Seminar: Abraham Jacob and George Umbrarescu, University College London

Trivariate Tricycle Codes and Practical Distance Finding for QEC Researchers. Abraham Jacob, University College London

As quantum computers move beyond the NISQ era, high-rate and high-distance quantum error-correcting codes are essential for fault-tolerant computation. To meet this demand, group algebra codes have emerged as a highly successful method for constructing qLDPC codes, offering superior rate and distance compared to established models like the Toric code. However, as these codes grow in complexity, evaluating their true distance becomes significantly harder. This talk addresses both challenges by introducing a novel 3D code architecture alongside a new suite of accessible distance-finding tools. In the first half of this talk, I will introduce Trivariate Tricycle (TT) codes—one of the first examples of 3D group algebra codes. TT codes simultaneously reduce qubit overheads, using up to 48x fewer qubits, while significantly increasing the code distance and retaining the single-shot decodability present in the 3D Toric code. I will detail their construction and properties, demonstrate their threshold under circuit-level noise (0.3%), and discuss the construction of CCZ gates via the cup product. Like many modern codes, TT codes possess a complex Tanner graph structure. Computing their true distance is therefore a difficult task that requires highly robust methodologies. To make such tools more accessible to the community, the second half of the talk will focus on a newly developed suite of distance-finding tools for QEC researchers. I will outline various heuristic and exact algorithms we benchmarked, showcase a new Python package which gives streamlined access to many cutting-edge algorithms and highlight their most appropriate use cases.

SyQMA: A memory-efficient, symbolic and exact universal simulator for quantum error correction. George Umbrarescu (University College London)

The classical simulation of universal quantum circuits is crucial fundamentally and practically for quantum computation. We propose SyQMA, a simulator with several convenient features, particularly suited for quantum error correction (QEC). SyQMA simulates universal quantum circuits with incoherent Pauli noise and computes exact expectation values and measurement probabilities as symbolic functions of circuit parameters: rotation angles, measurement outcomes, and noise rates. This simulator can sample from the measurements, enabling the simulation of dynamic quantum programs where circuit composition depends on prior measurement outputs. For QEC, it performs circuit-level maximum-likelihood decoding, provides exact symbolic expressions for logical error rates, and verifies the fault distance of fault-tolerant (FT) stabiliser and magic state preparation protocols. These features are enabled by an intuitive extension of stabiliser simulators, where each non-Clifford Pauli rotation and incoherent Pauli channel is compactly represented via auxiliary qubits. The representation and evaluation of the state require polynomial memory in the circuit size, while only being exponential in the number of symbolic parameters. The FT preparation of stabiliser and magic states, including the first stage of magic state cultivation, is analysed without approximations. We also exactly convert the disjoint error probabilities of a general multi-qubit Pauli channel to independent ones, enabling precise hypergraph-to-graph reduction of detector error models