843 citations · 5.1k across the 104 of their papers we have counts for
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Entanglement of Periodic States, the Quantum Fourier Transform and Shor's Factoring Algorithm
Yonatan Most, Yishai Shimoni, Ofer Biham
The preprocessing stage of Shor's algorithm generates a class of quantum states referred to as periodic states, on which the quantum Fourier transform is applied. Such states also…
Formation of Multipartite Entanglement Using Random Quantum Gates
Yonatan Most, Yishai Shimoni, Ofer Biham
The formation of multipartite quantum entanglement by repeated operation of one and two qubit gates is examined. The resulting entanglement is evaluated using two measures: the ave…
Groverian Entanglement Measure of Pure Quantum States with Arbitrary Partitions
Yishai Shimoni, Ofer Biham
The Groverian entanglement measure of pure quantum states of qubits is generalized to the case in which the qubits are divided into any parties and the entanglement b…
Entangled Quantum States Generated by Shor's Factoring Algorithm
Yishai Shimoni, Daniel Shapira, Ofer Biham
The intermediate quantum states of multiple qubits, generated during the operation of Shor's factoring algorithm are analyzed. Their entanglement is evaluated using the Groverian m…
The Groverian Measure of Entanglement for Mixed States
Daniel Shapira, Yishai Shimoni, Ofer Biham
The Groverian entanglement measure introduced earlier for pure quantum states [O. Biham, M.A. Nielsen and T. Osborne, Phys. Rev. A 65, 062312 (2002)] is generalized to the case of…
Algebraic analysis of quantum search with pure and mixed states
D. Shapira, Y. Shimoni, O. Biham
An algebraic analysis of Grover's quantum search algorithm is presented for the case in which the initial state is an arbitrary pure quantum state of n qubits. This approach reveal…
One dimensional quantum walk with unitary noise
Daniel Shapira, Ofer Biham, A. J. Bracken +1
The effect of unitary noise on the discrete one-dimensional quantum walk is studied using computer simulations. For the noiseless quantum walk, starting at the origin (n=0) at time…
Characterization of pure quantum states of multiple qubits using the Groverian entanglement measure
Yishai Shimoni, Daniel Shapira, Ofer Biham
The Groverian entanglement measure, G(psi), is applied to characterize a variety of pure quantum states |psi> of multiple qubits. The Groverian measure is calculated analytically f…
The effect of unitary noise on Grover's quantum search algorithm
D. Shapira, S. Mozes, O. Biham
The effect of unitary noise on the performance of Grover's quantum search algorithm is studied. This type of noise may result from tiny fluctuations and drift in the parameters of…
Analysis of Grover's quantum search algorithm as a dynamical system
O. Biham, D. Shapira, Y. Shimoni
Grover's quantum search algorithm is analyzed for the case in which the initial state is an arbitrary pure quantum state of qubits. It is shown that the optimal time to p…
An entanglement monotone derived from Grover's algorithm
Ofer Biham, Michael A. Nielsen, Tobias J. Osborne
This paper demonstrates that how well a state performs as an input to Grover's search algorithm depends critically upon the entanglement present in that state; the more entanglemen…
Analysis of Generalized Grover's Quantum Search Algorithms Using Recursion Equations
Eli Biham, Ofer Biham, David Biron +3
The recursion equation analysis of Grover's quantum search algorithm presented by Biham et al. [PRA 60, 2742 (1999)] is generalized. It is applied to the large class of Grover's ty…
Grover's Quantum Search Algorithm for an Arbitrary Initial Amplitude Distribution
Eli Biham, Ofer Biham, David Biron +2
Grover's algorithm for quantum searching is generalized to deal with arbitrary initial complex amplitude distributions. First order linear difference equations are found for the ti…
Generalized Grover Search Algorithm for Arbitrary Initial Amplitude Distribution
David Biron, Ofer Biham, Eli Biham +2
Grover's algorithm for quantum searching of a database is generalized to deal with arbitrary initial amplitude distributions. First order linear difference equations are found for…
Simulating Ising Spin Glasses on a Quantum Computer
Daniel A. Lidar, Ofer Biham
A linear-time algorithm is presented for the construction of the Gibbs distribution of configurations in the Ising model, on a quantum computer. The algorithm is designed so that e…