the simple unitary into a multi-qubit gate that could become a building block for computations. Our analysis characterizes the gate performance under increasingly less ideal / more realistic conditions, eventually emphasizing a realization based on two superconducting qudits. Our results here generalize and expand on a recent proof-of-principle experiment [Blumenthal et al., npj Quantum Information 8, 88 (2022)], and suggest several pathways towards improvement of our Zeno gate under realistic conditions.

► BibTeX data

► References

[1] B. Misra and E. C. G. Sudarshan. ``The Zeno’s paradox in quantum theory''. Journal of Mathematical Physics 18, 756–763 (1977).
https:/​/​doi.org/​10.1063/​1.523304

[2] P Facchi and S Pascazio. ``Quantum Zeno dynamics: mathematical and physical aspects''. Journal of Physics A: Mathematical and Theoretical 41, 493001 (2008).
https:/​/​doi.org/​10.1088/​1751-8113/​41/​49/​493001

[3] Florian Schäfer, Ivan Herrera, Shahid Cherukattil, Cosimo Lovecchio, Francesco Saverio Cataliotti, Filippo Caruso, and Augusto Smerzi. ``Experimental realization of quantum zeno dynamics''. Nature communications 5, 3194 (2014).
https:/​/​doi.org/​10.1038/​ncomms4194

[4] J. M. Raimond, P. Facchi, B. Peaudecerf, S. Pascazio, C. Sayrin, I. Dotsenko, S. Gleyzes, M. Brune, and S. Haroche. ``Quantum Zeno dynamics of a field in a cavity''. Phys. Rev. A 86, 032120 (2012).
https:/​/​doi.org/​10.1103/​PhysRevA.86.032120

[5] Mazyar Mirrahimi, Zaki Leghtas, Victor V Albert, Steven Touzard, Robert J Schoelkopf, Liang Jiang, and Michel H Devoret. ``Dynamically protected cat-qubits: a new paradigm for universal quantum computation''. New Journal of Physics 16, 045014 (2014).
https:/​/​doi.org/​10.1088/​1367-2630/​16/​4/​045014

[6] Jérémie Guillaud and Mazyar Mirrahimi. ``Repetition cat qubits for fault-tolerant quantum computation''. Phys. Rev. X 9, 041053 (2019).
https:/​/​doi.org/​10.1103/​PhysRevX.9.041053

[7] Daniel Klaus Burgarth, Paolo Facchi, Vittorio Giovannetti, Hiromichi Nakazato, Saverio Pascazio, and Kazuya Yuasa. ``Exponential rise of dynamical complexity in quantum computing through projections''. Nature communications 5, 5173 (2014).
https:/​/​doi.org/​10.1038/​ncomms6173

[8] Eliya Blumenthal, Chen Mor, Asaf A. Diringer, Leigh S. Martin, Philippe Lewalle, Daniel Burgarth, K. Birgitta Whaley, and Shay Hacohen-Gourgy. ``Demonstration of universal control between non-interacting qubits using the quantum Zeno effect''. npj Quantum Information 8 (2022).
https:/​/​doi.org/​10.1038/​s41534-022-00594-4

[9] Nathan S. Williams and Andrew N. Jordan. ``Entanglement genesis under continuous parity measurement''. Phys. Rev. A 78, 062322 (2008).
https:/​/​doi.org/​10.1103/​PhysRevA.78.062322

[10] Leigh Martin, Mahrud Sayrafi, and K Birgitta Whaley. ``What is the optimal way to prepare a Bell state using measurement and feedback?''. Quantum Science and Technology 2, 044006 (2017).
https:/​/​doi.org/​10.1088/​2058-9565/​aa804c

[11] Leigh S. Martin and K. Birgitta Whaley. ``Single-shot deterministic entanglement between non-interacting systems with linear optics'' (2019). arXiv:1912.00067.
arXiv:1912.00067

[12] Philippe Lewalle, Cyril Elouard, Sreenath K. Manikandan, Xiao-Feng Qian, Joseph H. Eberly, and Andrew N. Jordan. ``Entanglement of a pair of quantum emitters via continuous fluorescence measurements: a tutorial''. Adv. Opt. Photon. 13, 517–583 (2021).
https:/​/​doi.org/​10.1364/​AOP.399081

[13] Philippe Lewalle, Cyril Elouard, and Andrew N. Jordan. ``Entanglement-preserving limit cycles from sequential quantum measurements and feedback''. Phys. Rev. A 102, 062219 (2020).
https:/​/​doi.org/​10.1103/​PhysRevA.102.062219

[14] Y. P. Huang and M. G. Moore. ``Interaction- and measurement-free quantum zeno gates for universal computation with single-atom and single-photon qubits''. Phys. Rev. A 77, 062332 (2008).
https:/​/​doi.org/​10.1103/​PhysRevA.77.062332

[15] L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage, T. A. Johnson, T. G. Walker, and M. Saffman. ``Demonstration of a neutral atom controlled-not quantum gate''. Phys. Rev. Lett. 104, 010503 (2010).
https:/​/​doi.org/​10.1103/​PhysRevLett.104.010503

[16] Yaoyun Shi. ``Both Toffoli and controlled-not need little help to do universal quantum computation'' (2002). arXiv:quant-ph/​0205115.
arXiv:quant-ph/0205115

[17] Sean D. Barrett and Pieter Kok. ``Efficient high-fidelity quantum computation using matter qubits and linear optics''. Phys. Rev. A 71, 060310 (2005).
https:/​/​doi.org/​10.1103/​PhysRevA.71.060310

[18] M. F. Santos, M. Terra Cunha, R. Chaves, and A. R. R. Carvalho. ``Quantum computing with incoherent resources and quantum jumps''. Phys. Rev. Lett. 108, 170501 (2012).
https:/​/​doi.org/​10.1103/​PhysRevLett.108.170501

[19] Daniel Burgarth, Paolo Facchi, Vittorio Giovannetti, Hiromichi Nakazato, Saverio Pascazio, and Kazuya Yuasa. ``Non-Abelian phases from quantum Zeno dynamics''. Phys. Rev. A 88, 042107 (2013).
https:/​/​doi.org/​10.1103/​PhysRevA.88.042107

[20] Jun Zhang. ``Geometric method in quantum control''. Chin. Sci. Bull. 57, 2223–222 (2012).
https:/​/​doi.org/​10.1007/​s11434-012-5186-z

[21] Vivek V. Shende and Igor L. Markov. ``On the CNOT-cost of Toffoli gates''. Quantum Info. Comput. 9, 461–486 (2009). arXiv:0803.2316.
arXiv:0803.2316

[22] Yelena Guryanova, Nicolai Friis, and Marcus Huber. ``Ideal Projective Measurements Have Infinite Resource Costs''. Quantum 4, 222 (2020).
https:/​/​doi.org/​10.22331/​q-2020-01-13-222

[23] Kyrylo Snizhko, Parveen Kumar, and Alessandro Romito. ``Quantum Zeno effect appears in stages''. Phys. Rev. Research 2, 033512 (2020).
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.033512

[24] Parveen Kumar, Alessandro Romito, and Kyrylo Snizhko. ``Quantum Zeno effect with partial measurement and noisy dynamics''. Phys. Rev. Research 2, 043420 (2020).
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.043420

[25] Patrick M. Harrington, Erich Mueller, and Kater Murch. ``Engineered dissipation for quantum information science'' (2022). arXiv:2202.05280.
arXiv:2202.05280

[26] H. M. Wiseman and G. J. Milburn. ``Quantum measurement and control''. Cambridge University Press. (2009).
https:/​/​doi.org/​10.1017/​CBO9780511813948

[27] Kurt Jacobs. ``Quantum measurement theory and its applications''. Cambridge University Press. (2014).
https:/​/​doi.org/​10.1017/​CBO9781139179027

