# Quantum Computing and Machine Learning in Medical Decision-Making: A Comprehensive Review
## 2 Foundational Concepts  
### Quantum Computing  
QC represents a paradigm shift in computation, leveraging the principles of quantum mechanics to process information in fundamentally new ways. Unlike classical computing, which relies on binary bits that exist in a state of 0 or 1, QC uses quantum bits, or qubits, that can exist in superpositions of states, enabling significantly enhanced computational power [9]. Qubits are the fundamental units of quantum information. Unlike classical bits, which are restricted to a binary state (0 or 1), qubits can exist in a superposition, representing multiple states simultaneously [10]. This property allows quantum computers to perform many calculations in parallel, offering exponential speedup for certain problems. Entanglement is a quantum phenomenon where the states of two or more qubits become intrinsically linked, such that the state of one qubit directly influences the state of the others,  
Figure 2: Comparison of classical computing vs. quantum computing: Classical computing uses bits (0 or 1) and is ideal for everyday tasks with low error rates. Quantum computing, utilizing qubits (0, 1, or both), offers potential exponential increases in computing power for complex problems but currently faces high error rates. Reproduced from reference [6] under the Creative Commons Attribution 4.0 International License ([[https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/)]([https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/)) (accessed on 24 January 2025)). regardless of distance [11]. This property enables highly efficient information sharing and parallel processing, which are key to the power of QC. Quantum gates are the building blocks of quantum circuits, analogous to logic gates in classical computing [12]. These gates manipulate qubits through operations that preserve quantum coherence, enabling complex transformations of quantum states. Common gates include the Hadamard gate (for creating superpositions), the CNOT gate (for generating entanglement), and the Pauli gates (for state rotations) [13; 14]. QC differs from classical computing in speed, complexity, and problem-solving capacity. Classical computers process information sequentially, limiting their efficiency for problems involving vast datasets or complex optimizations. Quantum computers, on the other hand, leverage superposition and entanglement to perform multiple computations simultaneously, significantly reducing the time required for tasks such as factorization, searching unsorted databases, and solving differential equations [15]. For instance, a classical computer searching an unsorted database requires O(N) operations, where N is the number of entries. [PERSON]'s algorithm, a quantum search algorithm, reduces this to O(\(\surd\)N), showcasing a quadratic speedup [16]. Similarly, [PERSON]'s algorithm, designed for integer factorization, achieves exponential speedup by solving problems in polynomial time that are infeasible for classical computers [17]. [PERSON]'s algorithm is designed for searching unsorted datasets. In medical decision-making, this algorithm could expedite searches through massive databases of patient records, genomic data, or drug libraries [18]. [PERSON]'s algorithm efficiently factors large integers, underpinning advancements in cryptography and data security. Its relevance in healthcare lies in safeguarding sensitive medical data during processing and transmission [19]. The Quantum Approximate Optimization Algorithm (QAOA) is used to solve combinatorial optimization problems [20]. Applications include optimizing treatment plans, scheduling surgeries, or resource allocation in hospitals. While QC offers potential advantages, it also faces significant challenges that hinder its practical deployment. One of the most pressing issues is quantum decoherence, where qubits lose their quantum state due to interactions with their environment, leading to loss of information and computational errors [21].