Related papers: The Grover algorithm with large nuclear spins in s…
We propose a mechanism of long-range coherent coupling between nuclear spins to be used as qubits in solid-state semiconductor-heterojunction quantum information processing devices. The coupling is via localized donor electrons which in…
We study the effects of dissipation or leakage on the time evolution of Grover's algorithm for a quantum computer. We introduce an effective two-level model with dissipation and randomness (imperfections), which is based upon the idea that…
Symmetry plays an important role in understanding the nuclear structure properties from the rotation of a nucleus to the spin, parity and isospin of nuclear states. This simplifies the complexity of the nuclear problems in one way or the…
A new notion of controllability, eigenstate controllability, is defined for finite-dimensional bilinear quantum mechanical systems which are neither strongly completely controllably nor completely controllable. And a quantum control…
Grover search algorithm drives a quantum system from an initial state to a desired final state by using selective phase inversions of these two states. In (1), we studied a generalization of Grover algorithm which relaxes the assumption of…
The goals of this paper are to show the following. First, Grover's algorithm can be viewed as a digital approximation to the analog quantum algorithm proposed in "An Analog Analogue of a Digital Quantum Computation", by E. Farhi and S.…
Constraint satisfiability problems, crucial to several applications, are solved on a quantum computer using Grover's search algorithm, leading to a quadratic improvement over the classical case. The solutions are obtained with high…
Amplitude estimation algorithms are based on Grover's algorithm: alternating reflections about the input state and the desired outcome. But what if we are given the ability to perform arbitrary rotations, instead of just reflections? In…
We survey recent work on designing and evaluating quantum computing implementations based on nuclear or bound-electron spins in semiconductor heterostructures at low temperatures and in high magnetic fields. General overview is followed by…
We describe a technique for quantum information processing based on localized en sembles of nuclear spins. A qubit is identified as the presence or absence of a collective excitation of a mesoscopic ensemble of nuclear spins surrounding a…
Spin-$\frac{1}{2}$ $^{119}$Sn nuclei in a silicon semiconductor could make excellent qubits. Nuclear spins in silicon are known to have long coherence times. Tin is isoelectronic with silicon, so we expect electrons can easily shuttle from…
We implement Grover's quantum search algorithm on a nuclear spin chain quantum computer, taking into Ising type interactions between nearest and second nearest neighbours into account. The performance of the realisation of the algorithm is…
We theoretically consider coherence times for spins in two quantum computer architectures, where the qubit is the spin of an electron bound to a P donor impurity in Si or within a GaAs quantum dot. We show that low temperature decoherence…
The Grover quantum search algorithm is generalized to deal with an arbitrary mixed initial state. The probability to measure a marked state as a function of time is calculated, and found to depend strongly on the specific initial state. The…
Because noisy, intermediate-scale quantum (NISQ) machines accumulate errors quickly, we need new approaches to designing NISQ-aware algorithms and assessing their performance. Algorithms with characteristics that appear less desirable under…
We introduce the concepts of Grover operators and Grover kernels to systematically analyse Grover's searching algorithms. Then, we investigate a one-parameter family of quantum searching algorithms of Grover's type and we show that the…
The use of nuclear spins for quantum computation is limited by the difficulty in creating genuine quantum entanglement between distant nuclei. Current demonstrations of nuclear entanglement in semiconductors rely upon coupling the nuclei to…
We present a novel benchmark application of a quantum algorithm to Feynman loop integrals. The two on-shell states of a Feynman propagator are identified with the two states of a qubit and a quantum algorithm is used to unfold the causal…
It has been shown in recent years that quantum information has a topological nature (\cite{AC}, \cite{Co}, \cite{Co2}). In \cite{V}, Vicary undergoes the study of quantum algorithms using this new topological approach. The advantage of this…
Given a parameterized quantum circuit such that a certain setting of these real-valued parameters corresponds to Grover's celebrated search algorithm, can a variational algorithm recover these settings and hence learn Grover's algorithm? We…