- Open Access
Resource-state generation for a multispin register in a hybrid matter-photon quantum information processor
Phys. Rev. Applied 25, 024002 – Published 2 February, 2026
DOI: https://doi.org/10.1103/185z-nxt1
Abstract
Hybrid quantum architectures that integrate matter and photonic degrees of freedom present a promising pathway toward scalable fault-tolerant quantum computing. This approach needs to combine well-established entangling operations between distant registers using photonic degrees of freedom with direct interactions between matter qubits within a solid-state register. The high-fidelity control of such a register, however, poses significant challenges. In this work, we address these challenges with pulsed control sequences that modulate all interspin interactions to preserve the nearest-neighbor couplings while eliminating unwanted long-range interactions. We derive pulse sequences, including broadband and selective gates, using composite-pulse and shaped-pulse techniques as well as optimal-control methods. This ensures a general pulse sequence in the presence of spin-position bias, robustness against static offset detunings, and Rabi-frequency fluctuations of the control fields. The control techniques developed here apply well beyond the present setting to a broad range of physical platforms. We demonstrate the efficacy of our methods for the resource-state generation for fusion-based quantum computing in four- and six-spin systems encoded in the electronic ground states of nitrogen-vacancy centers or other molecular solid-state qubits. We also outline other elements of the proposed architecture, highlighting its potential for advancing quantum computing technology.
Physics Subject Headings (PhySH)
Article Text
References (113)
- D. Deutsch, Quantum theory, the Church-Turing principle and the universal quantum computer, Proc. Roy. Soc. A 400, 97 (1985).
- V. Vedral and M. B. Plenio, Basics of quantum computation, Prog. Quantum Electron. 22, 1 (1998).
- D. Gottesman and I. L. Chuang, Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations, Nature 402, 390 (1999).
- J. Eisert, K. Jacobs, P. Papadopoulos, and M. B. Plenio, Optimal local implementation of nonlocal quantum gates, Phys. Rev. A 62, 052317 (2000).
- R. Raussendorf and H. J. Briegel, A one-way quantum computer, Phys. Rev. Lett. 86, 5188 (2001).
- M. A. Nielsen, Optical quantum computation using cluster states, Phys. Rev. Lett. 93, 040503 (2004).
- H. J. Briegel, D. E. Browne, W. Dür, R. Raussendorf, and M. Van den Nest, Measurement-based quantum computation, Nat. Phys. 5, 19 (2009).
- R. Raussendorf, D. E. Browne, and H. J. Briegel, Measurement-based quantum computation on cluster states, Phys. Rev. A 68, 022312 (2003).
- M. A. Nielsen, Cluster-state quantum computation, Rep. Math. Phys. 57, 147 (2006).
- E. Knill, R. Laflamme, and G. J. Milburn, A scheme for efficient quantum computation with linear optics, Nature 409, 46 (2001).
- D. E. Browne and T. Rudolph, Resource-efficient linear optical quantum computation, Phys. Rev. Lett. 95, 010501 (2005).
- M. A. Nielsen and C. M. Dawson, Fault-tolerant quantum computation with cluster states, Phys. Rev. A 71, 042323 (2005).
- H. Bombin, I. H. Kim, D. Litinski, N. Nickerson, M. Pant, F. Pastawski, S. Roberts, and T. Rudolph, Interleaving: Modular architectures for fault-tolerant photonic quantum computing, arXiv:2103.08612 [quant-ph].
- S. Bartolucci, P. Birchall, H. Bombín, H. Cable, C. Dawson, M. Gimeno-Segovia, E. Johnston, K. Kieling, N. Nickerson, M. Pant, F. Pastawski, T. Rudolph, and C. Sparrow, Fusion-based quantum computation, Nat. Commun. 14, 912 (2023).
- S. Bose, P. L. Knight, M. B. Plenio, and V. Vedral, Proposal for teleportation of an atomic state via cavity decay, Phys. Rev. Lett. 83, 5158 (1999).
- PsiQuantum team, A manufacturable platform for photonic quantum computing, Nature 641, 876 (2025).
- I. Schwartz, D. Cogan, E. R. Schmidgall, Y. Don, L. Gantz, O. Kenneth, N. H. Lindner, and D. Gershoni, Deterministic generation of a cluster state of entangled photons, Science 354, 434 (2016).
- M. V. Larsen, X. Guo, C. R. Breum, J. S. Neergaard-Nielsen, and U. L. Andersen, Deterministic generation of a two-dimensional cluster state, Science 366, 369 (2019).
