Optimal State Transfer and Entanglement Generation in Power-law Interacting Systems

Abstract

We present an optimal protocol for encoding an unknown qubit state into a multiqubit Greenberger-Horne-Zeilinger-like state and, consequently, transferring quantum information in large systems exhibiting power-law (1/r α ) interactions. For all power-law exponents α between d and 2d + 1, where d is the dimension of the system, the protocol yields a polynomial speedup for α > 2d and a superpolynomial speedup for α ≤ 2d, compared to the state of the art. For all α > d, the protocol saturates the Lieb-Robinson bounds (up to subpolynomial corrections), thereby establishing the optimality of the protocol and the tightness of the bounds in this regime. The protocol has a wide range of applications, including in quantum sensing, quantum computing, and preparation of topologically ordered states.

Photon-mediated interactions near a Dirac photonic crystal slab

“…An interesting outlook of our theory is applying it to other non-trivial band-structure points appearing in two-dimensional PhC slabs, such as Van-Hove singularities [36,[60][61][62], where strong super/sub-radiant effects [61,62] or highly anisotropic coherent interactions [63] have been predicted. Another research direction consists in harnessing the long-range nature of the photon-mediated in such Dirac light-matter interfaces for some of the quantum information and simulation applications mentioned in the introduction [11][12][13][14][15][16][17][18][19][20][21][22]. The authors acknowledge support from i-COOP program from CSIC with project reference COOPA20280.…”

“…2(b) we plot these analytical approximations (in shaded blue surface) together with the numerically obtained energy bands using the GME method (orange surface), showing a good agreement between the two. Interestingly, from the simplified eigenvalue problem obtained through the k • p approximation, we can also obtain the following magnetic and electric field expansions around the Dirac points (14) where k 0 can be K or K ; and the subindices 1, 2 indicate the two degenerate modes at K ( ) . The parameters ξ ± and η ± have the following values for K ( ) :…”

“…Long-range interactions are instrumental for many quantum information and simulation applications. For example, they can be harnessed to induce long-distance entanglement [11], to improve the speed of quantum state transfer protocols [12][13][14][15], or to explore (non-) equilibrium phenomena in frustrated spin models [16][17][18][19][20][21][22]. In free-space, photon-mediated interactions are naturally long-ranged (scaling with 1/r 3 (1) in the near (far) field), but they are unavoidable accompanied by dissipation [23,24].…”

Optimal Frobenius light cone in spin chains with power-law interactions

“…The classic Lieb-Robinson bounds were entirely ineffective at constraining information dynamics in long-range systems. Over the past few years, increasingly sophisticated methods have been developed [2,[16][17][18][19][20][21][22][23] to ultimately conclusively settle the question of how tight Lieb-Robinson-like bounds can be. In a d-dimensional system, the time it takes to prepare an EPR state between two qubits separated by distance r scales as t ∼ r min(α−2d,1) for α > 2d.…”

“…Our results have a number of interesting implications. Firstly, at α = 2 the growth of operators is hardly faster than with nearest neighbor interactions, while existing state transfer protocol may sends a single qubit in time t ∼ log r [22]! This demonstrates the qualitative discrepancy between Lieb-Robinson and Frobenius light cones, and implies that any task which is controlled by the Frobenius light cone may be exponentially slower at α = 2.…”