One of the biggest problems facing researchers today is producing the intricate, highly entangled states required to construct sophisticated, scalable quantum computers. Using high-spin donor atoms embedded in silicon, a group led by Gözde Üstün from UNSW Sydney and Simon J. Devitt from the University of Technology Sydney has now compared two different and state-of-the-art methods for creating these vital resource states, also referred to as qudit graph states.
This important study examines the relative benefits of directly creating large quantum structures using a system of connected emitters and deterministic gates vs creating them from a single quantum emitter using a probabilistic technique known as fusion. This work offers fresh perspectives on creating scalable quantum systems with silicon-based spin qubits by utilising cutting-edge materials research, nanofabrication, and quantum control approaches.
You can also read SDT Inc. QuEra Alliance Strengthens Neutral-Atom Computing
The Promise of High-Dimensional Qudits
The use of qudits quantum systems, which use several energy levels to encode more information than conventional two-level qubits, is the basis of this study. The researchers use silicon-implanted antimony (123Sb) donors. When combined with a bound electron, the high nuclear spin of a single antimony donor defines a 16-dimensional Hilbert space. A single electron connected to two antimony donors creates a system that functions in a huge 128-dimensional Hilbert space.
By adding weighted edges, represented as powers of the controlled-Z (CZ) gate, high-dimensional qudit graph states extend graph states. Without adding more physical systems, more data may be stored with the same degree of error resilience by using qudits. This is especially important for Fusion-Based Quantum Computing (FBQC), a scalable photonic quantum computation model that mainly uses fusion operations and entangled resource states.
Approach 1: Building Complexity with Fusion
The researchers’ first plan suggests creating qudit graph states using a single silicon spin qubit, which is a single antimony donor. This procedure is almost deterministic and extremely resource-efficient.
The creation of qudit graph states is dependent on a time-bin multiplexing situation in which a microwave cavity is connected to the antimony donor. The linear graph state is produced by the donor coherently emitting a sequence of photons into temporal modes by the application of a Fourier gate and successive electron dipole spin resonance (EDSR) pulses. For example, a single photon can act as a qutrit by being released into three time-bins. To create an n-node linear qudit cluster state, the complete procedure is carried out several times.
Following the creation of the linear graphs, they are combined into more complicated resource states, including ring or ladder structures, which are necessary for performing quantum computation, using fusion, a destructive and non-deterministic measurement technique.
However, the fusion procedures’ intrinsic probabilistic character is this scheme’s main drawback. The success probabilities for high-dimensional fusion methods have improved recently, but the rates are still significantly lower than in the qubit regime. For instance, dimension four’s success probability is 0.125, while dimension six’s is 0.055. To grow to complicated architectures, the single-emitter method depends on overcoming these poor success rates.
Approach 2: Eliminating Probability with Coupled Emitters
The alternate technique does not require fusion in the production of the single graph, instead using two spin qubits coupled together to directly generate the same complicated resource states. Two antimony donors share a single electron (a Sb 2+ molecule) in this system.
By linking the two emitters via a Controlled-Z (CZ) gate, this arrangement enables the creation of qudit graph states of any shape. The shared electron and suitable nuclear states are used to create the CZ gate, which uses electron spin resonance (ESR) pulses to induce a geometric phase. This approach substitutes a very dependable gate for the probabilistic fusion procedure, making it deterministic. The CZ gate operates in a matter of microseconds.
The 6-ring graph state, which has been thoroughly researched for fault-tolerant surface code implementations in the qubit regime, and a 2D ladder graph state are two examples of complicated states produced in this manner that the researchers present.
You can also read ConScience AB’s QiB1 and QiB2 to Boost Superconducting Qubit
Challenges and the Path to Scalability
Although deterministic graph construction is a major benefit of the coupled-emitter technique, it also presents new difficulties, mainly related to the molecular implantation procedure. The electron links asymmetrically to the two nuclei, strongly to one and weakly to the other, because the two antimony atoms are only roughly 5 nanometres apart and share a single electron.
With a difference of roughly 95 MHz, this asymmetry causes the two donors’ hyperfine interactions to be drastically different. This frequency difference implies that the photons emitted by the two distinct nuclei will have different frequencies and, therefore, be recognisable, since the concept suggests employing microwave cavities tuned to the EDSR transition frequency to emit photons. Architectural designs that depend on fusion between various resource states have difficulties since distinguishable photons cannot be fused.
Additionally, because the system only uses one shared electron, only one photon may be released at a time, which results in longer circuit operation periods because one nucleus is often left idle.
The researchers suggest an important next step: implanting individual antimony donors spaced about 15 nanometres apart, as opposed to implanting them as a molecule, in order to get over these architectural limitations and guarantee the scalability of the two-donor technique. By enabling simultaneous photon emission, each donor could house its own electron in this situation, greatly reducing operation durations and doing away with idle intervals. Crucially, it is anticipated that this single implantation will guarantee that the hyperfine interactions fall within the same range, increasing the likelihood that the photons released would be identical, allowing for the required fusion operations between resource states.
This comparative work advances the field towards the realization of scalable, high-threshold quantum architectures by elucidating the essential trade-offs between two potent paths to high-dimensional quantum processing in silicon. More theoretical research is required to determine which qudit graph states resource states are most appropriate for various quantum error correcting codes due to the continuous development of FBQC in higher dimensions.
You can also read Quantum world tour: Quantum Saudi Arabia Next-gen ecosystem