- D. Istrati, Y. Pilnyak, J. C. Loredo, C. Antón, N. Somaschi, P. Hilaire, H. Ollivier, M. Esmann, L. Cohen, L. Vidro, C. Millet, A. Lemaître, I. Sagnes, A. Harouri, L. Lanco, P. Senellart, and H. S. Eisenberg, Sequential generation of linear cluster states from a single photon emitter, Nat. Commun. 11, 5501 (2020).
- V. S. Ferreira, G. Kim, A. Butler, H. Pichler, and O. Painter, Deterministic generation of multidimensional photonic cluster states with a single quantum emitter, Nat. Phys. 20, 865 (2024).
- G. de Gliniasty, P. Hilaire, P.-E. Emeriau, S. C. Wein, A. Salavrakos, and S. Mansfield, A spin-optical quantum computing architecture, Quantum 8, 1423 (2024).
- K. Nemoto, M. Trupke, S. J. Devitt, A. M. Stephens, B. Scharfenberger, K. Buczak, T. Nöbauer, M. S. Everitt, J. Schmiedmayer, and W. J. Munro, Photonic architecture for scalable quantum information processing in diamond, Phys. Rev. X 4, 031022 (2014).
- J.-Y. Zhang, Z.-W. Zhou, and G.-C. Guo, Eliminating next-nearest-neighbor interactions in the preparation of cluster state, Chin. Phys. Lett. 28, 050301 (2011).
- M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko, J. Wrachtrup, and L. C. L. Hollenberg, The nitrogen-vacancy colour centre in diamond, Phys. Rep. 528, 1 (2013).
- Y. Wu, F. Jelezko, M. B. Plenio, and T. Weil, Diamond quantum devices in biology, Angew. Chem. Int. Ed. 55, 6586 (2016).
- F. Dolde, V. Bergholm, Y. Wang, I. Jakobi, B. Naydenov, S. Pezzagna, J. Meijer, F. Jelezko, P. Neumann, T. Schulte-Herbrügen, J. Biamonte, and J. Wrachtrup, High-fidelity spin entanglement using optimal control, Nat. Commun. 5, 3371 (2014).
- C. E. Bradley, J. Randall, M. H. Abobeih, R. C. Berrevoets, M. J. Degen, M. A. Bakker, M. Markham, D. J. Twitchen, and T. H. Taminiau, A ten-qubit solid-state spin register with quantum memory up to one minute, Phys. Rev. X 9, 031045 (2019).
- T. Xie, Z. Zhao, S. Xu, X. Kong, Z. Yang, M. Wang, Y. Wang, F. Shi, and J. Du, 99.92%-fidelity cnot gates in solids by noise filtering, Phys. Rev. Lett. 130, 030601 (2023).
- H. P. Bartling, J. Yun, K. N. Schymik, M. van Riggelen, L. A. Enthoven, H. B. van Ommen, M. Babaie, F. Sebastiano, M. Markham, D. J. Twitchen, and T. H. Taminiau, Universal high-fidelity quantum gates for spin qubits in diamond, Phys. Rev. Appl. 23, 034052 (2025).
- T. Joas, F. Ferlemann, R. Sailer, P. J. Vetter, J. Zhang, R. S. Said, T. Teraji, S. Onoda, T. Calarco, G. Genov, M. M. Müller, and F. Jelezko, High-fidelity electron spin gates for scaling diamond quantum registers, Phys. Rev. X 15, 021069 (2025).
- I. Jakobi, S. A. Momenzadeh, F. Fávaro de Oliveira, J. Michl, F. Ziem, M. Schreck, P. Neumann, A. Denisenko, and J. Wrachtrup, Efficient creation of dipolar coupled nitrogen-vacancy spin qubits in diamond, J. Phys.: Conf. Ser. 752, 012001 (2016).
- A. Tobalina, C. Munuera-Javaloy, E. Torrontegui, J. G. Muga, and J. Casanova, Tailored ion beam for precise colour centre creation, Philos. Trans. R. Soc., A 380, 20210271 (2022).
- G. Jacob, K. Groot-Berning, S. Wolf, S. Ulm, L. Couturier, S. T. Dawkins, U. G. Poschinger, F. Schmidt-Kaler, and K. Singer, Transmission microscopy with nanometer resolution using a deterministic single ion source, Phys. Rev. Lett. 117, 043001 (2016).
