相关论文: Protocol for making a $2$-qutrit entangling gate i…
We present a way to physically realize a circulant 2-qubit entangling gate in the Kauffman-Jones version of SU(2) Chern-Simons theory at level 4. Our approach uses qubit and qutrit ancillas, braids, fusions and interferometric measurements.…
We provide ways to turn ancillas into phase gates (chapter 1), leading to irrational phase gates (chapter 2). We realize all the 2-qubit permutation gates (chapter 3).
The model of a topological quantum computer is a promising one due to its natural resistance to noise and other errors. Operations in such a computer are implemented by braiding the trajectories of anyons. While it is easy to understand how…
As part of a protocol, we braid in a certain way six anyons of topological charges $222211$ in the Kauffman-Jones version of $SU(2)$ Chern-Simons theory at level $4$. The gate we obtain is a braid for the usual qutrit $2222$ but with…
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…
We provide an analytic way to implement any arbitrary two-qubit unitary operation, given an entangling two-qubit gate together with local gates. This is shown to provide explicit construction of a universal quantum circuit that exactly…
We examine a class of operations for topological quantum computation based on fusing and measuring topological charges for systems with SU$(2)_4$ or $k=4$ Jones-Kauffman anyons. We show that such operations augment the braiding operations,…
This paper addresses the question how to implement a desired two-qubit gate U using a given tunable two-qubit entangling interaction H_int. We present a general method which is based on the K_1 A K_2 decomposition of unitary matrices in…
Chern-Simons theory in application to the quantum computing is actively developing at the present. However, most discussed are the questions of using materials with known parameters and building corresponding quantum gates and algorithms.…
We study the generation of two-qudit entangling quantum logic gates using two techniques in quantum optimal control. We take advantage of both continuous, Lie-algebraic control and digital, Lie-group control. In both cases, the key is…
The circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations. The ability to execute parallel entangling quantum gates offers clear…
We construct the functional integral of Abelian Chern-Simons theory with toral gauge group $\mathbb T=\mathfrak t/\Lambda \cong U(1)^n$ at level $K$, where $K:\Lambda\times\Lambda\to\mathbb Z$ is an even, integral, nondegenerate symmetric…
In the paper, we consider quantum circuits for the Quantum Fourier Transform (QFT) algorithm. The QFT algorithm is a very popular technique used in many quantum algorithms. We present a generic method for constructing quantum circuits for…
We describe a new method for the decomposition of an arbitrary $n$ qubit operator with entries in $\mathbb{Z}[i,\frac{1}{\sqrt{2}}]$, i.e., of the form $(a+b\sqrt{2}+i(c+d\sqrt{2}))/{\sqrt{2}^{k}}$, into Clifford+$T$ operators where $n\le…
Here we apply our SU(N) and U(N) parameterizations to the question of entanglement in the two qubit and qubit/qutrit system. In particular, the group operations which entangle a two qubit pure state will be given, as well as the…
In this contribution we consider an advantageous building block with potential for various quantum applications: a device based on coupled spins capable of generating and sharing out an entangled pair of qubits. Our model device is a…
We propose and investigate a method to optimize recurrence entanglement purification protocols. The approach is based on a numerical search in the whole set of SU(4) matrices with the aid of a quasi-Newton algorithm. Our method evaluates…
Quantum information carriers, just like most physical systems, naturally occupy high-dimensional Hilbert spaces. Instead of restricting them to a two-level subspace, these high-dimensional (qudit) quantum systems are emerging as a powerful…
In the late 1980s Witten used the Chern-Simons form of a connection to construct new invariants of 3-manifolds and knots, recovering in particular the Jones invariants. Since then the associated topological quantum field theory (TQFT) has…
Most quantum computing architectures to date natively support multi-valued logic, albeit being typically operated in a binary fashion. Multi-valued, or qudit, quantum processors have access to much richer forms of quantum entanglement,…