[28] Alexandre Blais, Arne L. Grimsmo, S. M. Girvin, and Andreas Wallraff. ``Circuit quantum electrodynamics''. Rev. Mod. Phys. 93, 025005 (2021).
https:/​/​doi.org/​10.1103/​RevModPhys.93.025005

[29] D Ristè, M Dukalski, C A Watson, G de Lange, M J Tiggelman, Ya M Blanter, K W Lehnert, R N Schouten, and L DiCarlo. ``Deterministic entanglement of superconducting qubits by parity measurement and feedback''. Nature 502, 350 (2013).
https:/​/​doi.org/​10.1038/​nature12513

[30] N. Roch, M. E. Schwartz, F. Motzoi, C. Macklin, R. Vijay, A. W. Eddins, A. N. Korotkov, K. B. Whaley, M. Sarovar, and I. Siddiqi. ``Observation of measurement-induced entanglement and quantum trajectories of remote superconducting qubits''. Phys. Rev. Lett. 112, 170501 (2014).
https:/​/​doi.org/​10.1103/​PhysRevLett.112.170501

[31] Ananda Roy, Liang Jiang, A. Douglas Stone, and Michel Devoret. ``Remote entanglement by coherent multiplication of concurrent quantum signals''. Phys. Rev. Lett. 115, 150503 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.115.150503

[32] Shay Hacohen-Gourgy, Leigh S Martin, Emmanuel Flurin, Vinay V Ramasesh, K Birgitta Whaley, and Irfan Siddiqi. ``Quantum dynamics of simultaneously measured non-commuting observables''. Nature 538, 491 (2016).
https:/​/​doi.org/​10.1038/​nature19762

[33] Zlatko K Minev, Shantanu O Mundhada, Shyam Shankar, Philip Reinhold, Ricardo Gutiérrez-Jáuregui, Robert J Schoelkopf, Mazyar Mirrahimi, Howard J Carmichael, and Michel H Devoret. ``To catch and reverse a quantum jump mid-flight''. Nature 570, 200–204 (2019).
https:/​/​doi.org/​10.1038/​s41586-019-1287-z

[34] Crispin Gardiner and Peter Zoller. ``Quantum noise: a handbook of Markovian and non-Markovian quantum stochastic methods with applications to quantum optics''. Volume 56. Springer Science & Business Media. (2004). url: link.springer.com/​book/​9783540223016.
https:/​/​link.springer.com/​book/​9783540223016

[35] Jay Gambetta, Alexandre Blais, M. Boissonneault, A. A. Houck, D. I. Schuster, and S. M. Girvin. ``Quantum trajectory approach to circuit qed: Quantum jumps and the zeno effect''. Phys. Rev. A 77, 012112 (2008).
https:/​/​doi.org/​10.1103/​PhysRevA.77.012112

[36] Philippe Lewalle, Sreenath K. Manikandan, Cyril Elouard, and Andrew N. Jordan. ``Measuring fluorescence to track a quantum emitter's state: a theory review''. Contemporary Physics 61, 26–50 (2020).
https:/​/​doi.org/​10.1080/​00107514.2020.1747201

[37] Daniel Burgarth, Paolo Facchi, Hiromichi Nakazato, Saverio Pascazio, and Kazuya Yuasa. ``Generalized Adiabatic Theorem and Strong-Coupling Limits''. Quantum 3, 152 (2019).
https:/​/​doi.org/​10.22331/​q-2019-06-12-152

[38] Alexandre Blais, Ren-Shou Huang, Andreas Wallraff, S. M. Girvin, and R. J. Schoelkopf. ``Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation''. Phys. Rev. A 69, 062320 (2004).
https:/​/​doi.org/​10.1103/​PhysRevA.69.062320

