相关论文: Note on the Khaneja Glaser Decomposition

We provide a new algorithm that translates a unitary matrix into a quantum circuit according to the G=KAK theorem in Lie group theory. With our algorithm, any matrix decomposition corresponding to type-AIII KAK decompositions can be derived…

We present a novel algorithm for performing the Cartan-Khaneja-Glaser decomposition of unitary matrices in $SU(2^n)$, a critical task for efficient quantum circuit design. Building upon the approach introduced by S\'a Earp and Pachos…

We present an explicit numerical method to obtain the Cartan-Khaneja-Glaser decomposition of a general element G of SU(2^N) in terms of its `Cartan' and `non-Cartan' components. This effectively factors G in terms of group elements that…

A scheme to perform the Cartan decomposition for the Lie algebra su(N) of arbitrary finite dimensions is introduced. The schme is based on two algebraic structures, the conjugate partition and the quotient algebra, that are easily generated…

This paper proposes a new optimized quantum block-ZXZ decomposition method [7,8,10] that results in more optimal quantum circuits than the quantum Shannon decomposition (QSD)[27], which was introduced in 2006 by Shende et al. The…

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…

Recent research in generalizing quantum computation from 2-valued qudits to d-valued qudits has shown practical advantages for scaling up a quantum computer. A further generalization leads to quantum computing with hybrid qudits where two…

The KAK decomposition is a fundamental tool in Lie theory and quantum computing. Despite its widespread use, the mathematical foundations remain incomplete, particularly regarding the precise conditions for the decomposition and the…

The two-qubit canonical decomposition SU(4) = [SU(2) \otimes SU(2)] Delta [SU(2) \otimes SU(2)] writes any two-qubit quantum computation as a composition of a local unitary, a relative phasing of Bell states, and a second local unitary.…

The ground state degeneracy of an $SU(N)_k$ topological phase with $n$ quasiparticle excitations is relevant quantity for quantum computation, condensed matter physics, and knot theory. It is an open question to find a closed formula for…

We give explicit, practical conditions that determine whether or not a closed, connected subgroup H of G = SU(2,n) has the property that there exists a compact subset C of G with CHC = G. To do this, we fix a Cartan decomposition G = K A K…

In the 3rd episode of the serial exposition, quotient algebra partitions of rank zero earlier introduced undergo further partitions generated by bi-subalgebras of higher ranks. The refined versions of quotient algebra partitions admit not…

A novel invariant decomposition of diagonalizable $n \times n$ matrices into $n$ commuting matrices is presented. This decomposition is subsequently used to split the fundamental representation of $\mathfrak{su}(3)$ Lie algebra elements…

We study the indefinite Kac-Moody algebras AE(n), arising in the reduction of Einstein's theory from (n+1) space-time dimensions to one (time) dimension, and their distinguished maximal regular subalgebras sl(n) and affine A_{n-2}^{(1)}.…

Ulmer and Kaissl formulas for the deconvolution of one-dimensional Gaussian kernels are generalized to the three-dimensional case. The generalization is based on the use of the scalar version of the Grad's multivariate Hermite polynomials…

Multi-controlled unitary gates have been a subject of interest in quantum computing since its inception, and are widely used in quantum algorithms. The current state-of-the-art approach to implementing n-qubit multi-controlled gates…

Recursive Cartan decompositions (CDs) provide a way to exactly factorize quantum circuits into smaller components, making them a central tool for unitary synthesis. Here we present a detailed overview of recursive CDs, elucidating their…

The intrinsic symmetries of physical systems have been employed to reduce the number of degrees of freedom of systems, thereby simplifying computations. In this work, we investigate the properties of $\mathcal{M}SU(2^N)$,…

An SU(3) symmetric model with high predictivity for octet meson (\pi, K) quark fragmentation functions with a simple approach to SU(3) symmetry breaking (due to the relatively heavy strange quarks) is extended to the singlet sector, with…

We propose and benchmark a modified time evolution block decimation (TEBD) algorithm that uses a truncation scheme based on the QR decomposition instead of the singular value decomposition (SVD). The modification reduces the scaling with…