Over the past few years, we have been experiencing an abundance of data generation, and by 2029, this size is expected to reach 527 ZB according to latest updates from Statista. This explosion of data has led to an increasing demand for pre-processing, post-processing, and advanced analytics. Classical cloud infrastructures are struggling to keep up, particularly with the rise of AI applications driven by large language models like ChatGPT and Gemini, which power everything from video generation to industry applications such as supply chain optimization.

Quantum computing promises to tackle some of these challenges using fewer resources than classical computing. However, quantum computers do not operate in isolation; they work in conjunction with classical computers, which handle some tasks in pre-processing and post-processing. This hybrid computing requires efficient communication between them, making data loading from classical to quantum a crucial step.

What is Data Loading in Quantum? 

Data loading in quantum computing can be described as a two-step process:

•     Problem formulation (or reformulation): Here, we model the problem mathematically so that it can be solved on a quantum computer. For example, the Max-Cut problem must be reformulated as a Quadratic Unconstrained Binary Optimization (QUBO)problem.  

•     Data Encoding: This step maps classical data into a quantum circuit. It is a transformation of data point from classical space to the high-dimensional Hilbert space of a quantum system. Simply transferring classical data as in classical computing is not enough; special encoding methods are needed, often also called embedding or feature mapping.

Types of Data Encodings: 

1. Basis Encoding: Each data point is mapped directly to a computational basis state. For example, a binary string 1011 is encoded as the quantum state ∣1011⟩. This method is conceptually simple and requires minimal gate overhead, but it scales poorly, as the number of qubits grows linearly with the data size, making it impractical for high-dimensional inputs.

2. Angle (or Parameter) Encoding: Data points are encoded as rotation angles of quantum gates as Rx(theta).  This method is more efficient than basis encoding, providing more efficient(tolerable) quantum circuit depth. 

3. Amplitude Encoding: Data is encoded into the amplitudes of a quantum state. The method is qubit-efficient, but challenged by a deep circuit. 

Why is Data Loading Challenging?

The difficulty comes from a fundamental mismatch:

• Classical data is large and explicit

• Quantum states are compact but fragile

For example, a dataset with 2^n  values can theoretically be represented using only n qubits via amplitude encoding. This sounds incredibly efficient until we consider that preparing such a state may require an exponential number of quantum operations. Quantum Random Access Memory (QRAM) is often proposed as a solution to the data loading problem. In theory, QRAM could load large classical datasets into quantum superposition efficiently. However, QRAM remains currently experimentally unrealized at scale and sensitive to noise and decoherence. 

In a full computational pipeline, each step, data loading, quantum processing, and measurement/readout should be efficient. These challenges, in combination, open up new research questions and directions.