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ABSTRACT:The need for precise characterization of dual-phase xenon detectors has grown as the technology has matured into a state of high efficacy for rare event searches. The Michigan Xenon detector was constructed to study the microphysics of particle interactions in liquid xenon across a large energy range in an effort to probe aspects of radiation detection in liquid xenon. We report the design and performance of a small 3D position sensitive dual-phase liquid xenon time projection chamber with high light yield (L 122 y = 15.2 pe/keV at zero field), long electron lifetime (τ > 200 µs), and excellent energy resolution (σ /E = 1% for 1,333 keV gamma rays in a drift field of 200 V/cm). Liquid xenon time projection chambers with such high energy resolution may find applications not only in dark matter direct detection searches, but also in neutrinoless double beta decay experiments and other applications.

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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.

ABSTRACT. In this paper, we fix a polynomial with complex coefficients and determine the eigenforms for SL 2 (Z) which can be expressed as the fixed polynomial evaluated at other eigenforms. In particular, we show that when one excludes trivial cases, only finitely many such identities hold for a fixed polynomial.