相关论文: Efficient Quantum Circuits for Schur and Clebsch-G…

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…

We describe an efficient quantum algorithm for the quantum Schur transform. The Schur transform is an operation on a quantum computer that maps the standard computational basis to a basis composed of irreducible representations of the…

The Schur transform, which block-diagonalizes the tensor representation $U^{\otimes n}$ of the unitary group $\mathbf{U}_d$ on $n$ qudits, is an important primitive in quantum information and theoretical physics. We give a generalization of…

The quantum Schur transform is a fundamental building block that maps the computational basis to a coupled basis consisting of irreducible representations of the unitary and symmetric groups. Equivalently, it may be regarded as a change of…

Many quantum algorithms can be represented in a form of a classical circuit positioned between quantum Fourier transformations. Motivated by the search for new quantum algorithms, we turn to circuits where the latter transformation is…

The Schur transform is a unitary operator that block diagonalizes the action of the symmetric and unitary groups on an $n$ fold tensor product $V^{\otimes n}$ of a vector space $V$ of dimension $d$. Bacon, Chuang and Harrow \cite{BCH07}…

This thesis presents an efficient quantum algorithm and explicit circuits for generating eigenstates of arbitrary SU(2) and SU(3) representations. These include a wide variety of highly entangled states. The algorithm uses Schur transform…

Universal quantum computation may be realized based on quantum walk, by formulating it as a scattering problem on a graph. In this paper, we simulate quantum gates through electric circuits, following a recent report that a one-dimensional…

Permutational Quantum Computing (PQC) [\emph{Quantum~Info.~Comput.}, \textbf{10}, 470--497, (2010)] is a natural quantum computational model conjectured to capture non-classical aspects of quantum computation. An argument backing this…

The quantum Schur transform maps the computational basis of a system of $n$ qudits onto a \textit{Schur basis}, which spans the minimal invariant subspaces of the representations of the unitary and the symmetric groups acting on the state…

In recent decades, the field of quantum computing has experienced remarkable progress. This progress is marked by the superior performance of many quantum algorithms compared to their classical counterparts, with Shor's algorithm serving as…

We take inspiration from the Okounkov-Vershik approach to the representation theory of the symmetric groups to develop a new way of understanding how the Schur-Weyl duality can be used to perform the Quantum Schur Transform. The Quantum…

We construct quantum circuits for solving one-dimensional Schr\"odinger equations. Simulations of three typical examples, i.e., harmonic oscillator, square-well and Coulomb potential, show that reasonable results can be obtained with eight…

Constructing general programmable circuits to be able to run any given unitary operator efficiently on a quantum processor is of fundamental importance. We present a new quantum circuit design technique resulting two general programmable…

We study representation theory of the partially transposed permutation matrix algebra, a matrix representation of the diagrammatic walled Brauer algebra. This algebra plays a prominent role in mixed Schur-Weyl duality that appears in…

Quantum mechanics requires the operation of quantum computers to be unitary, and thus makes it important to have general techniques for developing fast quantum algorithms for computing unitary transforms. A quantum routine for computing a…

Shor's algorithm for the prime factorization of numbers provides an exponential speedup over the best known classical algorithms. However, nontrivial practical applications have remained out of reach due to experimental limitations. The…

Quantum computation may well be performed with the use of electric circuits. Especially, the Schr\"{o}dinger equation can be simulated by the lumped-element model of transmission lines, which is applicable to low-frequency electric…

The accurate evaluation of diagonal unitary operators is often the most resource-intensive element of quantum algorithms such as real-space quantum simulation and Grover search. Efficient circuits have been demonstrated in some cases but…

We define and construct efficient depth-universal and almost-size-universal quantum circuits. Such circuits can be viewed as general-purpose simulators for central classes of quantum circuits and can be used to capture the computational…