Topological quantum computing
Says "hello world" with recent breakthrough
Hey there!
Quantum computing is part technology and part initiative needing more belief to transfer the weight from initiative to technology. A significant boost in this belief came from a team of researchers from Quantinuum, Harvard, Caltech and U of Chicago (read about their research, cover by The Quantum Insider) as they provided first ever demonstration of elements of topological quantum computing (TQC). In this issue, of The Quantum Vibe I demystify this landmark achievement and talk about what lies ahead.
Topological quantum computing
Quantum computers are improving everyday and getting ready for a near-future impact. However, we are still in the NISQ era- the age of Noisy Intermediate Scale Quantum computers, where quantum devices are prone to errors. Immense amount of resources are spent to manage these errors and extract useful pieces of information. One promising solution to this problem is TQC, and the recent work on TQC's foundational elements has fueled hopes for its practical realization.
First things first, what is topological quantum computing? In simple words, if a system is topological it remains unaffected by small perturbations. It has been known that collective excitations of elementary particles, say electrons, can host topological properties. These special collective excitations form quasi-particles, called anyons which are fundamental to implementing TQC. Operations are performed by braiding anyons, moving them around one another, which changes their collective quantum state in a fault-tolerant way.
The execution of TQC can be divided into three steps: initialization (creation of anyons), processing (gate operations) and readout (close the computation process). However, things get complicated at all levels. For initialization, it is highly non-trivial to establish universal protocols for presence of anyons because they are observed indirectly through detection of fractional charges which can arise in a system for a number of reasons. For processing, braiding (non-Abelian) anyons braiding for gate operations is a formidable challenge. For readout, it depends on interference measurements which are notoriously sensitive and hard to stabilize.
The first demonstration of TQC elements
In the midst a number of complications in a physical topological system, there is an element of synthetic topology which can be exploited for better results. This is achieved by something called toric code. If you do a Google image search for topology, you will see a lot of donuts. In mathematics these donuts are called torus and thus the name of the code. Now, the mathematics of topology is such that a two-dminesional array can be mapped on to a torus. This is very well understood in solids (an array of atoms), and now there are efforts to utilize it in array of qubits. Following the principles of topology, a qubit array is mapped on to a torus and anyons are generated through local disturbances. Something similar was implement in demonstration of elements of TQC where a team of researchers from Quantinuum, Harvard, Caltech and U of Chicago came together to implement a toric code on a trapped-ion quantum processor. To summarize the technical details:
Encoding Qutrits: The system used 56 trapped ¹⁷¹Yb⁺ ions, each representing a pair of qubits. These pairs were encoded into qutrits (3-level quantum systems) to construct the Z₃ toric code.
Lattice Construction: Qutrits were placed on the vertices of a 2D square lattice with periodic boundary conditions, effectively creating a torus-like topology.
Preparation of the Ground State: The ground state of the Z₃ toric code was initialized using a circuit that enforced stabilizer conditions (operators ensuring the topological order). This involved applying laser-driven gates to project the lattice into the desired topological state.
Defect Creation: Specific qutrit operations were used to introduce topological defects, such as parafermions and charge conjugation defects, into the toric code.
Anyonic Manipulation: Using precise ion control, the researchers moved and fused anyons and defects, validating their braiding and fusion properties.
This implementation achieved high fidelity (>96%), and marks a crucial step in the realization of topologically protected quantum systems.
What lies ahead?
While this breakthrough represents a crucial step forward, the road to practical TQC is still long. Universal gate operations, required for full-fledged quantum computing, remain a distant goal. Fidelity must also improve significantly for real-world applications. However, progress in the field is accelerating, fueled by a growing talent pool and innovative experimental techniques. This work has undoubtedly lifted spirits in the quantum industry, sparking optimism about TQC’s future. By the way, quantum stocks recently surged with 100-400% bullish 📈.
So that’s that from this issue. Until next time, stay curious.