Towards measurement based quantum computation with multipods

Claire Benjamin1,2, Dániel Varjas3,4, Gábor Széchenyi5,6, Judit Romhányi1, László Oroszlány2,6
1Department of Physics and Astronomy, University of California, Irvine;
2Department of Physics of Complex Systems, Eötvös Loránd University;
3Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics;
4Institute for Theoretical Solid State Physics, IFW Dresden and Würzburg-Dresden Cluster of Excellence;
5Department of Materials Physics, Eötvös Loránd University;
6HUN-REN Wigner Research Centre for Physics

The Team

Dániel Varjas

BME & IFW

Gábor Széchenyi

ELTE & Wigner FK

Judit Romhányi

UC Irvine

Claire Benjamin

UC Irvine

Measurement based quantum computing

Raussendorf, Briegel Phys. Rev. Lett. 86, 5188 (2001)

Raussendorf

Looking for resource states

Wei, Affleck, Raussendorf Phys. Rev. Lett. 106, 070501 (2011)

Tzu-Chieh Wei

Ian Affleck

Looking for higher spins

Lieb Phys. Rev. Lett. 62, 1927 (1989)

Elliott Lieb

Stars are quite resilient!

S=1 AKLT: How to couple two stars?

AFM

AFM

FM

H=J\vec{S}_1\cdot\vec{S}_2+\beta\left ( \vec{S}_1\cdot\vec{S}_2 \right )^2
\sigma_2=\frac{|E_0-E_1|}{2t}

Effective model for spins from QDPT!

Day, et al. Phys. Codebases 50 (2025)

 pymablock.readthedocs.io

H_0 + p H_1 \Rightarrow \tilde{H}_0+\sum_n p^n \tilde{H}^{(n)}_1

S=1 AKLT: How to couple two stars, PT

\underbrace{H_0 + p H_1}_{c_{n\sigma}} \Rightarrow \underbrace{\tilde{H}_0+\sum_n p^n \tilde{H}^{(n)}_1}_{S_i}
\left(S_i S_j\right)^n=a_nI+b_n\left(S_i S_j\right)+c_n\left(S_i S_j\right)^2
\tilde{H}=A(t)I+f(t)\left(S_1 S_2\right)+g(t)\left(S_1 S_2\right)^2
f(t^*)=3g(t^*)

S=1 AKLT: How to couple many stars?

This is

promising!

We do not want:

 \( \vec{S}_1\cdot\vec{S}_3 \Rightarrow \) long range

 \( (\vec{S}_1\cdot\vec{S}_2) (\vec{S}_2\cdot\vec{S}_3) \) \(\Rightarrow\) multi spin

 

 

 

S=3/2 AKLT: How to couple two stars?

H=\sum_{nm}\left[\left(S_1\cdot S_2\right)+\frac{116}{243}\left(S_1 \cdot S_2\right)^2+\frac{16}{243}\left(S_1 \cdot S_2\right)^3\right]
f(t^*)=243/116g(t^*),\, f(t^*)=243/16h(t^*)

What about measurment?

Experimental realization

V. John et al. Nat. Commun. 16, 10560 (2025) 

Thanks!

C. Benjamin, D. Varjas, G. Széchenyi, J. Romhányi, L. Oroszlány

AKLT Hamiltonian from Hubbard tripods
https://arxiv.org/abs/2603.06455