Introduction to Quantum Algorithms

In 1981 Richard Feynman proposed the idea that a computer built of quantum mechanical elements obeying quantum mechanical laws can perform efficient simulations of quantum systems. Quantum computing works on the laws of quantum mechanical properties such as superposition, entanglement, and interference. Unlike in classical computing, in quantum computers a register can exist in all possible states at once due to its superposition properties. It is only when a quantum system is measured that we observe one of the possible states. Such a system is advantageous since, when measured, each state can appear with a certain probability encoded in the state prior to the measurement. Quantum computing works by increasing the probability of the desired state to a sufficiently high value so that the desired state can be obtained with high confidence with a minimal number of measurements. In this regard, quantum interference, which results from quantum superposition, plays a big role since it allows probability amplitudes corresponding to a given state to interfere and cancel each other. This property of quantum interference biases the measurement to a set of states that we desire as the outcome of quantum algorithms. Similarly, quantum entanglement allows one to create a strong correlation between quantum objects, especially qubits, to the advantage of quantum algorithms, as you will see throughout this chapter.