- K. Groot-Berning, T. Kornher, G. Jacob, F. Stopp, S. T. Dawkins, R. Kolesov, J. Wrachtrup, K. Singer, and F. Schmidt-Kaler, Deterministic single-ion implantation of rare-earth ions for nanometer-resolution color-center generation, Phys. Rev. Lett. 123, 106802 (2019).
- M. Haruyama, S. Onoda, T. Higuchi, W. Kada, A. Chiba, Y. Hirano, T. Teraji, R. Igarashi, S. Kawai, H. Kawarada, Y. Ishii, R. Fukuda, T. Tanii, J. Isoya, T. Ohshima, and O. Hanaizumi, Triple nitrogen-vacancy centre fabrication by ion implantation, Nat. Commun. 10, 2664 (2019).
- K. Kimura, S. Onoda, K. Yamada, W. Kada, T. Teraji, J. Isoya, O. Hanaizumi, and T. Ohshima, Creation of multiple NV centers by phthalocyanine ion implantation, Appl. Phys. Express 15, 066501 (2022).
- D. Reinhardt, T. Lühmann, P. Räcke, J. Heupel, M. Kieschnick, S. Mändl, C. Popov, J. B. Meijer, and R. Wunderlich, Subdiffraction distance measurement of dipolar emitting qubit pairs, ACS Photonics 11, 1382 (2024).
- B. Grotz, J. Beck, P. Neumann, B. Naydenov, R. Reuter, F. Reinhard, F. Jelezko, J. Wrachtrup, D. Schweinfurth, B. Sarkar, and P. Hemmer, Sensing external spins with nitrogen-vacancy diamond, New J. Phys. 13, 055004 (2011).
- J. Du, F. Shi, X. Kong, F. Jelezko, and J. Wrachtrup, Single-molecule scale magnetic resonance spectroscopy using quantum diamond sensors, Rev. Mod. Phys. 96, 025001 (2024).
- S. Choi, J. Choi, R. Landig, G. Kucsko, H. Zhou, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, V. Khemani, C. von Keyserlingk, N. Y. Yao, E. Demler, and M. D. Lukin, Observation of discrete time-crystalline order in a disordered dipolar many-body system, Nature 543, 221 (2017).
- G. Kucsko, S. Choi, J. Choi, P. C. Maurer, H. Zhou, R. Landig, H. Sumiya, S. Onoda, J. Isoya, F. Jelezko, E. Demler, N. Y. Yao, and M. D. Lukin, Critical thermalization of a disordered dipolar spin system in diamond, Phys. Rev. Lett. 121, 023601 (2018).
- J. Cai, A. Retzker, F. Jelezko, and M. B. Plenio, A large-scale quantum simulator on a diamond surface at room temperature, Nat. Phys. 9, 168 (2013).
- N. P. de Leon, K. M. Itoh, D. Kim, K. K. Mehta, T. E. Northup, H. Paik, B. S. Palmer, N. Samarth, S. Sangtawesin, and D. W. Steuerman, Materials challenges and opportunities for quantum computing hardware, Science 372, eabb2823 (2021).
- H. Zhang, K. Arai, C. Belthangady, J.-C. Jaskula, and R. L. Walsworth, Selective addressing of solid-state spins at the nanoscale via magnetic resonance frequency encoding, npj Quantum Inf. 3, 31 (2017).
- S. Bodenstedt, I. Jakobi, J. Michl, I. Gerhardt, P. Neumann, and J. Wrachtrup, Nanoscale spin manipulation with pulsed magnetic gradient fields from a hard disc drive writer, Nano Lett. 18, 5389 (2018).
- N. Bar-Gill, L. M. Pham, C. Belthangady, D. Le Sage, P. Cappellaro, J. R. Maze, M. D. Lukin, A. Yacoby, and R. Walsworth, Suppression of spin-bath dynamics for improved coherence of multi-spin-qubit systems, Nat. Commun. 3, 858 (2012).
- H. Y. Carr and E. M. Purcell, Effects of diffusion on free precession in nuclear magnetic resonance experiments, Phys. Rev. 94, 630 (1954).
- S. Meiboom and D. Gill, Modified spin-echo method for measuring nuclear relaxation times, Rev. Sci. Instrum. 29, 688 (1958).
- C. A. Ryan, J. S. Hodges, and D. G. Cory, Robust decoupling techniques to extend quantum coherence in diamond, Phys. Rev. Lett. 105, 200402 (2010).
- A. M. Souza, G. A. Álvarez, and D. Suter, Robust dynamical decoupling for quantum computing and quantum memory, Phys. Rev. Lett. 106, 240501 (2011).
