Related papers: Minimal Quantum Circuits for Simulating Fibonacci …
Multiterminal Josephson junctions constitute engineered topological systems in arbitrary synthetic dimensions defined by the superconducting phases. Microwave spectroscopy enables the measurement of the quantum geometric tensor, a…
These extended lecture notes survey a novel derivation of anyonic topological order (as seen in fractional quantum Hall systems) on single magnetized M5-branes probing Seifert orbi-singularities ("geometric engineering" of anyons), which we…
We consider a two-dimensional quantum memory of qubits on a torus which encode the extended Fibonaccistring-net code, and devise strategies for error correction when those qubits are subjected to depolarizing noise.Building on the concept…
The methods for realizing of non-Abelian gauge potentials have been proposed in many different systems in condensed matter1-5. The simplest realization among them may be in a graphene bilayer obtained by slightly relative rotation between…
The emergence of non-Abelian anyons from large collections of interacting elementary particles is a conceptually beautiful phenomenon with important ramifications for fault-tolerant quantum computing. Over the last few decades the field has…
We systematically map low-bond-dimension PEPs tensor networks to quantum circuits. By measuring and reusing qubits, we demonstrate that a simulation of an $N \times M$ square-lattice PEPs network, for arbitrary $M$, of bond dimension $2$…
Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have…
In a topological quantum computer, universal quantum computation is performed by dragging quasiparticle excitations of certain two dimensional systems around each other to form braids of their world lines in 2+1 dimensional space-time. In…
We consider a generic Fibonacci topological wave function on a square lattice, and the norm of this wave function can be mapped into the partition function of two-coupled $\phi ^{2}$-state Potts models with $\phi =(\sqrt{5}+1)/2$ as the…
Numerical optimization methods such as hillclimbing and simulated annealing have been applied to search for highly entangled multi-qubit states. Here the genetic algorithm is applied to this optimization problem -- to search not only for…
We give quantum circuits that simulate an arbitrary two-qubit unitary operator up to global phase. For several quantum gate libraries we prove that gate counts are optimal in worst and average cases. Our lower and upper bounds compare…
In topological quantum computation, quantum information is stored in states which are intrinsically protected from decoherence, and quantum gates are carried out by dragging particle-like excitations (quasiparticles) around one another in…
This work proposes numerical tests which determine whether a two-qubit operator has an atypically simple quantum circuit. Specifically, we describe formulae, written in terms of matrix coefficients, characterizing operators implementable…
Geometric phases induced in quantum evolutions have built-in noise-resilient characters, and thus can find applications in many robust quantum manipulation tasks. Here, we propose a feasible and fast scheme for universal quantum computation…
We propose and analyze a physical system capable of performing topological quantum computation with Majorana zero modes (MZM) in a one-dimensional topological superconductor (1DTS). One of the leading methods to realize quantum gates in…
Experimental realizations of Abelian fractional Chern insulators (FCIs) have demonstrated the potentials of moir\'e systems in synthesizing exotic quantum phases. Remarkably, twisted multilayer graphene system may also host non-Abelian…
Levin-Wen string-net models provide a construction of (2+1)D topologically ordered phases of matter with anyonic localized excitations described by the {Drinfeld} center of a unitary fusion category. Anyon condensation is a mechanism for…
We describe in detail a set of ideas for implementing qubits, quantum gates and quantum gate networks in a semiconductor heterostructure device. Our proposal is based on an extension of the technology used for surface acoustic wave (SAW)…
Braiding and fusion rules of topological excitations are indispensable topological invariants in topological quantum computation and topological orders. While excitations in 2D are always particle-like anyons, those in 3D incorporate not…
We introduce the Mixed-Integer Quadratically Constrained Quadratic Programming framework for the quantum compilation problem and apply it in the context of topological quantum computing. In this setting, quantum gates are realized by…