Researchers Achieve Universal Topological Gates Using 54-Qubits

Researchers are demonstrating a pathway towards fault-tolerant quantum computation by harnessing the exotic properties of anyons, quasiparticles that encode information in their braiding patterns. Chiu Fan Bowen Lo, Anasuya Lyons, and Dan Gresh, alongside colleagues from Quantinuum and Maxwell D. Urmey, have shown that even relatively simple topological order, previously thought limited in its computational power, can achieve universality when anyon fusion is considered a fundamental operation. Their work, conducted on Quantinuum’s H2 processor with a 54-qubit topological wavefunction, represents a significant step forward because it establishes that topological order can be both efficiently prepared and sufficiently complex to enable universal quantum computing, evidenced by the successful creation of a magic state and a universal gate set.

Urmey, have shown that even relatively simple topological order, previously thought limited in its computational power, can achieve universality when anyon fusion is considered a fundamental operation.

S3 Anyon Trapping Demonstrates Universal Quantum Computation

This breakthrough relies on treating anyon fusion as a fundamental computational primitive, enabling universality even in minimally non-Abelian topological orders which previously lacked this capability. This was further validated by preparing a magic state, a key component in fault-tolerant quantum computation. The study establishes that S3 topological order is sufficiently simple for efficient preparation, yet sufficiently rich to enable universal Topological quantum computation, overcoming limitations present in other approaches. This work represents a crucial step towards scalable and robust quantum technologies.

The research involved constructing a 54-qubit system representing the S3 quantum double model, a phase of matter where quantum information is encoded in the internal states of anyons. This model is based on the symmetry group S3, which dictates the rules governing how these anyons interact and fuse. By carefully manipulating these anyons through braiding, effectively exchanging their positions, and measuring their fusion products, the scientists created a set of quantum gates capable of performing any quantum computation. Experiments show that logical qutrits, quantum units with three possible states, were nonlocally encoded within the internal degrees of freedom of C2-fluxes, a specific type of anyon. Combining coherent anyon braiding, which creates entanglement between these qutrits, with precise measurements of their topological charge, allowed the team to implement a universal gate set. This gate set comprises three primitive operations: an entangling gate via braiding, X-basis measurement, and Z-basis measurement, demonstrating the ability to perform any quantum operation on pairs of qubits and qutrits.

S3 Toric Code Preparation and Anyon Trapping

Scientists engineered a 54-qubit toric code wavefunction associated with the S3 group on Quantinuum’s H2 processor to explore non-Abelian anyonic quasiparticles. This research demonstrates that minimally non-Abelian toric codes can achieve universality by treating anyon fusion as a fundamental operation. To prepare the S3 toric code, the team employed a gauging procedure, initially creating a Z3 qutrit toric code and subsequently applying another gauging operation to obtain the ground states of the S3 toric code. This construction utilized a fully unitary circuit, and measured projector expectation values were assessed to determine the fidelity of the prepared state.

The per-qudit fidelity of the prepared state on a 3×3 lattice with 18 sites was bounded as 0.970(5) ≤⟨gs| ρ |gs⟩1/18 ≤0.988(3). A comparable fidelity range of 0.930(8) to 0.978(2) was also achieved using a constant-depth adaptive preparation method, though the unitarily prepared ground states were favoured due to their slightly higher fidelity for the current system size. A hallmark of non-Abelian toric codes is the existence of low-lying excited states hosting single anyons on the torus. Scientists targeted a cyclic toric code, expecting it to enable universal computation via braiding and fusion.

They demonstrated the cyclicity of fusion rules by braiding a C3 flux around the horizontal noncontractible cycle of the torus, starting from a ground state with a C2 flux along the vertical cycle. This process toggled the fusion channel of the C3 pair, generating a single C3 flux anyon, representing the first experimental realization of a non-Abelian flux anyon in a lattice model with a toric code. This encoding ensures that encoded information remains unaffected during transport. The resulting fusion space yields a two-dimensional logical subspace, extending to a three-dimensional space due to the protected internal structure of the charge sector. Researchers labelled this logical qutrit using the fluxes of the constituent C2 fluxes, defining a Z-basis and establishing a nonlocal correlator to demonstrate entanglement between qutrits.

Universal quantum computation via anyon fusion and braiding

The research establishes that minimally non-Abelian TOs, previously considered insufficient for universal quantum computation via braiding alone, can achieve this capability when anyon fusion is treated as a primitive operation. Data shows that local stabilizers remained insensitive to the logical content of the qutrits, with BZ3 values consistently near 1/3, exhibiting a standard error of 0.034/0.059 at all flux endpoints. At fusion, the vertex projector AZ3 yielded 0.84(4) for the 0L state, consistent with vacuum annihilation, and 0.06(3) for the 1L state, indicating a remnant charge anyon. Tests prove that a C3 group element results in non-trivial braiding, with a 3/4 probability of obtaining a remnant [-] charge upon fusion.

Comparing the data state with the |1⟩L state, a violation was observed in the vertex projector AZ2 at t = 3, indicating the data qutrit was not in the |1⟩L state. Conversely, no additional violation was detected in the AZ2 vertex projector at t = 4, supporting that the data flux pair was indeed in the |0⟩L state. This comparison measurement facilitated a transition from absolute to relative encoding of the logical states. Researchers further demonstrated the preparation of states in the Z-basis bureau of standards, achieving values close to unity for ΠZ3 Wp1Wp2 projectors, 0.97(2), 0.99(1), and 0.98(1), demonstrating close approximation to ideally prepared 0L pairs. Measurements of ΠZ3 Wp1Wp2 and ΠZ3 Wp1Wp2Wp3 confirmed strong intra-pair and inter-pair Z correlations, yielding values of 0.32(4) and 0.92(2) respectively. Finally, the team successfully created a topological magic state, initiating the process by initializing the lowest two plaquettes with the input state 1L and the middle two with the reference state |2⟩L, demonstrating the potential for advanced quantum computations.

S3 Gauge Theory Enables Universal Quantum Control

Scientists have demonstrated a purely topological approach to universal quantum computation using quantum hardware. The findings establish non-Abelian anyons as programmable and computationally powerful entities, with the solvability of S3 facilitating scalable preparation and control. The authors acknowledge limitations related to qubit number and coherence, which currently constrain the scale of achievable topological states. Future work will focus on scaling system sizes to investigate logical error mechanisms and decoding strategies, alongside comparisons between ground-state and fusion-space encodings. This work suggests that finite-group non-Abelian topological orders offer a balance between computational capability and experimental feasibility, potentially extending surface code techniques while introducing new functionalities.