Generation of arbitrary all-photonic graph states from quantum emitters

Abstract

We present protocols to generate arbitrary photonic graph states from quantum emitters that are in principle deterministic. We focus primarily on two-dimensional cluster states of arbitrary size due to their importance for measurement-based quantum computing. Our protocols for these and many other types of two-dimensional graph states require a linear array of emitters in which each emitter can be controllably pumped, rotated about certain axes, and entangled with its nearest neighbors. We show that an error on one emitter produces a localized region of errors in the resulting graph state, where the size of the region is determined by the coordination number of the graph. We describe how these protocols can be implemented for different types of emitters, including trapped ions, quantum dots, and nitrogen-vacancy centers in diamond. is a 2×m cluster state, where m is the number of cycles. Schemes to create ladder-type cluster states using trapped ions have also been proposed [29]. However, for universal quantum computation, a larger twodimensional grid (n by m, with n, m?2) is needed; moreover, fault-tolerant universal computation requires a three-dimensional grid [30]. One interesting proposal to create a larger two-dimensional grid using feedback and atom-photon interactions in a cavity has been put forward [31]. However, this approach requires coupling the emitter to a chiral waveguide, which has yet to be demonstrated experimentally with high efficiency.In this paper, we propose an in-principle deterministic method to produce an arbitrary graph state that does not require photon-photon interactions. Instead, the entanglement is created between emitters and then transferred onto photons through optical pumping. This is similar to the idea presented in [28], although here, in addition to being able to create states corresponding to arbitrary graphs of any size, our scheme also allows for the entangling operations between emitters to occur after the photon pumping. Combined with heralding of the emission process, this allows one to perform the typically costly entangling operation only if there is a successful photon emission. Moreover, we show that, in a precise sense, our approach allows for the maximum possible delay in transferring the entanglement from the emitters onto the photons. Our protocol allows for arbitrary sized n by m clusters, given a linear array of n emitters, where each emitter can be entangled with its nearest neighbors. The operations required of the linear array are only a single two-emitter entangling gate and a photon pumping operation. For three-dimensional clusters, which permit fault-tolerant universal computation, our protocol requires a two-dimensional grid of nearest-neighbor connected emitters.This paper is organized as follows. First, a brief overview of the graph state formalism is provided. Second, our new framework to produce arbitrary graph states using emitters, assuming entangling gates are available between emitters, is presented. Then, we discuss concrete realizations ...

Photonic resource state generation from a minimal number of quantum emitters

“…Given that arbitrary graph states can be generated solely with Clifford gates 41,42 , which were also exclusively used in the protocols of refs. 24,25,[27][28][29][30][31]36 , restricting ourselves to this set does not affect the generality of our approach. Clifford gates enable the use of the stabilizer formalism, such that we can manipulate Pauli operators instead of keeping track of the whole state.…”

“…This idea was extended further to develop protocols that deterministically generate resource states for quantum repeaters [29][30][31][32] -tailored to color centers in refs. 33,34 -and one-way computing 35,36 . References 32,35 allowed for the re-interference of photons with emitters to further enhance flexibility in entanglement creation.…”

“…Despite this progress and the intense interest this approach has generated among experimentalists, existing graph state generation protocols are limited to a small subset of graphs or require a number of emitters that scales linearly with the graph size 36,37 . This is extremely resource-intensive, especially in light of the schemes for generating repeater graph states presented in refs.…”

Multidimensional cluster states using a single spin-photon interface coupled strongly to an intrinsic nuclear register

“…In 2010, Economou et al extended this Lindner-Rudolph scheme by using multiple coupled spin-photon interfaces to create a multidimensional cluster state [28], necessary for quantum information processing [29]. This proposal has since been extended to leverage more recent experimental advances on interactions between QDs [30], and to produce arbitrary graph states from linear arrays of spin-photon interfaces [31].…”

Resource requirements for efficient quantum communication using all-photonic graph states generated from a few matter qubits

“…Refs. [42,43] built on this protocol and demonstrated that entanglement between emitters can be harnessed for the generation of more complex photonic graph states. These ideas have been extended further to general prescriptions and to protocols tailored to specific physical systems [44][45][46][47].…”