Related papers: Coherence and entanglement dynamics in Shor's algo…
Quantum walks constitute a rich area of quantum information science, where multipartite entanglement plays a central role in the dynamics and scalability of quantum advantage over classical simulators. In this work, we study the…
This paper studies the quantum computational complexity of the discrete logarithm (DL) and related group-theoretic problems in the context of generic algorithms -- that is, algorithms that do not exploit any properties of the group…
Entanglement lies at the heart of quantum mechanics and has no classical analogue. It is central to the speed up achieved by quantum algorithms over their classical counterparts. The Grover's search algorithm is one such algorithm which…
Quantum algorithms reformulate computational problems as quantum evolutions in a large Hilbert space. Most quantum algorithms assume that the time-evolution is perfectly unitary and that the full Hilbert space is available. However, in…
Quantum coherence is a basic feature of quantum physics. Combined with tensor product structure of state space, it gives rise to the novel concepts such as entanglement and quantum correlations, which play a crucial role in quantum…
The entanglement properties of random quantum states or dynamics are important to the study of a broad spectrum of disciplines of physics, ranging from quantum information to high energy and many-body physics. This work investigates the…
An efficient quantum modular exponentiation method is indispensible for Shor's factoring algorithm. But we find that all descriptions presented by Shor, Nielsen and Chuang, Markov and Saeedi, et al., are flawed. We also remark that some…
The road to computing on quantum devices has been accelerated by the promises that come from using Shor's algorithm to reduce the complexity of prime factorization. However, this promise hast not yet been realized due to noisy qubits and…
Shor's algorithm is well-known for its capability to address the elliptic curve discrete logarithm problem (ECDLP) in polynomial time. The enhancement of its quantum resources continues to be a crucial focus of research. Nevertheless, the…
The alignment, ordering and rotation of elongated granular particles was studied in shear flow. The time evolution of the orientation of a large number of particles was monitored in laboratory experiments by particle tracking using optical…
We study partial coherence and its connections with entanglement. First, we provide a sufficient and necessary condition for bipartite pure state transformation under partial incoherent operations: A bipartite pure state can be transformed…
We analyze the modification of entanglement dynamics in the Grover algorithm when the qubits are subjected to single-qubit amplitude-damping or phase-flip noise. We compare quantum trajectories with full density-matrix simulations,…
An alternative quantum algorithm for the discrete logarithm problem is presented. The algorithm uses two quantum registers and two Fourier transforms whereas Shor's algorithm requires three registers and four Fourier transforms. A crucial…
Here we investigate the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks. We do this for a variety of…
Topological order is defined by topological invariants, rather than symmetries and local order parameters. Nonetheless some topological phases can be characterized by string order parameters and entanglement. In this article we study how…
In this work, we study the dynamics of quantum coherence (total coherence, global coherence and local coherence) evolving under a local PT-symmetric Hamiltonian in maximally entangled bipartite and tripartite states. Our results indicate…
We describe a general procedure for mapping arbitrary $n$-qubit states to two-dimensional (2D) vector fields. The mappings use complex rational function representations of individual qubits, producing classical vector field configurations…
Amongst the most remarkable successes of quantum computation are Shor's efficient quantum algorithms for the computational tasks of integer factorisation and the evaluation of discrete logarithms. In this article we review the essential…
Quantifying entanglement is an important task by which the resourcefulness of a quantum state can be measured. Here, we develop a quantum algorithm that tests for and quantifies the separability of a general bipartite state by using the…
Some quantum algorithms have "quantum speedups": improved time complexity as compared with the best-known classical algorithms for solving the same tasks. Can we understand what fuels these speedups from an entropic perspective? Information…