This paper proposes a highly efficient quantum algorithm for portfolio optimisation targeted at near-term noisy intermediate-scale computers. Recent work by Hodson et al. (2019) explored potential application of hybrid quantum-classical algorithms to the problem financial rebalancing. In particular, they deal with using Quantum Approximate Optimisation Algorithm and Alternating Operator Ansatz. this paper, we demonstrate substantially better performance newly developed Walk in finding...

We propose a novel algorithm for quantum spatial search on star graph using interleaved continuous-time walks and marking oracle queries. Initializing the system in star's central vertex, we determine optimal walk times to reach full overlap with marked state ⌈(π/4)sqrt[N]-(1/2)⌉ queries, matching well-known lower bound of Grover's search. implement deterministic database size seven photonic hardware, demonstrate effective scaling approach up 115. This is first experimental demonstration...

This paper presents an approach to quantum approximate combinatorial optimization using interleaved continuous-time walks and solution quality-dependent phase shifts. Combinatorial indexing functions are used implement a walk over the subspace of feasible solutions.

The Quantum Approximate Optimization Algorithm (QAOA) is an algorithmic framework for finding approximate solutions to combinatorial optimization problems. It consists of interleaved unitary transformations induced by two operators labelled the mixing and problem Hamiltonians. To fit this framework, one needs transform original into a suitable form embed it these In paper, well-known NP-hard Traveling Salesman Problem (TSP), we encode its constraints Hamiltonian rather than conventional...

Compared to studies evaluating the benefits from agricultural research, there are relatively few empirical of net economic extension, and even fewer that consider both public private sector extension effort.In this study we examine regional differences in adoption lupins Western Australia (WA) order estimate extension.Impacts other variables on were analysed for 40 shires using multivariate regression analysis.The results suggest activities influenced farmer uptake lupins, particularly by...

This paper examines the performance of spatial search where Grover diffusion operator is replaced by continuous-time quantum walks on a class interdependent networks. We prove that for set optimal walk times and marked vertex phase shifts, deterministic algorithm structured established finds with 100% probability. improves original same graphs, which we show can only amplify to 50% Our method uses $\left\lceil\frac{\pi}{2\sqrt{2}}\sqrt{N}\right\rceil$ shifts an $N$-vertex graph, making it...

The Quantum Approximate Optimization Algorithm (QAOA) is an algorithmic framework for finding approximate solutions to combinatorial optimization problems, derived from approximation the Adiabatic (QAA). In solving problems with constraints in context of QAOA or QAA, one needs find a way encode problem into scheme. this paper, we formalize different constraint types linear equalities, inequalities, and arbitrary form. Based on this, propose constraint-encoding schemes well-fitting NP...

This paper demonstrates the applicability of Quantum Walk-based Optimisation Algorithm (QWOA) to Capacitated Vehicle Routing Problem (CVRP). Efficient algorithms are developed for indexing and unindexing solution space implementing required alternating phase-walk unitaries, which core components QWOA. Results numerical simulation demonstrate that QWOA is capable producing convergence near-optimal solutions a randomly generated eight location CVRP. Preparation amplified quantum state in this...

We present a novel methodological framework for quantum spatial search, generalising the Childs & Goldstone (CG) algorithm via alternating applications of marked-vertex phase shifts and continuous-time walks.We determine closed form expressions optimal walk time shift parameters periodic graphs.These are chosen to rotate system about subsets graph Laplacian eigenstates, amplifying probability measuring marked vertex.The state evolution is asymptotically any class graphs having fixed number...

In this paper we present an efficiently scaling quantum algorithm which finds the size of maximum common edge subgraph for a pair arbitrary graphs and thus provides meaningful measure graph similarity. The makes use two-part dynamic process: in first part obtain information crucial comparison two through linear computation. However, is hidden system with vanishingly small amplitude that even algorithms such as Grover's search are not fast enough to distill efficiently. order extract call...

We study the Morava $E$-theory (at a prime $p$) of $BGL_d(F)$, where $F$ is finite field with $|F|=1\pmod{p}$. Taking all $d$ together, we obtain structure two products $\times$ and $\bullet$. prove that it polynomial ring under $\times$, module $\times$-indecomposables inherits $\bullet$-product, describe resulting ring. In process, many auxiliary structural results.