相关论文: Hamilton's turns as visual tool-kit for designing …

Hamilton in the course of his studies on quaternions came up with an elegant geometric picture for the group SU(2). In this picture the group elements are represented by ``turns'', which are equivalence classes of directed great circle arcs…

We present a unitary control pulse design method for a scalable quantum computer architecture based on electron spins in lateral quantum dots. We employ simultaneous control of spin interactions and derive the functional forms of spin…

As physical systems, qubits must evolve from input to output state. We describe a simple scheme in which the effect of a quantum gate is described by the action of an effective Hamiltonian acting for some characteristic time. This model…

We derive the Hamiltonian in the rotating frame for NMR quantum computing with homonucleus molecules as its computational resource. The Hamiltonian thus obtained is different from conventional Hamiltonians that appear in literature. It is…

We provide new constructions of unitary $t$-designs for general $t$ on one qudit and $N$ qubits, and propose a design Hamiltonian, a random Hamiltonian of which dynamics always forms a unitary design after a threshold time, as a basic…

We present a self-contained discussion of the use of the transfer-matrix formalism to study one-dimensional scattering. We elaborate on the geometrical interpretation of this transfer matrix as a conformal mapping on the unit disk. By…

This paper presents a novel way to use the algebra of unit quaternions to express arbitrary roots or fractional powers of single-qubit gates, and to use such fractional powers as generators for algebras that combine these fractional input…

As a milestone for general-purpose computing machines, we demonstrate that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. Moreover, on noisy devices without error correction, we…

The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…

In this paper, we introduce the notion of a normal form of one qubit quantum circuits over the basis $\{H, P, T\}$, where $H$, $P$ and $T$ denote the Hadamard, Phase and $\pi/8$ gates, respectively. This basis is known as the {\it standard…

Using the circulant symmetry of a Hamiltonian describing three qubits, we realize the quantum Fourier transform. This symmetry allows us to construct a set of eigenvectors independently on the magnitude of physical parameters involved in…

Any single-qubit unitary operation or quantum gate can be considered a rotation. Typical experimental implementations of single-qubit gates involve two or three fixed rotation axes, and up to three rotation steps. Here we show that, if the…

Among the many proposals for the realization of a quantum computer, holonomic quantum computation (HQC) is distinguished from the rest in that it is geometrical in nature and thus expected to be robust against decoherence. Here we analyze…

To treat a problem with a Quantum Processing Unit (QPU), it must be transformed into a sequence of quantum operations, or gates: this is the quantum description of the problem. These operations are either packed into a query (i.e. quantum…

We describe a method for improving coherent control through the use of detailed knowledge of the system's Hamiltonian. Precise unitary transformations were obtained by strongly modulating the system's dynamics to average out unwanted…

We consider the effects of plane-wave states scattering off finite graphs, as an approach to implementing single-qubit unitary operations within the continuous-time quantum walk framework of universal quantum computation. Four semi-infinite…

Universal quantum computation requires the implementation of arbitrary control operations on the quantum register. In most cases, this is achieved by external control fields acting selectively on each qubit to drive single-qubit operations.…

Geometric phases have been used in NMR, to implement controlled phase shift gates for quantum information processing, only in weakly coupled systems in which the individual spins can be identified as qubits. In this work, we implement…

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 propose a method for quantum computation which uses control of spin-orbit coupling in a linear array of single electron quantum dots. Quantum gates are carried out by pulsing the exchange interaction between neighboring electron spins,…