Related papers: Realization of Topological Quantum Computation wit…
We propose a systematic and efficient quantum circuit composed solely of Clifford gates for simulating the ground state of the surface code model. This approach yields the ground state of the toric code in $\lceil…
A theory for constructing quantum error correcting codes from Toric surfaces by the Calderbank-Shor-Steane method is presented. In particular we study the method on toric Hirzebruch surfaces. The results are obtained by constructing a…
Geometric and holonomic quantum computation utilizes intrinsic geometric properties of quantum-mechanical state spaces to realize quantum logic gates. Since both geometric phases and quantum holonomies are global quantities depending only…
Measurement-based quantum computation describes a scheme where entanglement of resource states is utilized to simulate arbitrary quantum gates via local measurements. Recent works suggest that symmetry-protected topologically non-trivial,…
In recent years, surface codes have become a leading method for quantum error correction in theoretical large scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural…
Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…
One of the leading quantum computing architectures is based on the two-dimensional (2D) surface code. This code has many advantageous properties such as a high error threshold and a planar layout of physical qubits where each physical qubit…
Encoding and manipulation of quantum information by means of topological degrees of freedom provides a promising way to achieve natural fault-tolerance that is built-in at the physical level. We show that this topological approach to…
We survey some recent work on topological quantum computation with gapped boundaries and boundary defects and list some open problems.
The idea of topological quantum computation (TQC) is to store and manipulate quantum information in an intrinsically fault-tolerant manner by utilizing the physics of topologically ordered phases of matter. Currently, one of the most…
It is an ongoing quest to realize topologically ordered quantum states on different platforms including condensed matter systems, quantum simulators and digital quantum processors. Unlike conventional states characterized by their local…
We find that the overlapping of a topological quantum color code state, representing a quantum memory, with a factorized state of qubits can be written as the partition function of a 3-body classical Ising model on triangular or Union Jack…
Most quantum computing architectures can be realized as two-dimensional lattices of qubits that interact with each other. We take transmon qubits and transmission line resonators as promising candidates for qubits and couplers; we use them…
We elaborate the idea of quantum computation through measuring the correlation of a gapped ground state, while the bulk Hamiltonian is utilized to stabilize the resource. A simple computational primitive, by pulling out a single spin…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
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…
We prove several theorems characterizing the existence of homological error correction codes both classically and quantumly. Not every classical code is homological, but we find a family of classical homological codes saturating the Hamming…
Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical…
In seminal work (arxiv:quant-ph/9707021) Alexei Kitaev proposed topological quantum computing (arXiv:cond-mat/0010440, arxiv:quant-ph/9707021, arXiv:quant-ph/0001108, arXiv:0707.1889), whereby logic gates of a quantum computer are conducted…
Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed…