Non-Abelian braiding of graph vertices in a superconducting processor

Abstract

Indistinguishability of particles is a fundamental principle of quantum mechanics1. For all elementary and quasiparticles observed to date—including fermions, bosons and Abelian anyons—this principle guarantees that the braiding of identical particles leaves the system unchanged2,3. However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions4–8. Hence, it can change the observables of the system without violating the principle of indistinguishability. Despite the well-developed mathematical description of non-Abelian anyons and numerous theoretical proposals9–22, the experimental observation of their exchange statistics has remained elusive for decades. Controllable many-body quantum states generated on quantum processors offer another path for exploring these fundamental phenomena. Whereas efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasiparticles, superconducting quantum processors allow for directly manipulating the many-body wavefunction by means of unitary gates. Building on predictions that stabilizer codes can host projective non-Abelian Ising anyons9,10, we implement a generalized stabilizer code and unitary protocol23 to create and braid them. This allows us to experimentally verify the fusion rules of the anyons and braid them to realize their statistics. We then study the prospect of using the anyons for quantum computation and use braiding to create an entangled state of anyons encoding three logical qubits. Our work provides new insights about non-Abelian braiding and, through the future inclusion of error correction to achieve topological protection, could open a path towards fault-tolerant quantum computing.

Enhanced repetition codes for the cross-platform comparison of progress towards fault-tolerance

“…For the d = 3 example, such a schedule could be expressed as follows. schedule = [[(0,1), (3,5)], [(3,1), (6,5)]] Here two layers of entangling gates are used. In the first, a gate is applied to qubits 0 and 1 at the same time as one on qubits 3 and 5.…”

“…The last decade has seen a great deal of progress in the experimental demonstration of quantum error correction. A wide range of experiments have been carried out: from demonstrating detection of errors with the [[2, 0, 2]] code [1], to d = 3 and d = 5 surface codes [2][3][4]; from extremely minimal demonstrations of twist defects [5] to full implementations [6,7]. The scale of experiments can be expressed in terms of the number of qubits used, the code distance of the stored information and the number of syndrome measurement rounds.…”

Logical quantum processor based on reconfigurable atom arrays

“…However, in practice, useful QEC poses many challenges, ranging from large overhead in physical qubit numbers 23 to highly complex gate operations between the delocalized logical degrees of freedom 24 . Recent experiments have achieved milestone demonstrations of two logical qubits and one entangling gate 5 , 6 and explorations of new encodings 25 – 28 .…”

Ren-integrable and ren-symmetric integrable systems

“…Recently, unlike bosons and fermions, anyons with fractional charges, spin and statistics in two dimensions have attracted the attention of many scientists [38][39][40][41]. Anyons can be used to describe some kinds of quasi-particles (the lowenergy excitations in Hamiltonian systems) including the fractional quantum Hall states [42], vortices in topological superconductors [43] and Majorana zero modes in semiconductors proximitized by superconductors [44].…”