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       Chapter 3

       Quantum Computing: Basic Concepts

      … it seems that the laws of physics present no barrier to reducing the size of computers until bits are the size of atoms, and quantum behavior holds sway

      — Richard P. Feynman (1985)

       Abstract

      Quantum computing is a research frontier in physical science with a focus on developing information processing at the quantum scale. Quantum computing involves the use of algorithms to exploit the special properties of quantum mechanical objects (such as superposition, entanglement, and interference) to perform computation. In physics, quantum mechanics is the body of laws that describe the behavior and interaction of electrons, photons, and other subatomic particles that make up the universe. Quantum computing engages the rules of quantum mechanics to solve problems using quantum information. Quantum information is information concerning the state of a quantum system which can be manipulated using quantum information algorithms and other processing techniques. Although quantum computing is farther along than may be widely known, it is an early-stage technology fraught with uncertainty. The overall aim in the longer term is to construct universal fault-tolerant quantum computers.

3.1Introduction

      Quantum computers are in the early stages of development and would likely be complementary to existing computational infrastructure, interacting with classical devices, and being accessed either locally or as a cloud service. Currently, the top methods demonstrate 30–70 qubits of processing power and achieve fidelity rates above 99% (i.e. below a fault tolerance threshold of 1%). However, there is uncertainty about the realizability of scalable universal quantum computers. Quantum computers may excel at solving certain types of problems such as optimization. This could offer a step-up in computing such that it is possible to solve new classes of problems, but not all problems. For example, considering well-known optimization problems, it may be possible to search twice as many possibilities in half the time (exploring a fixed-size space in the square root of the amount of time required for a classical computer).

      Quantum computing is an early-stage technology with numerous risks and limitations (Dyakonov, 2018). The long-term goal of universal quantum computing is not immediate as many challenges including error correction need to be resolved. In the short term, the focus is on solving simple problems in which quantum computers offer an advantage over classical methods through NISQ devices (noisy intermediate-scale quantum devices) (Preskill, 2018).

3.1.1 Breaking RSA encryption

      One of the biggest questions is when it might