- Open Access
Maximizing the Nondemolition Nature of a Quantum Measurement Via an Adaptive Readout Protocol
PRX Quantum 7, 020330 – Published 15 May, 2026
DOI: https://doi.org/10.1103/jtn1-wzyl
Abstract
Quantum error correction benefits from high-fidelity, noninvasive measurements for fault-tolerant quantum computing. Deviations from ideal quantum nondemolition (QND) measurements can disturb the encoded information. To address this challenge, we develop a readout protocol for a -dimensional system that, after a single positive outcome, switches to probing only the remaining subspace. This adaptive switching strategy minimizes measurement-induced errors by relying on negative-result measurement results that do not perturb the Hamiltonian. We apply the protocol on an eight-dimensional nuclear qudit in silicon and achieve an increase in the readout fidelity from (98.93±0.07) % to (99.61±0.04) %, while reducing threefold the overall readout time. To highlight the broader relevance of measurement-induced errors, we study a ten-dimensional nuclear spin read out through Pauli spin blockade, revealing nuclear spin flips arising from hyperfine and quadrupole interactions. We discuss the applicability of our method to other quantum hardware platforms such as color centers in diamond, spins in lithographic quantum dots, clusters of donors in silicon, and dual-species neutral atom arrays. These results unveil the effect of nonideal QND readout across diverse platforms and introduce an efficient readout protocol that can be implemented with minimal field-programmable gate array (FPGA) logic on existing hardware.
Physics Subject Headings (PhySH)
Popular Summary
Quantum computers promise to solve problems far beyond the reach of classical computers, but today’s devices are extremely sensitive to errors. One major source of errors is the act of measurement. The best we can do is to use quantum nondemolition (QND) measurements, which repeatedly extract information while introducing only the minimum disturbance dictated by quantum mechanics. Deviations from QND introduce further errors, which we wish to avoid.
Quantum information is often encoded in spins. A spin behaves like a tiny magnet that aligns itself with the axis of an external magnetic field. Measuring a spin projects it onto this measurement axis, forcing it into one of the few discrete outcomes. To avoid disturbing the spin, we often measure it indirectly through a secondary spin, or ancilla, which acts like a messenger carrying the measurement information. But like in a game of Chinese whispers, each time the message is passed, there is a chance it gets distorted. Repeated measurements via the ancilla introduce a small tilt in the measurement axis, causing the spin to change its orientation. We address this challenge with an adaptive measurement protocol that minimizes the amount of error-producing “whispers.” Once the system is detected in a state, instead of repeating the full measurement, the protocol checks only the remaining dark states, which produce no signal and leave the system undisturbed.
We demonstrate the protocol on an eight-level nuclear spin measured via an electron ancilla and reduce measurement errors below the estimated threshold for fault-tolerance. This approach applies to many quantum platforms and directly supports building scalable, fault-tolerant quantum computers.
Article Text
Supplemental Material
References (57)
- Simon J. Devitt, William J. Munro, and Kae Nemoto, Quantum error correction for beginners, Rep. Progr. Phys. 76, 076001 (2013).
- Vladimir B. Braginsky and F. Ya Khalili, Quantum nondemolition measurements: The route from toys to tools, Rev. Mod. Phys. 68, 1 (1996).
- D. Ristè, S. Poletto, M. Z. Huang, A. Bruno, V. Vesterinen, O. P. Saira, and L. Dicarlo, Detecting bit-flip errors in a logical qubit using stabilizer measurements, Nat. Commun. 6, 6983 (2015).
- J. Kelly et al., State preservation by repetitive error detection in a superconducting quantum circuit, Nature 519, 66 (2015).
- W. G. Unruh, Quantum nondemolition and gravity-wave detection, Phys. Rev. D 19, 2888 (1979).
- Benjamin Joecker, Holly G. Stemp, Irene Fernández De Fuentes, Mark A. I. Johnson, and Andrea Morello, Error channels in quantum nondemolition measurements on spin systems, Phys. Rev. B 109, 085302 (2024).
