Related papers: Three-qubit entangled embeddings of CPT and Dirac …
We examine the geometric structure of qutrit state space by identifying the outcome probabilities of symmetric informationally complete (SIC) measurements with quantum states. We categorize the infinitely many qutrit SICs into eight SIC…
In the context of $p$-adic quantum mechanics, we investigate composite systems of $p$-adic qubits and $p$-adically controlled quantum logic gates. We build on the notion of a single $p$-adic qubit as a two-dimensional irreducible…
We use the concept of \textit{entangled graphs} with weighted edges to present a classification for four-qubit entanglement which is based neither on the LOCC nor the SLOCC. Entangled graphs, first introduced by Plesch et al. [Phys. Rev. A…
The Schur-Weyl states belong to a special class of states with a symmetry described by two Young and Weyl tableaux. Representation of physical systems in Hilbert space spanned on these states enables to extract quantum information hidden in…
Cavity-based large-scale quantum information processing (QIP) needs a large number of qubits and placing all of them in a single cavity quickly runs into many fundamental and practical problems such as the increase of cavity decay rate and…
We investigate the topological quantum compilation of two-qubit operations within a system of Fibonacci anyons. Our primary goal is to generate gates that are approximately leakage-free and equivalent to the controlled-NOT (CNOT) gate up to…
We perform a complete classification of all 56 subgroups of the two-qubit Clifford group containing the two-qubit Pauli group. We provide generators for these groups using gates familiar to the quantum information community and we reference…
Surface acoustic waves (SAWs) can create moving quantum dots in piezoelectric materials. Here we show how electron-spin qubits located on dynamic quantum dots can be entangled. Previous theoretical and numerical models of quantum-dot…
Relying on the mathematical analogy of the pure states of a two-qubit system with four-component Dirac spinors, we provide an alternative consideration of quantum entanglement using the mathematical formulation of Cartan's pure spinors. A…
This paper explores the representation of quantum computing in terms of unitary reflections (unitary transformations that leave invariant a hyperplane of a vector space). The symmetries of qubit systems are found to be supported by…
The Clifford hierarchy is a foundational concept for universal quantum computation (UQC). It was introduced to show that UQC can be realized via quantum teleportation, given access to certain standard resources. While the full structure of…
We study non-local two-qubit operations from a geometric perspective. By applying a Cartan decomposition to su(4), we find that the geometric structure of non-local gates is a 3-Torus. We derive the invariants for local transformations, and…
We describe quantum circuits generating four-qubit maximally entangled states, the amount of entanglement being quantified by using the absolute value of the Cayley hyperdeterminant as an entanglement monotone. More precisely, we show that…
We propose a protocol based on a tunneling plus particle-detection process aimed at generating tripartite entanglement in a system of 3 indistinguishable fermions in a triple-well potential, initially prepared in a state exhibiting only…
All quantum gates with one and two qubits may be described by elements of $Spin$ groups due to isomorphisms $Spin(3) \simeq SU(2)$ and $Spin(6) \simeq SU(4)$. However, the group of $n$-qubit gates $SU(2^n)$ for $n > 2$ has bigger dimension…
Pairwise exchange couplings have long been the standard mechanism for entangling spin qubits in semiconductor systems. However, implementing quantum circuits based on pairwise exchange gates often requires a lengthy sequence of elementary…
High-order topological charge is of intensive interest in the field of topological matters. In real materials, cubic Dirac point is rare and the chiral charge of one Weyl point (WP) has never be found to exceed |C| = 3 for spin- 1/2…
The non-linear binary Kerdock codes are known to be Gray images of certain extended cyclic codes of length $N = 2^m$ over $\mathbb{Z}_4$. We show that exponentiating these $\mathbb{Z}_4$-valued codewords by $\imath \triangleq \sqrt{-1}$…
The capacity of a quantum gate to produce entangled states on a bipartite system is quantified in terms of the entangling power. This quantity is defined as the average of the linear entropy of entanglement of the states produced after…
We introduce a class of projected entangled pair states (PEPS) which is based on a group symmetry twisted by a 3-cocycle of the group. This twisted symmetry gives rise to a new standard form for PEPS from which we construct a family of…