Related papers: Primitive Quantum Gates for an SU(2) Discrete Subg…
Unitary operations are the building blocks of quantum programs. Our task is to design effcient or optimal implementations of these unitary operations by employing the intrinsic physical resources of a given n-qubit system. The most common…
Quantum Fourier transformations are an essential component of many quantum algorithms, from prime factoring to quantum simulation. While the standard abelian QFT is well-studied, important variants corresponding to \emph{nonabelian} groups…
We developed a general framework for synthesizing target gates by using a finite set of basic gates, which is a crucial step in quantum compilation. When approximating a gate in SU($n$), a naive brute-force search requires a computational…
In the near-future noisy intermediate-scale quantum (NISQ) era of quantum computing technology, applications of quantum computing will be limited to calculations of very modest scales in terms of the number of qubits used. The need to…
We present an efficient family of quantum circuits for a fundamental primitive in quantum information theory, the Schur transform. The Schur transform on n d-dimensional quantum systems is a transform between a standard computational basis…
Finite group extensions offer a natural language to quantum computing. In a nutshell, one roughly describes the action of a quantum computer as consisting of two finite groups of gates: error gates from the general Pauli group P and…
Our goal in this paper is to construct optimal topological generators for compact unitary Lie groups, extending the work of a letter of Sarnak and arXiv:1704.02106 on golden and super-golden gates to higher dimensions. To do so we consider…
Recently an algorithm has been constructed that shows the binary icosahedral group $\2I$ together with a $T$-like gate forms the most efficient single-qubit universal gate set. To carry out the algorithm fault tolerantly requires a code…
We propose a general, fully gate-based quantum algorithm for counterdiabatic driving. The algorithm does not depend on heuristics as in previous variational methods, and exploits regularisation of the adiabatic gauge potential to suppress…
The simulation of lattice gauge theories on quantum computers necessitates digitizing gauge fields. One approach involves substituting the continuous gauge group with a discrete subgroup, but the implications of this approximation still…
Recent developments in mapping lattice gauge theories relevant to the Standard Model onto digital quantum computers identify scalable paths with well-defined quantum compilation challenges toward the continuum. As an entry point to these…
A problem of universality in simulation of evolution of quantum system and in theory of quantum computations is related with the possibility of expression or approximation of arbitrary unitary transformation by composition of specific…
We study the computation power of lattices composed of two dimensional systems (qubits) on which translationally invariant global two-qubit gates can be performed. We show that if a specific set of 6 global two qubit gates can be performed,…
We study permutation groups of given minimal degree without the classical primitivity assumption. We provide sharp upper bounds on the order of a permutation group of minimal degree m and on the number of its elements of any given support.…
Three-dimensional bicovariant differential calculus on the quantum group SU_q(2) is constructed using the approach based on global covariance under the action of the stabilizing subgroup U(1). Explicit representations of possible q-deformed…
To each of the symmetry groups of the Platonic solids we adjoin a carefully designed involution yielding topological generators of PU(2) which have optimal covering properties as well as efficient navigation. These are a consequence of…
In this paper we provide an explicit parameterization of arbitrary unitary transformation acting on n qubits, in terms of one and two qubit quantum gates. The construction is based on successive Cartan decompositions of the semi-simple Lie…
High-precision, robust quantum gates are essential components in quantum computation and information processing. In this study, we present an alternative perspective, exploring the potential applicability of quantum gates that exhibit…
A key requirement to perform simulations of large quantum systems on near-term quantum hardware is the design of quantum algorithms with short circuit depth that finish within the available coherence time. A way to stay within the limits of…
In this work, we investigate the effect of decomposition basis on primitive qudit gates on superconducting radio-frequency cavity-based quantum computers with applications to lattice gauge theory. Three approaches are tested: SNAP &…