- Xiao Xue, Benjamin D’anjou, Thomas F. Watson, Daniel R. Ward, Donald E. Savage, Max G. Lagally, Mark Friesen, Susan N. Coppersmith, Mark A. Eriksson, William A. Coish, and Lieven M. K. Vandersypen, Repetitive quantum nondemolition measurement and soft decoding of a silicon spin qubit, Phys. Rev. X 10, 021006 (2020).
- J. Yoneda, K. Takeda, A. Noiri, T. Nakajima, S. Li, J. Kamioka, T. Kodera, and S. Tarucha, Quantum non-demolition readout of an electron spin in silicon, Nat. Commun. 11, 1144 (2020).
- Philipp Neumann, Johannes Beck, Matthias Steiner, Florian Rempp, Helmut Fedder, Philip R. Hemmer, Jörg Wrachtrup, and Fedor Jelezko, Single-shot readout of a single nuclear spin, Science 329, 542 (2010).
- Lucio Robledo, Lilian Childress, Hannes Bernien, Bas Hensen, Paul F. A. Alkemade, and Ronald Hanson, High-fidelity projective readout of a solid-state spin quantum register, Nature 477, 574 (2011).
- M. H. Abobeih, Y. Wang, J. Randall, S. J. H. Loenen, C. E. Bradley, M. Markham, D. J. Twitchen, B. M. Terhal, and T. H. Taminiau, Fault-tolerant operation of a logical qubit in a diamond quantum processor, Nature 606, 884 (2022).
- V. Negnevitsky, M. Marinelli, K. K. Mehta, H. Y. Lo, C. Flühmann, and J. P. Home, Repeated multi-qubit readout and feedback with a mixed-species trapped-ion register, Nature 563, 527 (2018).
- Shraddha Anand, Conor E. Bradley, Ryan White, Vikram Ramesh, Kevin Singh, and Hannes Bernien, A dual-species Rydberg array, Nat. Phys. 20, 1744 (2024).
- Romain Vincent, Svetlana Klyatskaya, Mario Ruben, Wolfgang Wernsdorfer, and Franck Balestro, Electronic read-out of a single nuclear spin using a molecular spin transistor, Nature 488, 357 (2012).
- Jarryd J. Pla, Kuan Y. Tan, Juan P. Dehollain, Wee H. Lim, John J. L. Morton, Floris A. Zwanenburg, David N. Jamieson, Andrew S. Dzurak, and Andrea Morello, High-fidelity readout and control of a nuclear spin qubit in silicon, Nature 496, 334 (2013).
- Serwan Asaad, Vincent Mourik, Benjamin Joecker, Mark A. I. Johnson, Andrew D. Baczewski, Hannes R. Firgau, Mateusz T. Madzik, Vivien Schmitt, Jarryd J. Pla, Fay E. Hudson, Kohei M. Itoh, Jeffrey C. McCallum, Andrew S. Dzurak, Arne Laucht, and Andrea Morello, Coherent electrical control of a single high-spin nucleus in silicon, Nature 579, 205 (2020).
- Irene Fernández de Fuentes, Tim Botzem, Mark A. I. Johnson, Arjen Vaartjes, Serwan Asaad, Vincent Mourik, Fay E. Hudson, Kohei M. Itoh, Brett C. Johnson, Alexander M. Jakob, Jeffrey C. McCallum, David N. Jamieson, Andrew S. Dzurak, and Andrea Morello, Navigating the 16-dimensional Hilbert space of a high-spin donor qudit with electric and magnetic fields, Nat. Commun. 15, 1380 (2024).
- J. Reiner, Y. Chung, S. H. Misha, C. Lehner, C. Moehle, D. Poulos, S. Monir, K. J. Charde, P. Macha, L. Kranz, I. Thorvaldson, B. Thorgrimsson, D. Keith, Y. L. Hsueh, R. Rahman, S. K. Gorman, J. G. Keizer, and M. Y. Simmons, High-fidelity initialization and control of electron and nuclear spins in a four-qubit register, Nat. Nanotechnol. 19, 605 (2024).
- Evert W. Stolte, Jinwon Lee, Hester G. Vennema, Rik Broekhoven, Esther Teng, Allard J. Katan, Lukas M. Veldman, Philip Willke, and Sander Otte, Single-shot readout of the nuclear spin of an on-surface atom, Nat. Commun. 16, 7785 (2025).
