The structure of quantum mechanics allows for computations to be carried out in ways that are fundamentally different from classical computation, with certain algorithms (like Grover’s algorithm for searching unstructured databases, or Shor’s algorithm for factoring) holding the potential for outperforming the best classical algorithms for the respective tasks. Practically, the hope is that these advantages will persist when taking into account noise and imperfect implementations, once the latter have been scaled up to sufficiently large qubit numbers at some point in the future. In this endeavor, the overheads incurred for reaching fault tolerance represent a major bottleneck and work is ongoing to create stable and robust encodings of quantum information, improve gate fidelities, and to identify and characterize efficient quantum error correction codes along with suitable decoders.

One of the foci of interest within our research area is quantum error correction. Topological error correction codes are promising candidates to protect future quantum computers from the deteriorating effects of noise. While some codes provide high noise thresholds suitable for robust quantum memories, others allow straightforward gate implementation needed for data processing. To exploit the particular advantages of different topological codes for fault-tolerant quantum computation, it is necessary to be able to switch between them.

A practical solution to this problem is subsystem lattice surgery, which requires only two-body nearest-neighbor interactions in a fixed layout in addition to the indispensable error correction. This method can be used for the fault-tolerant transfer of quantum information between arbitrary topological subsystem codes in two dimensions and beyond. In particular, it can be employed to create a simple interface, a quantum bus, between noise resilient surface code memories and flexible color code processors [1]. A first experimental demonstration of using this technique to entangle two logical qubits encoded in two topological codes has been carried out in [2], and we are currently working on extending this lattice-surgery toolbox. In parallel, we are developing reinforcement-learning techniques for determining optimal code-switching strategies [4].

In addition, we are exploring the potential of high-dimensional quantum systems for quantum computing, which may entail advantages with respect to qubit-based approaches due to the reduced number of entangling gates that may have to be carried out [3]. We are actively working together with experimental groups to realize proof-of-concept demonstrations of components for quantum computing with high-dimensional systems in various platforms, including trapped ions [5] and optical platforms [6].

We are further interested in alternative paradigms of quantum computation, including synergies between parameter estimation and measurement-based quantum computation [7], black-box subroutines [8,9], and autonomous models of quantum computing [10].

References:

[1] Hendrik Poulsen Nautrup, Nicolai Friis, and Hans J. Briegel, Fault-tolerant interface between quantum memories and quantum processors, Nat. Commun. 8, 1321 (2017) [arXiv:1609.08062]

[2] Alexander Erhard, Hendrik Poulsen Nautrup, Michael Meth, Lukas Postler, Roman Stricker, Martin Stadler, Vlad Negnevitsky, Martin Ringbauer, Philipp Schindler, Hans J. Briegel, Rainer Blatt, Nicolai Friis, and Thomas Monz, Entangling logical qubits with lattice surgery, Nature 589, 220-224 (2021) [arXiv:2006.03071]

[3] Xiaoqin Gao, Paul Appel, Nicolai Friis, Martin Ringbauer, and Marcus Huber, On the role of entanglement in qudit-based circuit compression, Quantum 7, 1141 (2023) [arXiv:2209.14584].

[4] Hendrik Poulsen Nautrup, Nicolas Delfosse, Vedran Dunjko, Hans J. Briegel, and Nicolai Friis, Optimizing Quantum Error Correction Codes with Reinforcement Learning, Quantum 3, 215 (2019) [arXiv:1812.08451]

[5] Pavel Hrmo, Benjamin Wilhelm, Lukas Gerster, Martin W. van Mourik, Marcus Huber, Rainer Blatt, Philipp Schindler, Thomas Monz, and Martin Ringbauer, Native qudit entanglement in a trapped ion quantum processor, Nat. Commun. 14, 2242 (2023) [arXiv:2206.04104]

[6] Zhi-Feng Liu, Zhi-Cheng Ren, Pei Wan, Wen-Zheng Zhu, Zi-Mo Cheng, Jing Wang, Yu-Peng Shi, Han-Bing Xi, Marcus Huber, Nicolai Friis, Xiaoqin Gao, Xi-Lin Wang, and Hui-Tian Wang, Heralded High-Dimensional Photon-Photon Quantum Gate, preprint arXiv:2407.16356 [quant-ph] (2024).

[7] Nicolai Friis, Davide Orsucci, Michalis Skotiniotis, Pavel Sekatski, Vedran Dunjko, Hans J. Briegel, and Wolfgang Dür, Flexible resources for quantum metrology, New J. Phys. 19, 063044 (2017) [arXiv:1610.09999]

[8] Nicolai Friis, Vedran Dunjko, Wolfgang Dür, and Hans J. Briegel, Implementing quantum control for unknown subroutines, Phys. Rev. A 89, 030303(R) (2014) [arXiv:1401.8128].

[9] Nicolai Friis, Alexey A. Melnikov, Gerhard Kirchmair, and Hans J. Briegel,  Coherent controlization using superconducting qubits, Sci. Rep. 5, 18036 (2015) [arXiv:1508.00447].

[10] Florian Meier, Marcus Huber, Paul Erker, and Jake Xuereb, Autonomous Quantum Processing Unit: What does it take to construct a self-contained model for quantum computation? preprint arXiv:2402.00111 [quant-ph] (2024)