Methods for simulating string-net states and anyons on a digital quantum computer

Topological orders and anyons are fascinating phenomena that are both conceptually important and practically useful for quantum computing. However, topological orders lack conventional order parameters and are generically difficult to diagnose. Recent advances in quantum simulations have further emphasized the need for efficient methods for identifying topological orders. A breakthrough in this problem is the discovery of topological entanglement entropy, which can be used to...

We show that quantum systems of extended objects naturally give rise to a large class of exotic phases - namely topological phases. These phases occur when the extended objects, called ``string-nets'', become highly fluctuating and condense. We derive exactly soluble Hamiltonians for 2D local bosonic models whose ground states are string-net condensed states. Those ground states correspond to 2D parity invariant topological phases. These models reveal the mathematical framewo...

We develop methods to probe the excitation spectrum of topological phases of matter in two spatial dimensions. Applying these to the Fibonacci string nets perturbed away from exact solvability, we analyze a topological phase transition driven by the condensation of non-Abelian anyons. Our numerical results illustrate how such phase transitions involve the spontaneous breaking of a topological symmetry, generalizing the traditional Landau paradigm. The main technical tool is t...

Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and sparse representations of quantum information (qubits) and a simple construction of multi-qubit gates, for all anyon models from Chern-Simons-Witten SU(2)$_k$ theory that support universal quantum computation by braiding ($k\geq 3,\ k \neq 4$). ...

Topological orders can be used as media for topological quantum computing --- a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing device for special purposes, also offers a way of characterizing topological orders. Here, we show how to identify distinct topological orders via measuring their modular $S$ and $T$ matrices. In particular, we employ a nuclear magnetic resonan...

Non-Abelian anyons are exotic quasiparticle excitations hosted by certain topological phases of matter. They break the fermion-boson dichotomy and obey non-Abelian braiding statistics: their interchanges yield unitary operations, rather than merely a phase factor, in a space spanned by topologically degenerate wavefunctions. They are the building blocks of topological quantum computing. However, experimental observation of non-Abelian anyons and their characterizing braiding ...

Topological quantum computers provide a fault-tolerant method for performing quantum computation. Topological quantum computers manipulate topological defects with exotic exchange statistics called anyons. The simplest anyon model for universal topological quantum computation is the Fibonacci anyon model, which is a non-abelian anyon system. In non-abelian anyon systems, exchanging anyons always results a unitary operations instead of a simple phase changing in abelian anyon ...

The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven to be extremely challenging in both condensed matter and synthetic quantum systems. Here, we prepare the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measure a topol...

Realizing nonabelian topological orders and their anyon excitations is an esteemed objective. In this work, we propose a novel approach towards this goal: quantum simulating topological orders in the doubled Hilbert space - the space of density matrices. We show that ground states of all quantum double models (toric code being the simplest example) can be efficiently prepared in the doubled Hilbert space. In contrast, this is not the case in the conventional Hilbert space: Gr...

We describe how continuous-variable abelian anyons, created on the surface of a continuous-variable analogue of Kitaev's lattice model can be utilized for quantum computation. In particular, we derive protocols for the implementation of quantum gates using topological operations. We find that the topological operations alone are insufficient for universal quantum computation which leads us to study additional non-topological operations such as offline squeezing and single-mod...