- Hermann Edlbauer, Junliang Wang, A. M. Huq, Ian Thorvaldson, Michael Jones, A. F. M. Misha, William Pappas, Christian Moehle, Yu-Ling Hsueh, Henric Bornemann, Samuel Gorman, Yousun Chung, Joris Keizer, Ludwik Kranz, and Michelle Simmons, An 11-qubit atom processor in silicon, Nature 648, 569 (2025).
- Chunhui Zhang et al., Quantum error detection in a silicon quantum processor, Nat. Electron. 9, 295 (2026).
- Paul Steinacker, Gauri Goenka, Rocky Yue Su, Tuomo Tanttu, Wee Han Lim, Santiago Serrano, Tim Botzem, Jesus D. Cifuentes, Shao Qi Lim, Jeffrey C. McCallum, Brett C. Johnson, Fay E. Hudson, Kok Wai Chan, Christopher C. Escott, Andre Saraiva, Chih Hwan Yang, Vincent Mourik, Andrea Morello, Andrew S. Dzurak, and Arne Laucht, Coupling a nuclear spin to an electrostatically defined quantum dot, arXiv:2510.03981.
- J. M. Elzerman, R. Hanson, L. H. Willems van Beveren, B. Witkamp, L. M. K. Vandersypen, and L. P. Kouwenhoven, Single-shot read-out of an individual electron spin in a quantum dot, Nature 430, 431 (2004).
- M. Xiao, I. Martin, E. Yablonovitch, and H. W. Jiang, Electrical detection of the spin resonance of a single electron in a silicon field-effect transistor, Nature 430, 435 (2004).
- Andrea Morello, Jarryd J. Pla, Floris A. Zwanenburg, Kok W. Chan, Kuan Y. Tan, Hans Huebl, Mikko Möttönen, Christopher D. Nugroho, Changyi Yang, Jessica A. van Donkelaar, Andrew D. C. Alves, David N. Jamieson, Christopher C. Escott, Lloyd C. L. Hollenberg, Robert G. Clark, and Andrew S. Dzurak, Single-shot readout of an electron spin in silicon, Nature 467, 687 (2010).
- A. Morello, C. C. Escott, H. Huebl, L. H. Willems van Beveren, L. C. L. Hollenberg, D. N. Jamieson, A. S. Dzurak, and R. G. Clark, Architecture for high-sensitivity single-shot readout and control of the electron spin of individual donors in silicon, Phys. Rev. B: Condens. Matter Mater. Phys. 80, 081307(R) (2009).
- H. Geng, M. Kiczynski, A. V. Timofeev, E. N. Osika, D. Keith, J. Rowlands, L. Kranz, R. Rahman, Y. Chung, J. G. Keizer, S. K. Gorman, and M. Y. Simmons, High-fidelity sub-microsecond single-shot electron spin readout above 3.5 K, Nat. Commun. 16, 3382 (2025).
- Samuel J. Hile, Lukas Fricke, Matthew G. House, Eldad Peretz, Chin Yi Chen, Yu Wang, Matthew Broome, Samuel K. Gorman, Joris G. Keizer, Rajib Rahman, and Michelle Y. Simmons, Addressable electron spin resonance using donors and donor molecules in silicon, Sci. Adv. 4, eaaq1459 (2018).
- Mateusz T. Madzik, Serwan Asaad, Akram Youssry, Benjamin Joecker, Kenneth M. Rudinger, Erik Nielsen, Kevin C. Young, Timothy J. Proctor, Andrew D. Baczewski, Arne Laucht, Vivien Schmitt, Fay E. Hudson, Kohei M. Itoh, Alexander M. Jakob, Brett C. Johnson, David N. Jamieson, Andrew S. Dzurak, Christopher Ferrie, Robin Blume-Kohout, and Andrea Morello, Precision tomography of a three-qubit donor quantum processor in silicon, Nature 601, 348 (2022).
- Avshalom C. Elitzur and Lev Vaidman, Quantum mechanical interaction-free measurements, Found. Phys. 23, 987 (1993).
