Vector is the general format of input data of most algorithms. Designing unitary operation to load all information of vector into quantum registers of quantum CPU from classical memory is called quantum loading scheme (QLS). QLS assembles classical memory and quantum CPU as a whole computer, which will be important for further quantum computation. We present a QLS based on path interference with time complexity O(logN), while classical loading scheme has time complexity O(N), that is the efficiency bottleneck of classical computer.
Vector is the general format of input data of most algorithms. Designing unitary operation to load all information of vector into quantum registers of quantum CPU from classical memory is called quantum loading scheme (QLS). QLS assembles classical memory and quantum CPU as a whole computer, which will be important for further quantum computation. We present a QLS based on path interference with time complexity O(logN), while classical loading scheme has time complexity O(N), that is the efficiency bottleneck of classical computer.
This paper presents a simple and fast method to represent vector and matrix using quantum state. Two application examples of the method presented in this paper are given as follows. 1. Applying the method directly to design quantum loading scheme that evades the efficiency bottleneck of classical computer. CPU and memory are the most important two parts of computer, "CPU + Memory=Computer". Loading scheme is defined as loading data into registers of CPU from memory, it connects CPU and memory as a whole machine. Classical loading scheme has time complexity O(N) in terms of arbitrary algorithm, it is the efficiency bottleneck of classical computer. By contrast, quantum loading scheme presented in this paper has time complexity O(logN)! 2. The method is also suitable to represent image and brings many advantages to image compression.
Advantages in several fields of research and industry are expected with the rise of quantum computers. However, the computational cost to load classical data in quantum computers can impose restrictions on possible quantum speedups. Known algorithms to create arbitrary quantum states require quantum circuits with depth O(N) to load an N-dimensional vector. Here, we show that it is possible to load an N-dimensional vector with exponential time advantage using a quantum circuit with polylogarithmic depth and entangled information in ancillary qubits. Results show that we can efficiently load data in quantum devices using a divide-and-conquer strategy to exchange computational time for space. We demonstrate a proof of concept on a real quantum device and present two applications for quantum machine learning. We expect that this new loading strategy allows the quantum speedup of tasks that require to load a significant volume of information to quantum devices.
Modern computing has achieved extraordinary scale and speed. Electronic computers emerged commercially in the mid-20th century, and classical computing has since scaled through architectural advances and parallelism. However, many scientifically important problems remain computationally expensive because the underlying state spaces grow exponentially. Quantum computing addresses this challenge by representing and transforming information using quantum-mechanical state vectors and unitary operations. These conventional systems are referred to as classical computers, capable of handling everyday tasks with moderate computational power and speed. Classical computers represent information using bits and process it using deterministic logic operations. While modern classical systems use extensive parallelism (multi-core CPUs, GPUs, and clusters), many important problems still scale poorly because the resources required grow rapidly with input size. Even with significant parallelism, complex problems that involve large combinatorial structures or high-dimensional state spaces often require substantial computational time and resources, motivating the need for more powerful computational paradigms capable of handling such workloads.
Quantum computing may solve selected classes of problems more efficiently than classical computers, with applications in areas such as cryptography, chemistry, and optimization. However, current quantum systems remain limited in scale and reliability and depend on substantial classical-computing support. This thesis investigates this challenge in two complementary contexts: classical simulation, where efficient computation enables the exploration of larger quantum systems; and quantum error correction, where efficient real-time decoding enables more reliable quantum operation.The first part examines the classical simulation of quantum computers, focusing on the computational and memory challenges that limit its scalability. It organizes the field across device, gate, and algorithmic levels, with particular attention to state-vector, path-based, hybrid, and tensor-based methods. The survey relates their computation, memory, data-movement, and communication bottlenecks to acceleration approaches for CPUs, GPUs, FPGAs, and distributed systems. It further highlights recurring optimization strategies, including reduced precision, data compression, parallel execution, improved memory locality, specialized matrix units, and reconfigurable hardware, providing a common framework for current techniques and future acceleration opportunities.The second part addresses the real-time classical processing required for quantum error correction. Starting from a high-accuracy Graph Neural Network surface-code decoder, it applies algorithm-hardware co-design through hardware-guided pruning and retraining, input-graph filtering, quantization, and a custom FPGA architecture. For code distances up to d=7, the resulting designs satisfy both max-latency and average-latency decoding requirements while reducing the logical error rate by 13% and 40%, respectively, compared with the evaluated Minimum Weight Perfect Matching baseline.Together, these works show how classical computer-architecture techniques can support quantum computing from scalable exploration through simulation to reliable operation through real-time error correction.
In this thesis, I develop the theory required to use quantum computers to accelerate linear algebra and machine learning, in a manner akin to how GPUs are used today. I begin by analysing quantum random access memory (QRAM), the mechanism by which quantum algorithms can access classical (non-quantum) data. When used for linear algebra applications, I show that QRAM has substantial challenges making it harder to construct than an error-corrected quantum computer. Should QRAM prove to be unrealistic, I ask what types of classical data can be efficiently loaded into quantum computers, and prove that discretized continuous functions are one such option. Next, I introduce a framework for manipulating vectors with quantum computers. The primary result of this framework is a technique allowing for the non-linear transformations of vectors to be enacted efficiently for a broad class of functions, despite the underlying unitary (and thus linear) nature of quantum algorithms. In the final chapter, utilizing the preceding results and further developing the vector encoding framework, I demonstrate that quantum computers can accelerate inference for multilayer neural networks under a range of scenarios of QRAM feasibility. This chapter also notes a plausible path towards constructing a practically useful QRAM.
Quantum computers are gaining importance in various applications like quantum machine learning and quantum signal processing. These applications face significant challenges in loading classical datasets into quantum memory. With numerous algorithms available and multiple quality attributes to consider, comparing data loading methods is complex. Our objective is to compare (in a structured manner) various algorithms for loading classical datasets into quantum memory (by converting statevectors to circuits). We evaluate state preparation algorithms based on five key attributes: circuit depth, qubit count, classical runtime, statevector representation (dense or sparse), and circuit alterability. We use the Pareto set as a multi-objective optimization tool to identify algorithms with the best combination of properties. To improve comprehension and speed up comparisons, we also visually compare three metrics (namely, circuit depth, qubit count, and classical runtime). We compare seven algorithms for dense statevector conversion and six for sparse statevector conversion. Our analysis reduces the initial set of algorithms to two dense and two sparse groups, highlighting inherent trade-offs. This comparison methodology offers a structured approach for selecting algorithms based on specific needs. Researchers and practitioners can use it to help select data-loading algorithms for various quantum computing tasks.