What can unitary sequences tell us about multi-time physics?

Gregory A. L. White; Felix A. Pollock; Lloyd C. L. Hollenberg; Charles D. Hill; Kavan Modi

doi:10.22331/q-2025-04-08-1695

What can unitary sequences tell us about multi-time physics?

Gregory A. L. White^1,2,3, Felix A. Pollock², Lloyd C. L. Hollenberg³, Charles D. Hill^4,3,5, and Kavan Modi^6,2

¹Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
²School of Physics and Astronomy, Monash University, Clayton, VIC 3800, Australia
³School of Physics, University of Melbourne, Parkville, VIC 3010, Australia
⁴Silicon Quantum Computing, The University of New South Wales, Sydney, New South Wales 2052, Australia
⁵School of Mathematics and Statistics, University of Melbourne, Parkville, VIC, 3010, Australia
⁶Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore

Published:	2025-04-08, volume 9, page 1695
Editor:	Nicolai Friis
Eprint:	arXiv:2107.13934v7
Doi:	https://doi.org/10.22331/q-2025-04-08-1695
Citation:	Quantum 9, 1695 (2025).

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Abstract

Multi-time quantum processes are endowed with the same richness as multipartite states, including temporal entanglement and exotic causal structures. However, experimentally probing these rich phenomena leans heavily on fast and clean mid-circuit measurements, which are rarely available. We show here how surprisingly accessible these phenomena are in nascent quantum processors even when faced with substantially limited control. We work within the limitation where only unitary control is allowed, followed by a terminating measurement. Within this setting, we first develop a witness for genuine multi-time entanglement, and then methods to bound (from top and bottom) multi-time entanglement, non-Markovianity, purity, entropy, and other correlative measures. Our tools are designed to be implemented on quantum information processors, which we proceed to demonstrate. Finally, we discuss the limitations of these methods by testing them across random multi-time processes. Conceptually, this broadens our understanding of the extent to which temporal correlations may be determined with only deterministic control. Our techniques are pertinent to generic quantum stochastic dynamical processes, with a scope ranging across condensed matter physics, quantum biology, and in-depth diagnostics of NISQ-era quantum devices.

Featured image: Overview of the conceptual ideas studied in this paper. (a) Control instruments probe multi-time correlations in non-Markovian open quantum systems and can be used to perform tomography of process tensors. Typically one has to perform an informationally complete set of operations to do this uniquely. Such operations can be partitioned into non-unital, trace-decreasing, and unitary classes. But the first two are hard to perform. If one only performs unitary sequences, then it non-uniquely determines the process under study. (b) Nevertheless, we show how this set of non-uniquely determined processes can be analysed to quantify entanglement in time and total non-Markovianity despite the limited information.

Popular summary

Quantum systems evolving in time can show complexities similar to those seen in spatial quantum states. For instance, monitoring a single qubit across five sequential steps can be viewed analogously to analysing a state composed of ten entangled qubits. Such quantum stochastic processes can exhibit intricate patterns of correlations, including long-range entanglement and high quantum complexity. Characterising these complex multi-time quantum processes is challenging, especially since current quantum hardware typically struggles with fast and reliable mid-circuit measurements—crucial steps for complete characterisation. Here, we develop tools that bypass these challenges by characterising multi-time processes using only unitary control and a single terminating measurement, leveraging their causal structures. Surprisingly, our approach demonstrates that quantum correlations can be detected even without probabilistic measurement strategies, highlighting a stark difference from classical stochastic processes. We validate these methods using real superconducting quantum processors, as well as numerically modelled and randomly generated quantum processes. Our techniques allow us to quantify important aspects of quantum noise, such as memory effects (non-Markovianity), coherence, as well as broader characteristics. These new tools facilitate a greater understanding of quantum non-Markovianity and contribute to ongoing efforts to enhance fault-tolerant quantum technologies by precisely identifying and managing noise.

► BibTeX data

@article{White2025whatcanunitary,
  doi = {10.22331/q-2025-04-08-1695},
  url = {https://doi.org/10.22331/q-2025-04-08-1695},
  title = {What can unitary sequences tell us about multi-time physics?},
  author = {White, Gregory A. L. and Pollock, Felix A. and Hollenberg, Lloyd C. L. and Hill, Charles D. and Modi, Kavan},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1695},
  month = apr,
  year = {2025}
}

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