- J. T. Muhonen, J. P. Dehollain, A. Laucht, S. Simmons, R. Kalra, F. E. Hudson, A. S. Dzurak, A. Morello, D. N. Jamieson, J. C. McCallum, and K. M. Itoh, Coherent control via weak measurements in single-atom electron and nuclear spin qubits, Phys. Rev. B 98, 155201 (2018).
- See the Supplemental Material http://link.aps.org/supplemental/10.1103/jtn1-wzyl for details on the quadrupole characterization, measurement-induced transition model, additional data on the number of tunneling events per QND cycle and bare Markov matrices, and the experimental setups. The Supplemental Material includes Refs. [52, 53, 54, 55, 56, 57].
- Arjen Vaartjes, Martin Nurizzo, Lin Htoo Zaw, Benjamin Wilhelm, Xi Yu, Danielle Holmes, Daniel Schwienbacher, Anders Kringhøj, Mark R. van Blankenstein, Alexander M. Jakob, Fay E. Hudson, Kohei M. Itoh, Riley J. Murray, Robin Blume-Kohout, Namit Anand, Andrew S. Dzurak, David N. Jamieson, Valerio Scarani, and Andrea Morello, Certifying the quantumness of a nuclear spin qudit through its uniform precession, Newton 1, 100017 (2025).
- Mark A. I. Johnson, Mateusz T. Mądzik, Fay E. Hudson, Kohei M. Itoh, Alexander M. Jakob, David N. Jamieson, Andrew Dzurak, and Andrea Morello, Beating the thermal limit of qubit initialization with a Bayesian Maxwell’s demon, Phys. Rev. X 12, 041008 (2022).
- Arne Laucht, Rachpon Kalra, Juha T. Muhonen, Juan P. Dehollain, Fahd A. Mohiyaddin, Fay Hudson, Jeffrey C. McCallum, David N. Jamieson, Andrew S. Dzurak, and Andrea Morello, High-fidelity adiabatic inversion of a electron spin qubit in natural silicon, Appl. Phys. Lett. 104, 092115 (2014).
- Xi Yu, Benjamin Wilhelm, Danielle Holmes, Arjen Vaartjes, Daniel Schwienbacher, Martin Nurizzo, Anders Kringhøj, Mark R.van Blankenstein, Alexander M. Jakob, Pragati Gupta, Fay E. Hudson, Kohei M. Itoh, Riley J. Murray, Robin Blume-Kohout, Thaddeus D. Ladd, Namit Anand, Andrew S. Dzurak, Barry C. Sanders, David N. Jamieson, and Andrea Morello, Schrödinger cat states of a nuclear spin qudit in silicon, Nat. Phys. 21, 362 (2025).
- S. Monir, E. N. Osika, S. K. Gorman, I. Thorvaldson, Y. L. Hsueh, P. Macha, L. Kranz, J. Reiner, M. Y. Simmons, and R. Rahman, Impact of measurement backaction on nuclear spin qubits in silicon, Phys. Rev. B 109, 035157 (2024).
- Rostyslav Savytskyy, Tim Botzem, Irene Fernandez de Fuentes, Benjamin Joecker, Jarryd J. Pla, Fay E. Hudson, Kohei M. Itoh, Alexander M. Jakob, Brett C. Johnson, David N. Jamieson, Andrew S. Dzurak, and Andrea Morello, An electrically driven single-atom “flip-flop” qubit, Sci. Adv. 9, eadd9408 (2023).
- A. Vaartjes, Maximizing the nondemolition nature of a quantum measurement via an adaptive readout protocol [data set]. Zenodo, 2026, https://zenodo.org/records/18522131.
- Irina Heinz, Adam R. Mills, Jason R. Petta, and Guido Burkard, Analysis and mitigation of residual exchange coupling in linear spin-qubit arrays, Phys. Rev. Res. 6, 013153 (2024).
- Yun-Pil Shim and Charles Tahan, Charge-noise-insensitive gate operations for always-on, exchange-only qubits, Phys. Rev. B 93, 121410(R) (2016).
- Joseph D. Broz, Jesse C. Hoke, Edwin Acuna, and Jason R. Petta, Demonstration of an always-on exchange-only spin qubit, arXiv:2508.01033.
