The use of quantum processing units (QPUs) promises speed-ups for solving computational problems, in particular for discrete optimisation. While a few groundbreaking algorithmic approaches are known that can provably outperform classical computers, we observe a scarcity of programming abstractions for constructing efficient quantum algorithms. A good fraction of the literature that addresses solving concrete problems related to database management concentrates on casting them as quadratic unconstrained binary optimisation problems (QUBOs), which can then, among others, be processed on gate-based machines (using the quantum approximate optimisation algorithm), or quantum annealers. A critical aspect that affects efficiency and scalability of either of these approaches is how classical data are loaded into qubits, respectively how problems are encoded into QUBO representation. The effectiveness of encodings is known to be of crucial importance for quantum computers, especially since the amount of available qubits is strongly limited in the era of noisy, intermediate-size quantum computers.
The use of quantum processing units (QPUs) promises speed-ups for solving computational problems, in particular for discrete optimisation. While a few groundbreaking algorithmic approaches are known that can provably outperform classical computers, we observe a scarcity of programming abstractions for constructing efficient quantum algorithms. A good fraction of the literature that addresses solving concrete problems related to database management concentrates on casting them as quadratic unconstrained binary optimisation problems (QUBOs), which can then, among others, be processed on gate-based machines (using the quantum approximate optimisation algorithm), or quantum annealers. A critical aspect that affects efficiency and scalability of either of these approaches is how classical data are loaded into qubits, respectively how problems are encoded into QUBO representation. The effectiveness of encodings is known to be of crucial importance for quantum computers, especially since the amount of available qubits is strongly limited in the era of noisy, intermediate-size quantum computers.
As quantum computers are based on the laws of quantum mechanics, they are capable of solving certain problems faster than their classical counterparts. However, often algorithms which a theoretical speed-up assume that data can be loaded efficiently. In general, the runtime complexity of the loading routine depends on (i) the data encoding that defines how the data is represented and (ii) the data itself. In some cases, loading the data requires at least exponential time which destroys a potential speed-up. And especially for the first generation of devices that are currently available, the resources (qubits and operations) needed to encode the data are limited. Therefore, understanding the consequences of a particular data encoding is crucial. To capture knowledge about different encodings, we present two data encoding patterns that extend our previous collection of encoding patterns [1].
Abstract As quantum computers are based on the laws of quantum mechanics, they are capable of solving certain problems faster than their classical counterparts. However, quantum algorithms with a theoretical speed‐up often assume that data can be loaded efficiently. In general, the runtime complexity of the loading routine depends on (i) the data encoding that defines how the data is represented by the state of the quantum computer and (ii) the data itself. In some cases, loading the data requires at least exponential time that destroys a potential speed‐up. And especially for the first generation of devices that are currently available, the resources (qubits and operations) needed to encode the data are limited. In this work, we, therefore, present six patterns that describe how data is handled by quantum computers.
Bioinformatics has, among others, the issue of solving complex computational problems with vast amounts of sequencing data. Recently, a new computing architecture, the annealing machine, has emerged that applies to actual problems and is available for practical use. This novel architecture can solve discrete optimisation problems by replacing algorithms designed under the von Neumann architecture. To perform computations on the annealing machine, quadratic unconstrained binary optimisation (QUBO) formulations should be constructed and optimised according to the application. In this study, we developed an algorithm under the annealing machine architecture to solve sequence alignment problems, a known fundamental process widely used in genetic analysis, such as mutation detection and genome assembly. We constructed a QUBO formulation based on dynamic programming to solve a pairwise sequence alignment and derived its general form. We compared with conventional methods to solve 40 bp of pairwise alignment problem. Our implementation, named qualign, solved sequence alignment problems with accuracy comparable to that of conventional methods. Although a small pairwise alignment was solved owing to the limited memory size of this method, this is the first step of the application of annealing machines. We showed that our QUBO formulation solved the sequencing alignment problem. In the future, increasing the memory size of annealing machine will allow annealing machines to impact a wide range of bioinformatics applications positively.Availability: the source code of qualign is available at https://github.com/ymatsumoto/qualign
Encoding classical data into quantum systems is a foundational step in the execution of nearly all quantum algorithms, and a critical bottleneck in realizing practical quantum advantage. This review provides a comprehensive account of the concepts, algorithms, and practical considerations associated with quantum data encoding. We trace the development from its early conceptual foundations to recent advances, considering commonly used access models, such as quantum state preparation, unitary synthesis, QRAM and block encoding. We survey the circuit size, depth, space-time tradeoffs, as well as non-Clifford resources required for fault-tolerant implementation. We also discuss the roles of different access models in quantum algorithms. Special attention is given to structured data, such as sparse data, Boolean functions and data represented by tensor networks. This review bridges theory and applications, serving both as a pedagogical guide for newcomers and as a reference for active researchers. We also highlight the pivotal role of quantum data encoding in quantum computing and provide insights into future directions that will enable quantum advantage.
Mission planning often involves optimising the use of ISR (Intelligence, Surveillance and Reconnaissance) assets in order to achieve a set of mission objectives within allowed parameters subject to constraints. The missions of interest here, involve routing multiple UAVs visiting multiple targets, utilising sensors to capture data relating to each target. Finding such solutions is often an NP-Hard problem and cannot be solved efficiently on classical computers. Furthermore, during the mission new constraints and objectives may arise, requiring a new solution to be computed within a short time period. To achieve this we investigate near term quantum algorithms that have the potential to offer speed-ups against current classical methods. We demonstrate how a large family of these problems can be formulated as a Mixed Integer Linear Program (MILP) and then converted to a Quadratic Unconstrained Binary Optimisation (QUBO). The formulation provided is versatile and can be adapted for many different constraints with clear qubit scaling provided. We discuss the results of solving the QUBO formulation using commercial quantum annealers and compare the solutions to current edge classical solvers. We also analyse the results from solving the QUBO using Quantum Approximate Optimisation Algorithms (QAOA) and discuss their results. Finally, we also provide efficient methods to encode to the problem into the Variational Quantum Eigensolver (VQE) formalism, where we have tailored the ansatz to the problem making efficient use of the qubits available.
The prospect of achieving computational speedups by exploiting quantum phenomena makes the use of quantum processing units (QPUs) attractive for many algorithmic database problems. Query optimisation, which concerns problems that typically need to explore large search spaces, seems like an ideal match for quantum algorithms. We present the first quantum implementation of join ordering, one of the most investigated and fundamental query optimisation problems, based on a reformulation to quadratic binary unconstrained optimisation problems. We empirically characterise our method on two state-of-the-art approaches (gate-based quantum computing and quantum annealing), and identify speed-ups compared to the best know classical join ordering approaches for input sizes conforming to current quantum annealers. Yet, we also confirm that limits of early-stage technology are quickly reached. Current QPUs are classified as noisy, intermediate scale quantum computers (NISQ), and are restricted by a variety of limitations that reduce their capabilities as compared to ideal future QPUs, which prevents us from scaling up problem dimensions and reaching practical utility. To overcome these challenges, our formulation accounts for specific QPU properties and limitations, and allows us to trade between achievable solution quality and problem size. In contrast to all prior work on quantum computing for query optimisation and database-related challenges, we go beyond currently available QPUs, and explicitly target the scalability limitations: Using insights gained from numerical simulations and our experimental analysis, we identify key criteria for co-designing QPUs to improve their usefulness for join ordering, and show how even relatively minor physical architectural improvements can result in substantial enhancements. Finally, we outline a path towards practical utility of custom-designed QPUs.