Related papers: Realizing topologically ordered states on a quantu…
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated…
Ordered phases of matter have close connections to computation. Two prominent examples are spin glass order, with wide-ranging applications in machine learning and optimization, and topological order, closely related to quantum error…
Deciding if a given family of quantum states is topologically ordered is an important but nontrivial problem in condensed matter physics and quantum information theory. We derive necessary and sufficient conditions for a family of graph…
We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of…
We study a quantum phase transition between a phase which is topologically ordered and one which is not. We focus on a spin model, an extension of the toric code, for which we obtain the exact ground state for all values of the coupling…
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…
Quantum state preparation is a fundamental component of quantum algorithms, particularly in quantum machine learning and data processing, where classical data must be encoded efficiently into quantum states. Existing amplitude encoding…
We present a method of extracting information about the topological order from the ground state of a strongly correlated two-dimensional system computed with the infinite projected entangled pair state (iPEPS). For topologically ordered…
Topological phases of matter are considered the bedrock of novel quantum materials as well as ideal candidates for quantum computers that possess robustness at the physical level. The robustness of the topological phase at finite…
Quantum computing crucially relies on the ability to efficiently characterize the quantum states output by quantum hardware. Conventional methods which probe these states through direct measurements and classically computed correlations…
Finding physical realizations of topologically ordered states in experimental settings, from condensed matter to artificial quantum systems, has been the main challenge en route to utilizing their unconventional properties. We show how to…
Quantum computing promises to revolutionize various fields, yet the execution of quantum programs necessitates an effective compilation process. This involves strategically mapping quantum circuits onto the physical qubits of a quantum…
We present a numerical study of a quantum phase transition from a spin-polarized to a topologically ordered phase in a system of spin-1/2 particles on a torus. We demonstrate that this non-symmetry-breaking topological quantum phase…
Quantum spin liquids, exotic phases of matter with topological order, have been a major focus of explorations in physical science for the past several decades. Such phases feature long-range quantum entanglement that can potentially be…
Topologically ordered states are among the most interesting quantum phases of matter that host emergent quasi-particles having fractional charge and obeying fractional quantum statistics. Theoretical study of such states is however…
Decoherence is a major obstacle to the preparation of topological order in noisy intermediate-scale quantum devices. Here, we show that decoherence can also give rise to new types of topological order. Specifically, we construct concrete…
Here we investigate the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks. We do this for a variety of…
Finding the ground state of a Hamiltonian system is of great significance in many-body quantum physics and quantum chemistry. We propose an improved iterative quantum algorithm to prepare the ground state of a Hamiltonian. The crucial point…
Quantum computers are predicted to utilize quantum states to perform memory and to process tasks far faster than those of conventional classical computers. In this paper we show a new road towards building fault tolerance quantum computer…
We demonstrate that multipartite entanglement, witnessed by the quantum Fisher information (QFI), can characterize topological quantum phase transitions in the spin-$\frac{1}{2}$ toric code model on a square lattice with external fields. We…