Comparing Schemes for Creating Qudit Graph States from 16- & 128-dimensional Hilbert Space using Donors in Silicon

TL;DR

This paper compares two methods for creating qudit graph states in silicon, analyzing their efficiency and scalability for quantum computing applications.

Contribution

It introduces and evaluates two distinct schemes for generating qudit graph states using silicon spin qudits, highlighting their differences and potential advantages.

Findings

The first scheme uses a single emitter with fusion to build complex states.

The second scheme employs direct coupling of two emitters via CZ gates.

Both schemes can produce equivalent resource states, with different scalability prospects.

Abstract

In this work, we compare two schemes for generating arbitrary qudit graph states using spin qudits in silicon. The first scheme proposes the creation of qudit linear graph states from a single emitter - a silicon spin qudit. By employing fusion - a destructive and non-deterministic measurement technique - these linear graphs can then be combined to form more complex resource states (multi-photon entangled states), such as ring or ladder structures, which are used to carry out the computation. The second scheme employs two spin qudits. Instead of relying on fusion, the two emitters are directly coupled via CZ to generate the same resource states, thereby eliminating the need for fusion. We compare the two schemes in terms of their ability to produce equivalent resource states and discuss their respective advantages and limitations for building scalable architectures.