Related papers: Climbing the Clifford Hierarchy
This is an exposition of some basic mathematical aspects of quantum logic gates. At first we established some general formulas for the case of arbitrary quantum gate A with unique restriction A^2=I. The explicit form of the generators and…
We present an entirely 2D transversal realization of phase gates at any level of the Clifford hierarchy, and beyond, using non-Abelian surface codes. Our construction encodes a logical qubit in the quantum double $D(G)$ of a non-Abelian…
The geometric calculus based on Clifford algebra is a very useful tool for geometry and physics. It describes a geometric structure which is much richer than the ordinary geometry of spacetime. A Clifford manifold (C-space) consists not…
Non-stabilizerness, alongside entanglement, is a crucial ingredient for fault-tolerant quantum computation and achieving a genuine quantum advantage. Despite recent progress, a complete understanding of the generation and thermalization of…
The problem of decomposing an arbitrary Clifford element into a sequence of Clifford gates is known as Clifford synthesis. Drawing inspiration from similarities between this and the famous Rubik's Cube problem, we develop a machine learning…
The classical simulation of quantum circuits is of central importance for benchmarking near-term quantum devices. The fact that gates belonging to the Clifford group can be simulated efficiently on classical computers has motivated a range…
Let $C$ be a smooth irreducible projective algebraic curve defined over the complex numbers. The notion of the Clifford index of $C$ was extended a few years ago to semistable bundles of any rank. Recent work has been focussed mainly on the…
It is well known that Clifford (geometric) algebra offers a geometric interpretation for square roots of -1 in the form of blades that square to minus 1. This extends to a geometric interpretation of quaternions as the side face bivectors…
Topological subsystem color codes add to the advantages of topological codes an important feature: error tracking only involves measuring 2-local operators in a two dimensional setting. Unfortunately, known methods to compute with them were…
Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…
We show that single-qudit universality in Clifford-based gate sets follows a trichotomy determined by the prime factorization of the local dimension $d$. For prime $d$, any gate outside the Clifford group is universal. For prime-power…
Error correcting codes protect quantum information and form the basis of fault tolerant quantum computing. Leading proposals for fault-tolerant quantum computation require codes with an exceedingly rare property, a transverse non-Clifford…
The performance of computational methods for many-body physics and chemistry is strongly dependent on the choice of basis used to cast the problem; hence, the search for better bases and similarity transformations is important for progress…
The geometric calculus based on Clifford algebra is a very useful tool for geometry and physics. It describes a geometric structure which is much richer than the ordinary geometry of spacetime. A Clifford manifold ($C$-space) consists not…
The representation theory of the Clifford group is playing an increasingly prominent role in quantum information theory, including in such diverse use cases as the construction of protocols for quantum system certification, quantum…
The author's idea of {\it algebraic compositeness} of fundamental particles, allowing to understand the existence in Nature of three fermion generations, is revisited. It is based on two postulates. i) For all fundamental particles of…
Random quantum circuits continue to inspire a wide range of applications in quantum information science and many-body quantum physics, while remaining analytically tractable through probabilistic methods. Motivated by an interest in…
Quantum error correction is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation…
We introduce magic-augmented Clifford circuits -- architectures in which Clifford circuits are preceded and/or followed by constant-depth circuits of non-Clifford (``magic") gates -- as a resource-efficient way to realize approximate…
As quantum computing resources remain scarce and error rates high, minimizing the resource consumption of quantum circuits is essential for achieving practical quantum advantage. Here we consider the natural problem of, given a circuit $C$,…