- M. A. Ali Ahmed, G. A. Álvarez, and D. Suter, Robustness of dynamical decoupling sequences, Phys. Rev. A 87, 042309 (2013).
- M. H. Abobeih, J. Cramer, M. A. Bakker, N. Kalb, M. Markham, D. J. Twitchen, and T. H. Taminiau, One-second coherence for a single electron spin coupled to a multi-qubit nuclear-spin environment, Nat. Commun. 9, 2552 (2018).
- X. Rong, J. Geng, F. Shi, Y. Liu, K. Xu, W. Ma, F. Kong, Z. Jiang, Y. Wu, and J. Du, Experimental fault-tolerant universal quantum gates with solid-state spins under ambient conditions, Nat. Commun. 6, 8748 (2015).
- B. T. Torosov, B. W. Shore, and N. V. Vitanov, Coherent control techniques for two-state quantum systems: A comparative study, Phys. Rev. A 103, 033110 (2021).
- M. H. Levitt, Composite pulses, Prog. Nucl. Magn. Reson. Spectrosc. 18, 61 (1986).
- R. Tycko, Broadband population inversion, Phys. Rev. Lett. 51, 775 (1983).
- J. A. Jones, Composite pulses in NMR quantum computation, J. Indian Inst. Sci. 89, 303 (2009).
- J. A. Jones, Designing short robust not gates for quantum computation, Phys. Rev. A 87, 052317 (2013).
- H. L. Gevorgyan and N. V. Vitanov, Ultrahigh-fidelity composite rotational quantum gates, Phys. Rev. A 104, 012609 (2021).
- A. A. Maudsley, Modified Carr-Purcell-Meiboom-Gill sequence for NMR Fourier imaging applications, J. Magn. Reson. 69, 488 (1986).
- T. Gullion, D. B. Baker, and M. S. Conradi, New, compensated Carr-Purcell sequences, J. Magn. Reson. 89, 479 (1990).
- J. Casanova, Z.-Y. Wang, J. F. Haase, and M. B. Plenio, Robust dynamical decoupling sequences for individual-nuclear-spin addressing, Phys. Rev. A 92, 042304 (2015).
- M. Steffen and R. H. Koch, Shaped pulses for quantum computing, Phys. Rev. A 75, 062326 (2007).
- L. M. K. Vandersypen and I. L. Chuang, NMR techniques for quantum control and computation, Rev. Mod. Phys. 76, 1037 (2005).
- J. F. Haase, Z.-Y. Wang, J. Casanova, and M. B. Plenio, Soft quantum control for highly selective interactions among joint quantum systems, Phys. Rev. Lett. 121, 050402 (2018).
- S. Johnson, P. R. Dolan, and J. M. Smith, Diamond photonics for distributed quantum networks, Prog. Quantum Electron. 55, 129 (2017).
- I. Aharonovich, A. D. Greentree, and S. Prawer, Diamond photonics, Nat. Photonics 5, 397 (2011).
- H. K. C. Beukers, M. Pasini, H. Choi, D. Englund, R. Hanson, and J. Borregaard, Remote-entanglement protocols for stationary qubits with photonic interfaces, PRX Quantum 5, 010202 (2024).
- M. Ruf, N. H. Wan, H. Choi, D. Englund, and R. Hanson, Quantum networks based on color centers in diamond, J. Appl. Phys. 130, 070901 (2021).
- D. E. Browne, M. B. Plenio, and S. F. Huelga, Robust creation of entanglement between ions in spatially separate cavities, Phys. Rev. Lett. 91, 067901 (2003).
- S. D. Barrett and P. Kok, Efficient high-fidelity quantum computation using matter qubits and linear optics, Phys. Rev. A 71, 060310(R) (2005).
- H. Bernien, B. Hensen, W. Pfaff, G. Koolstra, M. S. Blok, L. Robledo, T. H. Taminiau, M. Markham, D. J. Twitchen, L. Childress, and R. Hanson, Heralded entanglement between solid-state qubits separated by three metres, Nature 497, 86 (2013).
- B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres, Nature 526, 682 (2015).
- M. Pompili, S. L. N. Hermans, S. Baier, H. K. C. Beukers, P. C. Humphreys, R. N. Schouten, R. F. L. Vermeulen, M. J. Tiggelman, L. dos Santos Martins, B. Dirkse, S. Wehner, and R. Hanson, Realization of a multinode quantum network of remote solid-state qubits, Science 372, 259 (2021).
