#projectivemeasurements

Topological Quantum Computing Breakthrough: Projective Measurements Restore Anyon Braiding's Universality

Topological quantum computing researchers Themba Hodge, Philipp Frey, and Stephan Rachel from the University of Melbourne made a major advance by breaking a scaling barrier. Their work shows how projective measurements can be used in the braiding process of non-Abelian anyons to enable universal quantum computations with any number of qubits. This work enables fault-tolerant quantum computing by building sophisticated quantum circuits with over 99% fidelity on five qubits and scaling to 10 qubits.

Stable computation with topological quantum computing

Topological quantum computing is promising because it encodes and processes quantum information using non-Abelian anyon. Exotic quasiparticles like Majorana zero modes (MZMs) have peculiar statistics and are error-resistant, making this technique noise-resistant. Braiding operations of these anyons are employed to generate quantum gates in this framework.

Overcoming Naive Braiding Scalability Issues

Although braiding processes are resilient to local shocks, scaling topological quantum computing beyond two qubits is difficult. Braiding cannot do all quantum computations only because it is expanded to many qubits. Simple expansions of braiding-based gates cannot accommodate all quantum processes, including the Clifford group. The Hilbert space is limited by global fermion parity constraints, making braiding alone unable to dynamically prepare arbitrary quantum states.

Restoring Universality with Projective Measurements

Projective measurements during braiding are the primary novelty. These metrics are crucial for these reasons:

Switching qubit encodings: Dense and sparse encodings offer better error protection or are better for certain calculations. Projective measures overcome the shortcomings of each encoding by allowing seamless transitions. Dense encoding allows qubit entanglement, while sparse allows all single-qubit Clifford gates.

Multi-qubit operations require entangled states, which can be constructed using measurements. This includes the more complex GHZ state for five qubits and the Bell state for two.

Projective measurements project the state into a carefully defined subspace, allowing researchers to replicate braiding without explicitly replicating sophisticated MZM dynamics.

Projective measurements enable the creation of universal quantum gates, avoiding the disadvantages of naïve braiding.

Showing feasibility and fault tolerance

Researchers used many-body simulations of braiding dynamics improved with measurement-based switching to demonstrate this strategy's durability and resilience. Relevant findings are:

Successful State Preparation: They specifically prepared the GHZ state for five-qubit systems and the Bell state for two-qubit systems to demonstrate precise control.

Complex Circuits: A random unitary circuit on five qubits achieved over 99% fidelity. This implies precision in complex computations.

Non-Abelian anyons have intrinsic fault tolerance due to topological protection of their states. Projective measures increase fault tolerance. Simulations showed that computation fidelity remained above 99% even with substantial static potential disturbance. Working quantum computers require this ability to survive defects since noise is inevitable in real-world systems.

A simple MZM hosting model, the Kitaev chain, was employed for simulations. Gates were dynamically operated by timed MZM hybridisation or braiding. Despite exponential growth in projective measurements, the simulation method avoids the exponential expense of storing the complete quantum state by maximising parallel overlaps. The approach is suitable for large-scale simulations.

Scalability, Future Outlook

After simulating a ten-qubit system, the researchers developed a random unitary circuit with 77 gates and 18 projective measurements. This was the largest topological quantum circuit simulation on a MZM platform and demonstrated their scalability.