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Unused “Neglectons” Could Lead to Quantum Computing Universality

USC mathematicians and physicists have discovered a groundbreaking way that could revolutionise quantum computing and boost its mainstream application. According to Nature Communications, this achievement was made possible by the unexpected usefulness of a previously disregarded particle called the “neglecton”.

Quantum computers have great potential since they can address issues beyond the capabilities of today's supercomputers. However, quantum bits, or “qubits,” are brittle, which has slowed their progress. Due to their great susceptibility to environmental disturbances, these information-storing devices quickly collect flaws that threaten calculations.

One of the best ways to overcome fragility is topological quantum computing. This unique method protects quantum information by encapsulating it in anyons' geometric properties. These particles, which may be found in two-dimensional materials, are expected to be more noise- and interference-resistant than qubits.

Ising anyons, which are being extensively studied in condensed matter labs, are promising candidates for a dependable quantum computer. They are appealing because they can be realised in exotic systems like topological superconductors and fractional quantum Hall states.

However, the study's lead author, USC Dornsife College of Letters, Arts, and Sciences professor of mathematics, physics, and astronomy Aaron Lauda, noted a major downside. A general-purpose quantum computer cannot be operated by ising anyons alone. Their quantum logic calculations include “braiding,” the physical movement of anyons around each other. Ising anyons can only perform a finite number of clifford gates with this braiding, which is insufficient for global quantum computing.

Mathematical Discard to Quantum Discovery

The USC-led team found an unanticipated way around this restriction. They showed that Ising anyons can be universal by introducing a new type of anyon that was previously overlooked in topological quantum computation frameworks. This indicates that braiding alone might do any quantum computing. The physicists called these stored particles “neglectons,” indicating their importance and neglect. A bigger mathematical framework naturally produced this new anyon, which completed the computational toolset.

This crucial discovery is hidden in a new family of mathematical theories termed non-semisimple topological quantum field theories (TQFTs). These concepts extend the “semisimple” frameworks physicists have used to describe anyons. The mathematics behind traditional models is simplified by eliminating objects with “quantum trace zero,” making them worthless.

Lauda likened the discovery to “discovering treasure in what everyone else thought was mathematical garbage,” “but those discarded objects turn out to be the missing piece.” By intentionally retaining these ignored bits, the new framework unveils a novel anyon termed the neglecton, which, when combined with Ising anyons, allows braiding-based universal computing. Importantly, the system only needs one neglecton and stays in a constant state while the Ising anyons braid around it to compute.

upcoming unitality issues

This remarkable discovery was mathematically complex. The anomalies introduced by the non-semi simple framework appear to violate unitality, a critical characteristic of quantum physics that guarantees probability. Most scientists would consider such a violation catastrophic.

But Lauda's team devised a smart solution. They developed quantum encoding to separate mathematical abnormalities from computing activities. “Think of it like designing a quantum computer in a house with some unstable rooms,” Lauda said. Instead of fixing every room, you use the stable spaces for computing and keep the problematic ones off-limits. By limiting quantum information to well-behaved elements of the theory, scientists "quarantined the strange parts," allowing computation to proceed despite the peculiar global mathematical structure.

Mathematics to Quantum Reality

This breakthrough shows how abstract mathematics can solve concrete engineering difficulties in unanticipated ways. “We opened a whole new chapter for quantum information science by embracing mathematical structures that were previously thought to be useless,” Lauda said.

The study presents intriguing theoretical and practical opportunities. Adding more parameter values to their framework and elaborating on unitarity in non-semisimple TQFTs are the team's mathematical aims. By experimenting, they seek to find material platforms where stationary neglecton naturally occurs and establish protocols to turn their braiding-based technique into practical quantum processes.