- P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Linear optical quantum computing with photonic qubits, Rev. Mod. Phys. 79, 135 (2007).
- A. Reiserer and G. Rempe, Cavity-based quantum networks with single atoms and optical photons, Rev. Mod. Phys. 87, 1379 (2015).
- M. K. Bhaskar, R. Riedinger, B. Machielse, D. S. Levonian, C. T. Nguyen, E. N. Knall, H. Park, D. Englund, M. Lončar, D. D. Sukachev, and M. D. Lukin, Experimental demonstration of memory-enhanced quantum communication, Nature 580, 60 (2020).
- D. Riedel, I. Söllner, B. J. Shields, S. Starosielec, P. Appel, E. Neu, P. Maletinsky, and R. J. Warburton, Deterministic enhancement of coherent photon generation from a nitrogen-vacancy center in ultrapure diamond, Phys. Rev. X 7, 031040 (2017).
- V. Yurgens, Y. Fontana, A. Corazza, B. J. Shields, P. Maletinsky, and R. J. Warburton, Cavity-assisted resonance fluorescence from a nitrogen-vacancy center in diamond, npj Quantum Inf. 10, 112 (2024).
- F. Omlor, B. Tissot, and G. Burkard, Entanglement generation using single-photon pulse reflection in realistic networks, Phys. Rev. A 111, 012612 (2025).
- K. Koshino and Y. Matsuzaki, Entangling homogeneously broadened matter qubits in the weak-coupling cavity-QED regime, Phys. Rev. A 86, 020305(R) (2012).
- J. M. Lukens and P. Lougovski, Frequency-encoded photonic qubits for scalable quantum information processing, Optica 4, 8 (2017).
- M. Clementi, F. A. Sabattoli, M. Borghi, L. Gianini, N. Tagliavacche, H. El Dirani, L. Youssef, N. Bergamasco, C. Petit-Etienne, E. Pargon, J. E. Sipe, M. Liscidini, C. Sciancalepore, M. Galli, and D. Bajoni, Programmable frequency-bin quantum states in a nano-engineered silicon device, Nat. Commun. 14, 176 (2023).
- T. V. Tscherbul, J. Ye, and A. M. Rey, Robust nuclear spin entanglement via dipolar interactions in polar molecules, Phys. Rev. Lett. 130, 143002 (2023).
- N. H. Le, M. Cykiert, and E. Ginossar, Scalable and robust quantum computing on qubit arrays with fixed coupling, npj Quantum Inf. 9, 1 (2023).
- F. Rajabi, S. Motlakunta, C.-Y. Shih, N. Kotibhaskar, Q. Quraishi, A. Ajoy, and R. Islam, Dynamical Hamiltonian engineering of 2D rectangular lattices in a one-dimensional ion chain, npj Quantum Inf. 5, 1 (2019).
- B. T. Torosov and N. V. Vitanov, High-fidelity error-resilient composite phase gates, Phys. Rev. A 90, 012341 (2014).
- A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, Elementary gates for quantum computation, Phys. Rev. A 52, 3457 (1995).
- M. V. G. Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, Quantum register based on individual electronic and nuclear spin qubits in diamond, Science 316, 1312 (2007).
- P. Neumann, R. Kolesov, B. Naydenov, J. Beck, F. Rempp, M. Steiner, V. Jacques, G. Balasubramanian, M. L. Markham, D. J. Twitchen, S. Pezzagna, J. Meijer, J. Twamley, F. Jelezko, and J. Wrachtrup, Quantum register based on coupled electron spins in a room-temperature solid, Nat. Phys. 6, 249 (2010).
- Y. Wu, Y. Wang, X. Qin, X. Rong, and J. Du, A programmable two-qubit solid-state quantum processor under ambient conditions, npj Quantum Inf. 5, 9 (2019).
- S. L. Bayliss, D. W. Laorenza, P. J. Mintun, B. D. Kovos, D. E. Freedman, and D. D. Awschalom, Optically addressable molecular spins for quantum information processing, Science 370, 1309 (2020).
- A. Gaita-Ariño, F. Luis, S. Hill, and E. Coronado, Molecular spins for quantum computation, Nat. Chem. 11, 301 (2019).
- S. L. Bayliss, P. Deb, D. W. Laorenza, M. Onizhuk, G. Galli, D. E. Freedman, and D. D. Awschalom, Enhancing spin coherence in optically addressable molecular qubits through host-matrix control, Phys. Rev. X 12, 031028 (2022).