- Daniel Gottesman, Quantum fault tolerance in small experiments, arXiv:1610.03507.
- Jonathan A. Gross, Designing codes around interactions: The case of a spin, Phys. Rev. Lett. 127, 010504 (2021).
- Jonathan A. Gross, Clément Godfrin, Alexandre Blais, and Eva Dupont-Ferrier, Hardware-efficient error-correcting codes for large nuclear spins, Phys. Rev. Appl. 22, 014006 (2024).
- Pragati Gupta, Arjen Vaartjes, Xi Yu, Andrea Morello, and Barry C. Sanders, Robust macroscopic Schrödinger’s cat on a nucleus, Phys. Rev. Res. 6, 013101 (2024).
- Ashley M. Stephens, Fault-tolerant thresholds for quantum error correction with the surface code, Phys. Rev. A 89, 022321 (2014).
- Gözde Üstün, Andrea Morello, and Simon Devitt, Single-step parity check gate set for quantum error correction, Quantum Sci. Technol. 9, 035037 (2024).
- Cameron Jones, Piper Wysocki, Meng Ke Feng, Gerardo A. Paz-Silva, Corey I. Ostrove, Tuomo Tanttu, Kenneth M. Rudinger, Samuel K. Bartee, Kevin Young, Fay E. Hudson, Wee Han Lim, Nikolay V. Abrosimov, Hans-Joachim Pohl, Michael L. W. Thewalt, Robin Blume-Kohout, Andrew S. Dzurak, Andre Saraiva, Arne Laucht, and Chih Hwan Yang, Mid-circuit logic executed in the qubit layer of a quantum processor, arXiv:2512.12648.
- Vinay Tripathi, Noah Goss, Arian Vezvaee, Long B. Nguyen, Irfan Siddiqi, and Daniel A. Lidar, Qudit dynamical decoupling on a superconducting quantum processor, Phys. Rev. Lett. 134, 050601 (2025).
- Jonathan Y. Huang et al., High-fidelity spin qubit operation and algorithmic initialization above 1 K, Nature 627, 772 (2024).
- Laura A. O’Neill, Benjamin Joecker, Andrew D. Baczewski, and Andrea Morello, Engineering local strain for single-atom nuclear acoustic resonance in silicon, Appl. Phys. Lett. 119, 174001 (2021).
- David P. Franke, Florian M. Hrubesch, Markus Künzl, Hans Werner Becker, Kohei M. Itoh, Martin Stutzmann, Felix Hoehne, Lukas Dreher, and Martin S. Brandt, Interaction of strain and nuclear spins in silicon: Quadrupolar effects on ionized donors, Phys. Rev. Lett. 115, 057601 (2015).
- U. Vool, I. M. Pop, K. Sliwa, B. Abdo, C. Wang, T. Brecht, Y. Y. Gao, S. Shankar, M. Hatridge, G. Catelani, M. Mirrahimi, L. Frunzio, R. J. Schoelkopf, L. I. Glazman, and M. H. Devoret, Non-Poissonian quantum jumps of a fluxonium qubit due to quasiparticle excitations, Phys. Rev. Lett. 113, 247001 (2014).
- J. J. Wesdorp, L. Grünhaupt, A. Vaartjes, M. Pita-Vidal, A. Bargerbos, L. J. Splitthoff, P. Krogstrup, B. van Heck, and G. de Lange, Dynamical polarization of the fermion parity in a nanowire Josephson junction, Phys. Rev. Lett. 131, 117001 (2023).
- S. Asmussen, Applied Probability and Queues (Springer, New York, NY, 2003).
- Amanda E. Seedhouse, Tuomo Tanttu, Ross C. C. Leon, Ruichen Zhao, Kuan Yen Tan, Bas Hensen, Fay E. Hudson, Kohei M. Itoh, Jun Yoneda, Chih Hwan Yang, Andrea Morello, Arne Laucht, Susan N. Coppersmith, Andre Saraiva, and Andrew S. Dzurak, Pauli blockade in silicon quantum dots with spin-orbit control, PRX Quantum 2, 010303 (2021).