[39] Alexander N. Korotkov. ``Quantum Bayesian approach to circuit QED measurement with moderate bandwidth''. Phys. Rev. A 94, 042326 (2016).
https:/​/​doi.org/​10.1103/​PhysRevA.94.042326

[40] Francesco Ciccarello, Salvatore Lorenzo, Vittorio Giovannetti, and G. Massimo Palma. ``Quantum collision models: Open system dynamics from repeated interactions''. Physics Reports 954, 1–70 (2022).
https:/​/​doi.org/​10.1016/​j.physrep.2022.01.001

[41] Salvatore Lorenzo, Francesco Ciccarello, and G. Massimo Palma. ``Composite quantum collision models''. Phys. Rev. A 96, 032107 (2017).
https:/​/​doi.org/​10.1103/​PhysRevA.96.032107

[42] John Steinmetz, Debmalya Das, Irfan Siddiqi, and Andrew N. Jordan. ``Continuous measurement of a qudit using dispersively coupled radiation''. Phys. Rev. A 105, 052229 (2022).
https:/​/​doi.org/​10.1103/​PhysRevA.105.052229

[43] A. A. Clerk, M. H. Devoret, S. M. Girvin, Florian Marquardt, and R. J. Schoelkopf. ``Introduction to quantum noise, measurement, and amplification''. Rev. Mod. Phys. 82, 1155–1208 (2010).
https:/​/​doi.org/​10.1103/​RevModPhys.82.1155

[44] Andrew W. Cross and Jay M. Gambetta. ``Optimized pulse shapes for a resonator-induced phase gate''. Phys. Rev. A 91, 032325 (2015).
https:/​/​doi.org/​10.1103/​PhysRevA.91.032325

[45] Hanhee Paik, A. Mezzacapo, Martin Sandberg, D. T. McClure, B. Abdo, A. D. Córcoles, O. Dial, D. F. Bogorin, B. L. T. Plourde, M. Steffen, A. W. Cross, J. M. Gambetta, and Jerry M. Chow. ``Experimental demonstration of a resonator-induced phase gate in a multiqubit circuit-QED system''. Phys. Rev. Lett. 117, 250502 (2016).
https:/​/​doi.org/​10.1103/​PhysRevLett.117.250502

[46] K W Murch, S J Weber, C Macklin, and I. Siddiqi. ``Observing single quantum trajectories of a superconducting quantum bit''. Nature 502, 211 (2013).
https:/​/​doi.org/​10.1038/​nature12539

[47] Daniel Szombati, Alejandro Gomez Frieiro, Clemens Müller, Tyler Jones, Markus Jerger, and Arkady Fedorov. ``Quantum rifling: Protecting a qubit from measurement back action''. Phys. Rev. Lett. 124, 070401 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.124.070401

[48] Lorenza Viola and Seth Lloyd. ``Dynamical suppression of decoherence in two-state quantum systems''. Phys. Rev. A 58, 2733–2744 (1998).
https:/​/​doi.org/​10.1103/​PhysRevA.58.2733

[49] Lorenza Viola. ``Advances in decoherence control''. Journal of Modern Optics 51, 2357–2367 (2004).
https:/​/​doi.org/​10.1080/​09500340408231795

[50] G. Koolstra, N. Stevenson, S. Barzili, L. Burns, K. Siva, S. Greenfield, W. Livingston, A. Hashim, R. K. Naik, J. M. Kreikebaum, K. P. O'Brien, D. I. Santiago, J. Dressel, and I. Siddiqi. ``Monitoring fast superconducting qubit dynamics using a neural network''. Phys. Rev. X 12, 031017 (2022).
https:/​/​doi.org/​10.1103/​PhysRevX.12.031017

[51] William K. Wootters. ``Entanglement of Formation of an Arbitrary State of Two Qubits''. Phys. Rev. Lett. 80, 2245–2248 (1998).
https:/​/​doi.org/​10.1103/​PhysRevLett.80.2245

