#quditgraphstates

Researchers struggle to create the complex, highly entangled states needed to build scalable quantum computers. A team led by Gözde Üstün from UNSW Sydney and Simon J. Devitt from the University of Technology Sydney compared two cutting-edge qudit graph state creation methods using high-spin donor atoms embedded in silicon.

The benefits of directly constructing huge quantum structures utilising a system of connected emitters and deterministic gates vs fusion from a single quantum emitter are compared in this key work. Innovative materials research, nanofabrication, and quantum control methods are used to create scalable quantum systems with silicon-based spin qubits.

The High-Dimensional Qudits Promise

This study relies on qudits quantum systems, which encode more information than two-level qubits. They use silicon-implanted antimony (123Sb) donors. The high nuclear spin of a single antimony donor creates a 16-dimensional Hilbert space with a bound electron. A system with one electron and two antimony donors operates in a vast 128-dimensional Hilbert space.

High-dimensional qudit graph states enhance graph states by adding weighted edges as controlled-Z (CZ) gate powers. With qudits, more data can be stored with the same fault resilience without increasing physical devices. Fusion-Based Quantum Computing (FBQC), a scalable photonic quantum computation architecture that combines fusion operations and entangled resource states, needs this.

First, build complexity using fusion

The researchers' first idea is to create qudit graph states with a single silicon spin qubit, an antimony donor. This method is nearly deterministic and resource-efficient.

Creating qudit graph states requires time-bin multiplexing with a microwave cavity coupled to the antimony donor. The donor coherently emits photons into temporal modes using a Fourier gate and subsequent electron dipole spin resonance (EDSR) pulses to create the linear graph state. A single photon emitted into three time-bins can operate as a qutrit. The same technique is repeated to produce an n-node linear qudit cluster state.

Combining linear graphs into more complex resource states, such as ring or ladder structures, is crucial for quantum computation employing fusion, a destructive and non-deterministic measurement technique.

The fundamental downside of this method is the intrinsic probabilistic nature of fusion operations. High-dimensional fusion approaches have improved recently, but their success rates are still much lower than in the qubit regime. Dimension four has 0.125 success probability, while dimension six has 0.055. To evolve to intricate designs, the single-emitter approach must overcome these low success rates.

Coupled emitters eliminate probability in Approach 2.

The alternative method uses two spin qubits coupled together to directly generate the same intricate resource states without fusing to produce the single graph. This system shares an electron (Sb 2+ molecule) between two antimony donors.

By connecting the emitters via a Controlled-Z (CZ) gate, qudit graph states of any shape can be created. The shared electron and suitable nuclear states generate the CZ gate, which induces a geometric phase with electron spin resonance (ESR) pulses. This method replaces probabilistic fusion with a reliable gate, making it deterministic. The CZ gate works in microseconds.

This method produces sophisticated states like the 6-ring graph state, which has been extensively studied for fault-tolerant surface code implementations in the qubit domain, and a 2D ladder graph state.

Challenges and Scalability Path

While deterministic graph generation is a major feature of the coupled-emitter approach, it also introduces new problems, mostly related to molecular implantation. Since the two antimony atoms are barely 5 nanometres apart and share an electron, the electron binds strongly to one nucleus and weakly to the other.

This asymmetry leads the two donors' hyperfine interactions to diverge greatly by 95 MHz. The concept recommends using microwave cavities adjusted to the EDSR transition frequency to emit photons from the two nuclei, which will have different frequencies and be identifiable. Architectural solutions that rely on fusion between resource states are problematic because distinct photons cannot merge.

Because the system only uses one shared electron, only one photon may be released at a time, which prolongs circuit operation because one nucleus is often idle.

The researchers advise implanting individual antimony donors 15 nanometres apart instead of as a molecule to overcome these architectural limits and ensure the scalability of the two-donor strategy. By emitting photons simultaneously, each donor could house its own electron, shortening operation time and eliminating idle periods. Importantly, this single insertion should ensure that hyperfine interactions fall within the same range, increasing the possibility that photons released will be identical, allowing for resource state fusion operations.