Gaia Forghieri - University of Milan

Long-range interaction effects on quantum-walk-based computing

Quantum walks are fundamental tools for quantum information processing applications, as their efficient transport properties allow to enhance search algorithms, quantum state transfer, and more [1]. It has also been shown that controlled two-particle scattering of interacting quantum walks generates sufficient entanglement for the implementation of two-qubit gates in quantum-walk-based architectures [2]. This description however is typically restricted to on-site interactions (or first-neighbor for fermion statistics). Here, we generalize this framework by introducing long-range interactions between walkers evolving on correlated lattices [3]. We first evaluate the impact of the potential shape on transport properties and entanglement generation. We show that, while nearest-neighbor interactions always suppress transport, longer-range terms can restore semi-ballistic behavior while preserving relatively high entanglement, thus leading to highly correlated dynamics. We then analyze the effect of including several interacting neighbors on scattering processes for controlled-phase gates in a dual-rail encoding. Specifically, we find that the additional interaction terms allow to reach unitary fidelity for distinguishable particles, while, with single-term interactions, this was previously only obtainable for indistinguishable plane waves [4]. Through careful tuning of the interaction terms, this property is maintained for finite-size wave packets as well. This opens up the possibility for alternative circuit configurations for quantum-walk-based computation, possibly reducing the effective lengths of implemented quantum circuits.

References

[1] M. Frigerio, C. Benedetti, S. Olivares, and M.G.A. Paris, Phys. Rev. A, 105, 032425 (2022)

[2] R. Asaka, K. Sakai and R. Yahagi, Phys. Rev. A 107, 022415 (2023)

[3] G. Forghieri and M.G.A. Paris, in preparation (2026)

[3] A.M. Childs, D. Gosset and Z. Webb, Science 339, 791-794 (2013)