Quantum Search Algorithms for Wireless Communications

Abstract

Faster, ultra-reliable, low-power and secure communications has always been high on the wireless evolutionary agenda. However, the appetite for faster, more reliable, greener and more secure communications continues to grow. The stateof-the-art methods conceived for achieving the performance targets of the associated processes may be accompanied by an increase in computational complexity. Alternatively, a degraded performance may have to be accepted due to the lack of jointly optimized system components. In this survey we investigate the employment of quantum computing for solving problems in wireless communication systems. By exploiting the inherent parallelism of quantum computing, quantum algorithms may be invoked for approaching the optimal performance of classical wireless processes, despite their reduced number of cost-function evaluations. In this contribution we discuss the basics of quantum computing using linear algebra, before presenting the operation of the major quantum algorithms, which have been proposed in the literature for improving wireless communications systems. Furthermore, we investigate a number of optimization problems encountered both in the physical and network layer of wireless communications, while comparing their classical and quantumassisted solutions. Finally, we state a number of open problems in wireless communications that may benefit from quantum computing.

When Entanglement Meets Classical Communications: Quantum Teleportation for the Quantum Internet

“…In (28), we note the presence of two components. The unitary evolution component depends both on Planck's constant , whose value must be experimentally determined, and on the Hermitian operator H s , referred to as the Hamiltonian of the system 24 .…”

“…To characterize a quantum state in the state space, a basis that is orthonormal to this state space has to be chosen. In the following, we adopt the conventional bra-ket notation 5 for denoting a qubit [5], [17], [28], [30]. The most commonly used basis is the standard (or computational) basis, which corresponds to the convention:…”

“…To elaborate a little further, the state of a qubit is often represented geometrically by the Bloch sphere, which is depicted in Fig. 1 and surveyed in more depth in [5], [17], [18], [28]. Specifically, any pure quantum state is represented by a point on the sphere's surface, with θ and φ denoting the spherical coordinates.…”

“…The amplitudes of the state |ψ in (2) can be manipulated by quantum gates, as we will see further below, but they also have a bearing on the linkage between the quantum and classical world. In fact, according to one of the postulates of quantum mechanics -namely, the quantum measurement -although a qubit may reside in a superposition of two orthogonal states, when we want to observe or measure its value, it collapses into one of the two orthogonal states [5], [17], [28]. More explicitly, |α| 2 and |β| 2 uniquely determine the probabilities of obtaining |0 or |1 , respectively, by measuring the qubit state on the basis {|0 , |1 } 6 .…”

Channel Decoding with Quantum Approximate Optimization Algorithm

“…Since the cost expectation can be decomposed as F p (γ, β) = ν C ν , we focus the νth cost Hamiltonian whose degree is d c ν = |I c ν |. For example in Hamming code generator (9), the 5th column [G] :,5 = [1, 1, 0, 1] T corresponds to the Hamiltonian…”