Related papers: Topological Quantum Compiling
Semiconductor nanowires provide an ideal platform for various low-dimensional quantum devices. In particular, topological phases of matter hosting non-Abelian quasi-particles can emerge when a semiconductor nanowire with strong spin-orbit…
We study the problem of universality in the anyon model described by the $SU(2)$ Witten-Chern-Simons theory at level $k$. A classic theorem of Freedman-Larsen-Wang states that for $k \geq 3, \ k \neq 4$, braiding of the anyons of…
While the realization of scalable quantum computation will arguably require topological stabilization and, with it, topological-hardware-aware quantum programming and topological-quantum circuit verification, the proper combination of these…
Quantum compiling fills the gap between the computing layer of high-level quantum algorithms and the layer of physical qubits with their specific properties and constraints. Quantum compiling is a hybrid between the general-purpose…
We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-local qubit Hamiltonians with a small set of physically…
This paper considers the problem of quantum compilation from an optimization perspective by fixing a circuit structure of CNOTs and rotation gates then optimizing over the rotation angles. We solve the optimization problem classically and…
We study the emergence of topological matter in two-dimensional systems of neutral Rydberg atoms in Ruby lattices. While Abelian anyons have been predicted in such systems, non-Abelian anyons, which would form a substrate for fault-tolerant…
A quantum computer consists of a set of quantum bits upon which operations called gates are applied to perform computations. In order to perform quantum algorithms, physicists would like to design arbitrary gates to apply to quantum bits.…
Given a quantum algorithm, it is highly nontrivial to devise an efficient sequence of physical gates implementing the algorithm on real hardware and incorporating topological quantum error correction. In this paper, we present a first step…
Holonomic quantum computation is the idea to use non-Abelian geometric phases to implement universal quantum gates that are robust to fluctuations in control parameters. Here, we propose a compact design for a holonomic quantum computer…
We introduce a numerical method for identifying topological order in two-dimensional models based on one-dimensional bulk operators. The idea is to identify approximate symmetries supported on thin strips through the bulk that behave as…
We show that braidings of the metaplectic anyons $X_\epsilon$ in $SO(3)_2=SU(2)_4$ with their total charge equal to the metaplectic mode $Y$ supplemented with measurements of the total charge of two metaplectic anyons are universal for…
The idea of topological quantum computation is to build powerful and robust quantum computers with certain macroscopic quantum states of matter called topologically ordered states. These systems have degenerate ground states that can be…
In three spatial dimensions, particles are limited to either bosonic or fermionic statistics. Two-dimensional systems, on the other hand, can support anyonic quasiparticles exhibiting richer statistical behaviours. An exciting proposal for…
This research presents a novel approach in quantum computing by transforming ARM assembly instructions for use in quantum algorithms. The core achievement is the development of a method to directly map the ARM assembly language, a staple in…
We show that a topological quantum computer based on the evaluation of a Witten-Reshetikhin-Turaev TQFT invariant of knots can always be arranged so that the knot diagrams with which one computes are diagrams of hyperbolic knots. The…
Before executing a quantum algorithm, one must first decompose the algorithm into machine-level instructions compatible with the architecture of the quantum computer, a process known as quantum compiling. There are many different quantum…
Recent demonstrations of non-Abelian braiding of graph vertices on noisy intermediate-scale quantum (NISQ) superconducting processor, and the experimental realization of topological order in general on various quantum hardware platforms…
We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any…
Quantum Approximation Optimization Algorithm (QAOA) is a highly advocated variational algorithm for solving the combinatorial optimization problem. One critical feature in the quantum circuit of QAOA algorithm is that it consists of…