[52] Daniel Sank, Zijun Chen, Mostafa Khezri, J. Kelly, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. Fowler, E. Jeffrey, E. Lucero, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O'Malley, C. Quintana, P. Roushan, A. Vainsencher, T. White, J. Wenner, Alexander N. Korotkov, and John M. Martinis. ``Measurement-induced state transitions in a superconducting qubit: Beyond the rotating wave approximation''. Phys. Rev. Lett. 117, 190503 (2016).
https:/​/​doi.org/​10.1103/​PhysRevLett.117.190503

[53] T. Walter, P. Kurpiers, S. Gasparinetti, P. Magnard, A. Potočnik, Y. Salathé, M. Pechal, M. Mondal, M. Oppliger, C. Eichler, and A. Wallraff. ``Rapid high-fidelity single-shot dispersive readout of superconducting qubits''. Phys. Rev. Applied 7, 054020 (2017).
https:/​/​doi.org/​10.1103/​PhysRevApplied.7.054020

[54] Raphaël Lescanne, Lucas Verney, Quentin Ficheux, Michel H. Devoret, Benjamin Huard, Mazyar Mirrahimi, and Zaki Leghtas. ``Escape of a driven quantum Josephson circuit into unconfined states''. Phys. Rev. Applied 11, 014030 (2019).
https:/​/​doi.org/​10.1103/​PhysRevApplied.11.014030

[55] Moein Malekakhlagh, Alexandru Petrescu, and Hakan E. Türeci. ``Lifetime renormalization of weakly anharmonic superconducting qubits. I. Role of number nonconserving terms''. Phys. Rev. B 101, 134509 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.101.134509

[56] Alexandru Petrescu, Moein Malekakhlagh, and Hakan E. Türeci. ``Lifetime renormalization of driven weakly anharmonic superconducting qubits. II. The readout problem''. Phys. Rev. B 101, 134510 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.101.134510

[57] Daria Gusenkova, Martin Spiecker, Richard Gebauer, Madita Willsch, Dennis Willsch, Francesco Valenti, Nick Karcher, Lukas Grünhaupt, Ivan Takmakov, Patrick Winkel, Dennis Rieger, Alexey V. Ustinov, Nicolas Roch, Wolfgang Wernsdorfer, Kristel Michielsen, Oliver Sander, and Ioan M. Pop. ``Quantum nondemolition dispersive readout of a superconducting artificial atom using large photon numbers''. Phys. Rev. Applied 15, 064030 (2021).
https:/​/​doi.org/​10.1103/​PhysRevApplied.15.064030

[58] Ross Shillito, Alexandru Petrescu, Joachim Cohen, Jackson Beall, Markus Hauru, Martin Ganahl, Adam G.M. Lewis, Guifre Vidal, and Alexandre Blais. ``Dynamics of transmon ionization''. Phys. Rev. Appl. 18, 034031 (2022).
https:/​/​doi.org/​10.1103/​PhysRevApplied.18.034031

[59] Nicolas Didier, Jérôme Bourassa, and Alexandre Blais. ``Fast quantum nondemolition readout by parametric modulation of longitudinal qubit-oscillator interaction''. Phys. Rev. Lett. 115, 203601 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.115.203601

[60] Leigh S. Martin. ``Quantum feedback for measurement and control'' (2020). arXiv:2004.09766.
arXiv:2004.09766

[61] A. Eddins, S. Schreppler, D. M. Toyli, L. S. Martin, S. Hacohen-Gourgy, L. C. G. Govia, H. Ribeiro, A. A. Clerk, and I. Siddiqi. ``Stroboscopic qubit measurement with squeezed illumination''. Phys. Rev. Lett. 120, 040505 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.120.040505

[62] Jing Zhang, Yu xi Liu, Re-Bing Wu, Kurt Jacobs, and Franco Nori. ``Quantum feedback: Theory, experiments, and applications''. Physics Reports 679, 1–60 (2017).
https:/​/​doi.org/​10.1016/​j.physrep.2017.02.003

