Related papers: The magic of universal quantum computing with perm…
The Clifford hierarchy is a fundamental structure in quantum computation whose mathematical properties are not fully understood. In this work, we characterize permutation gates -- unitaries which permute the $2^n$ basis states -- in the…
We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as…
Any unitary transformation of quantum computational networks is explicitly decomposed, in an exact and unified form, into a sequence of a limited number of one-qubit quantum gates and the two-qubit diagonal gates that have diagonal unitary…
We propose a new implementation of a universal set of one- and two-qubit gates for quantum computation using the spin states of coupled single-electron quantum dots. Desired operations are effected by the gating of the tunneling barrier…
A central question in quantum computation is to identify the resources that are responsible for quantum speed-up. Quantum contextuality has been recently shown to be a resource for quantum computation with magic states for odd-prime…
An exposition of quantum permutation groups where an alternative to the 'Gelfand picture' of compact quantum groups is proposed. This point of view is inspired by algebraic quantum mechanics and posits that states on the algebra of…
How to find universal sets quantum gates (gates whose composition can form any othergate within a given range) is an important part of the development of quantum computation science that has been explored in the past with success. However,…
Quantum gates, that play a fundamental role in quantum computation and other quantum information processes, are unitary evolution operators $\hat U$ that act on a composite system changing its entanglement. In the present contribution we…
Magic is a property of quantum states that enables universal fault-tolerant quantum computing using simple sets of gate operations. Understanding the mechanisms by which magic is created or destroyed is, therefore, a crucial step towards…
Quantum permutation matrices and quantum magic squares are generalizations of permutation matrices and magic squares, where the entries are no longer numbers but elements from arbitrary (non-commutative) algebras. The famous Birkhoff--von…
Quantum computing with qudits, quantum systems with $d > 2$ levels, offers a powerful extension beyond qubits, expanding the computational possibilities of quantum systems, allowing the simplification of the implementation of several…
Quantum computation using electron spins in three coupled dot with different size is proposed. By using the energy selectivity of both photon assisted tunneling and spin rotation of electrons, logic gates are realized by static and…
Quantum computing offers advantages over classical computation, yet the precise features that set the two apart remain unclear. In the standard quantum circuit model, adding a 1-qubit basis-changing gate -- commonly chosen to be the…
In this paper we study universality for quantum gates acting on qudits.Qudits are states in a Hilbert space of dimension d where d is at least two. We determine which 2-qudit gates V have the properties (i) the collection of all 1-qudit…
The computational efficiency of quantum mechanics can be defined in terms of the qubit circuit model, which is characterized by a few simple properties: each computational gate is a reversible transformation in a connected matrix group;…
Simulating physical systems on near-term quantum computers often requires preparing states within constrained subspaces, like those with fixed particle number or spin. We use Lie algebraic techniques to prove that hardware-efficient gates…
The Clifford hierarchy is a fundamental structure in quantum computation, classifying unitary operators based on their commutation relations with the Pauli group. Despite its significance, the mathematical structure of the hierarchy is not…
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…
To any complex Hadamard matrix we associate a quantum permutation group. The correspondence is not one-to-one, but the quantum group encapsulates a number of subtle properties of the matrix. We investigate various aspects of the…
We show how to represent the state and the evolution of a quantum computer (or any system with an $N$--dimensional Hilbert space) in phase space. For this purpose we use a discrete version of the Wigner function which, for arbitrary $N$, is…