- P. A. Ivanov, N. V. Vitanov, and M. B. Plenio, Creation of cluster states of trapped ions by collective addressing, Phys. Rev. A 78, 012323 (2008).
- H. Wunderlich, C. Wunderlich, K. Singer, and F. Schmidt-Kaler, Two-dimensional cluster-state preparation with linear ion traps, Phys. Rev. A 79, 052324 (2009).
- T. Ichikawa, U. Güngördü, M. Bando, Y. Kondo, and M. Nakahara, Minimal and robust composite two-qubit gates with Ising-type interaction, Phys. Rev. A 87, 022323 (2013).
- S. S. Ivanov and N. V. Vitanov, Composite two-qubit gates, Phys. Rev. A 92, 022333 (2015).
- A. O. Niskanen, K. Harrabi, F. Yoshihara, Y. Nakamura, S. Lloyd, and J. S. Tsai, Quantum coherent tunable coupling of superconducting qubits, Science 316, 723 (2007).
- Y. Sung, L. Ding, J. Braumüller, A. Vepsäläinen, B. Kannan, M. Kjaergaard, A. Greene, G. O. Samach, C. McNally, D. Kim, A. Melville, B. M. Niedzielski, M. E. Schwartz, J. L. Yoder, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Realization of high-fidelity CZ and -free iSWAP gates with a tunable coupler, Phys. Rev. X 11, 021058 (2021).
- X. Li, T. Cai, H. Yan, Z. Wang, X. Pan, Y. Ma, W. Cai, J. Han, Z. Hua, X. Han, Y. Wu, H. Zhang, H. Wang, Y. Song, L. Duan, and L. Sun, Tunable coupler for realizing a controlled-phase gate with dynamically decoupled regime in a superconducting circuit, Phys. Rev. Appl. 14, 024070 (2020).
- P. Zhao, P. Xu, D. Lan, J. Chu, X. Tan, H. Yu, and Y. Yu, High-contrast interaction using superconducting qubits with opposite-sign anharmonicity, Phys. Rev. Lett. 125, 200503 (2020).
- J. Ku, X. Xu, M. Brink, D. C. McKay, J. B. Hertzberg, M. H. Ansari, and B. L. T. Plourde, Suppression of unwanted interactions in a hybrid two-qubit system, Phys. Rev. Lett. 125, 200504 (2020).
- Y. Liang, M.-J. Liang, S. Li, Z. D. Wang, and Z.-Y. Xue, Scalable protocol to mitigate crosstalk in universal quantum gates, Phys. Rev. Appl. 21, 024016 (2024).
- L. Xie, J. Zhai, Z. Zhang, J. Allcock, S. Zhang, and Y.-C. Zheng, Suppressing ZZ crosstalk of Quantum computers through pulse and scheduling co-optimization, in ASPLOS ’22: Proceedings of the 27th ACM International Conference on Architectural Support for Programming Languages and Operating Systems (Association for Computing Machinery (ACM), New York, NY, USA, 2022), pp. 499–513.
- V. Tripathi, H. Chen, M. Khezri, K.-W. Yip, E. M. Levenson-Falk, and D. A. Lidar, Suppression of crosstalk in superconducting qubits using dynamical decoupling, Phys. Rev. Appl. 18, 024068 (2022).
- matlab Optimization Toolbox (r2023a), the MathWorks, Natick, Massachusetts. https://de.mathworks.com/products/optimization.html.
- C. Van Loan, Computing integrals involving the matrix exponential, IEEE Trans. Autom. Control 23, 395 (1978).
- I. Najfeld and T. F. Havel, Derivatives of the matrix exponential and their computation, Adv. Appl. Math. 16, 321 (1995).
- F. Carbonell, J. C. Jímenez, and L. M. Pedroso, Computing multiple integrals involving matrix exponentials, J. Comput. Appl. Math. 213, 300 (2008).
- D. L. Goodwin and I. Kuprov, Auxiliary matrix formalism for interaction representation transformations, optimal control, and spin relaxation theories, J. Chem. Phys. 143, 084113 (2015).
- H. Haas, D. Puzzuoli, F. Zhang, and D. G. Cory, Engineering effective Hamiltonians, New J. Phys. 21, 103011 (2019).
- E. D. Herbschleb, H. Kato, Y. Maruyama, T. Danjo, T. Makino, S. Yamasaki, I. Ohki, K. Hayashi, H. Morishita, M. Fujiwara, and N. Mizuochi, Ultra-long coherence times amongst room-temperature solid-state spins, Nat. Commun. 10, 3766 (2019).