[63] Raphaël Lescanne, Marius Villiers, Théau Peronnin, Alain Sarlette, Matthieu Delbecq, Benjamin Huard, Takis Kontos, Mazyar Mirrahimi, and Zaki Leghtas. ``Exponential suppression of bit-flips in a qubit encoded in an oscillator''. Nature Physics 16, 509–513 (2020).
https:/​/​doi.org/​10.1038/​s41567-020-0824-x

[64] Ronan Gautier, Alain Sarlette, and Mazyar Mirrahimi. ``Combined dissipative and hamiltonian confinement of cat qubits''. PRX Quantum 3, 020339 (2022).
https:/​/​doi.org/​10.1103/​PRXQuantum.3.020339

[65] Lev-Arcady Sellem, Philippe Campagne-Ibarcq, Mazyar Mirrahimi, Alain Sarlette, and Pierre Rouchon. ``Exponential convergence of a dissipative quantum system towards finite-energy grid states of an oscillator''. In 2022 IEEE 61st Conference on Decision and Control (CDC). Pages 5149–5154. (2022).
https:/​/​doi.org/​10.1109/​CDC51059.2022.9992722

[66] Lev-Arcady Sellem, Rémi Robin, Philippe Campagne-Ibarcq, and Pierre Rouchon. ``Stability and decoherence rates of a GKP qubit protected by dissipation'' (2023). arXiv:2304.03806.
arXiv:2304.03806

[67] Ronan Gautier, Mazyar Mirrahimi, and Alain Sarlette. ``Designing high-fidelity gates for dissipative cat qubits'' (2023). arXiv:2303.00760.
arXiv:2303.00760

[68] François-Marie Le Régent and Pierre Rouchon. ``Adiabatic elimination for composite open quantum systems: Heisenberg formulation and numerical simulations'' (2023). arXiv:2303.05089.
arXiv:2303.05089

[69] Maris Ozols. ``How to generate a random unitary matrix'' (2009).

[70] Michael A Nielsen. ``A simple formula for the average gate fidelity of a quantum dynamical operation''. Physics Letters A 303, 249–252 (2002).
https:/​/​doi.org/​10.1016/​S0375-9601(02)01272-0

[71] Shay Hacohen-Gourgy and Leigh S. Martin. ``Continuous measurements for control of superconducting quantum circuits''. Advances in Physics: X 5, 1813626 (2020).
https:/​/​doi.org/​10.1080/​23746149.2020.1813626

Cited by

[1] A. H. Abbas and Ivan S. Maksymov, "Reservoir Computing Using Measurement-Controlled Quantum Dynamics", Electronics 13 6, 1164 (2024).

[2] Yunzhao Wang, Kyrylo Snizhko, Alessandro Romito, Yuval Gefen, and Kater Murch, "Dissipative preparation and stabilization of many-body quantum states in a superconducting qutrit array", Physical Review A 108 1, 013712 (2023).

[3] Philippe Lewalle, Yipei Zhang, and K. Birgitta Whaley, "Optimal Zeno Dragging for Quantum Control: A Shortcut to Zeno with Action-based Scheduling Optimization", arXiv:2311.01631, (2023).

[4] Sven Jandura, Vineesha Srivastava, Laura Pecorari, Gavin Brennen, and Guido Pupillo, "Non-Local Multi-Qubit Quantum Gates via a Driven Cavity", arXiv:2303.13127, (2023).

[5] A. H. Abbas and Ivan S. Maksymov, "Reservoir Computing Using Measurement-Controlled Quantum Dynamics", arXiv:2403.01024, (2024).

[6] Maria Elovenkova and Alexander Pechen, "Control landscape of measurement-assisted transition probability for a three-level quantum system with dynamical symmetry", arXiv:2307.07450, (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2024-06-22 03:31:20) and SAO/NASA ADS (last updated successfully 2024-06-22 03:31:21). The list may be incomplete as not all publishers provide suitable and complete citation data.