Measurement-based Quantum Computation

Measurement-based quantum computation (MBQC) is one of the leading paradigms for quantum computation [1]. However, it is rather different from the standard circuit model where unitaries are directly implemented on a qubit register. In MBQC our starting point is a two-dimensional highly entangled quantum state, the resource. We do still have a qubit register, which is one dimension of the resource state. However, now the other dimension takes the role of simulated time. Simulated time? Yes, because we will make our qubits evolve from left to right using a process similar to quantum teleportation, where information is teleported by measuring single qubits.


MBQC is a fascinating paradigm : computation is driven by local measurements on a fixed entangled resource state and unitaries are implemented by choosing adequate measurement bases. As it turns out, with certain resource states such as the cluster state [2] MBQC can facilitate arbitrary quantum computation. It is universal!

MBQC has been around for almost 20 years and, yet, there are still many exciting open questions one can address. In our group we investigate many of these questions, ranging from the understanding of the ultimate scope of quantum computers, to practical aspects about feasibility and applications.

What constitutes a universal resource?


Without entanglement, MBQC cannot work. But with little entanglement, it can [3]. At the same time, too much entanglement can be equally detrimental as no entanglement [4]. So, what does constitute a good resource for MBQC? This is a rather vexing question, and there is still no complete answer. However, over the years, we have made leaps and bounds towards a unifying answer [5, 6]. In particular, we have furthered a fascinating connection to condensed matter physics: certain phases of quantum matter can be used as universal resources for MBQC [7, 8, 9]. Specifically, we found that one unifying link are is provided by quantum cellular automata, which further a completely new perspective on the almost 20 year old MBQC. We are excited to explore this connection with many of our collaborators all over the world, from Vancouver to Berlin.

How to implement a quantum computer based on MBQC?


MBQC is a fascinating framework where a quantum computation is realized by simply performing single-qubit measurements on an initially entangled state. This new approach makes MBQC particularly suitable for certain technological platforms such as photons [10, 11] or trapped ions [12]. Considering the ongoing research on resources for MBQC, one may even find certain phases of matter [8, 9] which occur naturally in certain experiments or materials to facilitate MBQC. We are always happy to collaborate with experimentalists and discuss contemporary research and novel implementations.

What is the role of MBQC in quantum communication?

The cluster state [2] and, more generally, graph states [13], form the basis of standard MBQC. Graph states have surprising and useful properties and provide a playground for the study of entanglement [14]. This line of research has had a remarkable impact on quantum communication, and facilitated significant improvements in various protocols such as entanglement purification and quantum repeaters. For instance, we demonstrated a significant increase in the robustness of these protocols against typical sources of noise. Our goal is not only to develop (special purpose) small-scale quantum machines for practical application in quantum communication [15] but also to facilitate the development of large-scale quantum networks [16].

For more details, see [Quantum Networks].

Can MBQC enhance decision-making in AI?


Resources for MBQC such as the cluster state can be defined for arbitrary graphs. Interestingly, the specific layout of the underlying graph carries meaning and facilitates different computations or communications scenarios [17]. Analogously, Projective Simulation is a model for artificial intelligence [18] where decision making is modelled by a memory-network described by a weighted graph. We are working towards an integration and further development of the two paradigms to design a quantum AI based on MBQC.


Can AI improve MBQC protocols?



Machine learning has proven to be a powerful tool that already permeates our every-day life. We want to leverage this technology for quantum information science. Indeed, due to its flexibility and broad applicability, MBQC may serve as an optimal playground to test the capabilities of artificial intelligence in quantum physics. In this endeavor, we have already shown that reinforcement learning can help develop quantum communication protocols and we are excited to see where else this development will lead us!

For more details, see [Artificial Intelligence and Science].

[1] A one-way quantum computer, R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001) [arXiv:quant-ph/0010033].

[2] Persistent entanglement in arrays of interacting particles, H. J. Briegel and R. Raussendorf, Phys. Rev. Lett. 86, 910 (2001) [arXiv:quant-ph/0004051].

[3] (external) Universal quantum computation with little entanglement, M. Van den Nest, Phys. Rev. Lett. 110, 060504 (2013) [arXiv:1204.3107].

[4] (external) Most quantum states are too entangled to be useful as computational resources, D. Gross, S. T. Flammia and J. Eisert, Phys. Rev. Lett 102, 190501 (2009) [arXiv:0810.4331].

[5] Universal resources for measurement-based quantum computation, M. Van den Nest, A. Miyake, W. Dür, H. J. Briegel, Phys. Rev. Lett. 97, 150504 (2006) [arXiv:quant-ph/0604010].

[6] Measurement-based quantum computation, H. J. Briegel, D. E. Browne, W. Dür, R. Raussendorf, M. Van den Nest, Nature Physics 5 (1), 19-26 (2009) [arXiv:0910.1116].

[7] Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian, G. K. Brennen and A. Miyake, Phys. Rev. Lett. 101, 010502 (2008) [arXiv:0803.1478].

[8] Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter, D. T. Stephen, H. Poulsen Nautrup, J. Bermejo-Vega, J. Eisert, and R. Raussendorf, Quantum 3, 142 (2019), [arXiv:1806.08780].

[9] A computationally universal phase of quantum matter, R. Raussendorf, C. Okay, D.-S. Wang, D. T. Stephen, and H. Poulsen Nautrup, Phys. Rev. Lett. 122, 090501 (2019), [arXiv:1803.00095].

[10] Demonstrating elements of measurement-based quantum error correction, S. Barz, R. Vasconcelos, C. Greganti, M. Zwerger, W. Dür, H. J. Briegel, and P. Walther, Phys. Rev. A 90, 042302 (2013), [arXiv:1308.5209].

[12] Measurement-based quantum computation with trapped ions, B. P. Lanyon, P. Jurcevic, M. Zwerger, C. Hempel, E. A. Martinez, W. Dür, H. J. Briegel, R. Blatt, C. F. Roos, Phys. Rev. Lett. 111, 210501 (2013), [arXiv:1308.5102].

[13] Multiparty entanglement in graph states, M. Hein, J. Eisert, and H. J. Briegel, Phys. Rev. A 69, 062311, [arXiv:quant-ph/0307130].

[15] Measurement-based Quantum Communication, M. Zwerger, H. J. Briegel, and W. Dür,  Appl. Phys. B 122, 50 (2016) [arXiv:1308.5209].

[16] Modular architectures for quantum networks, A. Pirker, J. Wallnöfer, and W. Dür, New J. Phys. 20, 053054 (2018) [arXiv:1711.02606].

[17] Machine Learning for long-distance quantum communication, J. Wallnöfer, A. A. Melnikov, W. Dür, and H. J. Briegel, PRX Quantum 1, 010301 (2020) [arXiv:1904.10797].

[18] Projective simulation for artificial intelligence, H. J. Briegel and G. De las Cuevas, Sci. Rep. 2, 400 (2012) [arXiv:1104.3787].

Nach oben scrollen