advances in recent decades have led to the practical realizability of quantum computers. First, in the 1990s was the discovery of quantum error correction. Unlike classical bits that persistently stay in a 1 or 0 state, quantum bits are extremely sensitive to environmental noise and may decohere before they can be used to perform a computation. Quantum error correction overcomes some of the challenges of working in quantum mechanical domains.
Second, since 2012, there have been advances in room-temperature superconducting materials and a proliferation of ways of making qubits such that quantum systems have increased from 1–2 qubits to 50–100 qubits. A research goal is demonstrating quantum advantage, which is specific cases in which quantum computing confers an advantage over classical computing.
3.2.1 Quantum computing and classical computing
Quantum information processing is not only a potentially faster means of computing but also a new paradigm in that information is conceived and managed in a completely different way due to the different properties of quantum objects. According to W.D. Phillips, 1997 Nobel Prize winner in physics and NIST scientist, “Quantum information is a radical departure in information technology, more fundamentally different from current technology than the digital computer is from the abacus” (Williams, 2007).
Some of the special properties of quantum objects (be it atoms, ions, or photons) are superposition, entanglement, and interference (SEI properties). Superposition means that particles can exist across all possible states simultaneously. This is known as a superposition of states. For example, an electron may exist in two possible spin states simultaneously, referred to as 1 and 0, or spin-up and spin-down. Entanglement is the situation that groups of particles are related and can interact in ways such that the quantum state of each particle cannot be described independently of the state of the others even when the particles are separated by a large distance. Across large distances, this is called Bell pair entanglement or nonlocality. Interference relates to the wave-like behavior of particles. Interference can be positive or negative, in that when two waves come together, they are either reinforced or diminished.
Classical computing is based on electrical conductivity, using Boolean algebra (namely expressions evaluating as true/false, and/or, etc.) to manipulate bits. Quantum computing is based on quantum mechanics, using vectors and linear algebra to manipulate matrices of complex numbers. Aiming toward a universal model of quantum computation, the idea is to package the quantum mechanical matrix manipulations such that they run quantum states that are executed with a set of gates that offer the same kind of Boolean logic as in classical computing.
3.2.2 Bit and qubit
In classical computing, the bit is the fundamental computational unit. The bit is an abstract mathematical entity that is either a 0 or a 1. Computations are constructed as a series of manipulations of 0s and 1s. In the physical world, a bit might be represented in terms of a voltage inside a computer, a magnetic domain on a hard disk, or light in an optical fiber. The qubit (quantum bit) is the equivalent system in quantum mechanics. The qubit is likewise an abstract mathematical entity (a logical qubit), existing in a superposition state of being both a 0 and a 1, until collapsed in the measurement at the end of the computation into being a classical 0 or 1. The qubit can be instantiated in different ways in the physical world. There are realizations of qubits in atoms, photons, electrons, and other kinds of physical systems. The quantum state of a qubit is a vector in a 2D space. This is a linear combination of the 1 and the 0 (the trajectory or probability that it is in the 1 or the 0 state). A model of computation can be built up by assigning states closer to the 0 as being 0 and states closer to the 1 as being 1 (when measured).
A bit is always in a state of either 1 or 0. A qubit exists in a state of being both 1 and 0 until it is collapsed into a 1 or a 0 at the end of the computation. A bit is a classical object that exists in an electronic circuit register. A qubit is a quantum object (an atom, photon, or electron) that bounces around in a 3D space with a different probability of being at any particular place in the 3D sphere called a Hilbert space (and has vector coordinates in the X, Y, and Z directions). Figure 3.1 shows the physical space of the states of the bit and the qubit.
The interpretation is that whereas a classical bit is either on or off (in the state of 1 or 0), a qubit can be on and off (1 and 0) at the same time, a property called superposition. One example of this is the spin of the electron in which the two levels can be understood as spin-up and spin-down. Another example is the polarization of a single photon in which the two states can be taken to be the vertical polarization and the horizontal polarization (single photons are often transmitted in communications networks on the basis of polarization). In a classical system, a bit needs to be in one state or the other. However, in a quantum mechanical system, the qubit can be in a coherent superposition of both states or levels of the system simultaneously, a property which is fundamental to quantum mechanics and indicates the greater potential range of computation in quantum systems.
Figure 3.1. Potential states of bit and qubit.
Compared to classical states, quantum states are much richer and have more depth. Superposition means that quantum states can have weight in all possible classical states. Each step in the execution of a quantum algorithm mixes the states into more complex superpositions. For example, starting with the qubit in a position of 0–0–0 leads to a superposition of 1–0–0, 1–0–1, and 1–1–1. Then each of the three parts of the superposition state branches out into even more states. This indicates the extensibility of quantum computers that could allow faster problem solving than is available in classical computers.
3.2.3 Creating qubits
A qubit can be created in any quantum system which has two levels of energy that can be manipulated (Steane, 1997). Qubits can be conceived as being similar to harmonic oscillators at the macroscale. Physical systems that vibrate in a wave-like form between two levels of energy are called harmonic oscillators. Some examples include electrical circuits with oscillating current, sound waves in gas, and pendulums. Harmonic oscillators can be modeled as a wave function that cycles between the peak and trough energy levels. The same wave function concept is true at the quantum scale. In this sense, whenever there is a quantum system with two levels of energy, it can be said to be a qubit and possibly engaged as a two-state quantum device. This implies that there can be many different ways of building qubits. Hence, the method for creating qubits might be an engineering choice similar to the way that different methods have been used in classical computing for the physical implementation of logic gates (methods have ranged over time and included vacuum tubes, relays, and most recently integrated circuits).
3.3Quantum Hardware Approaches
3.3.1 The DiVincenzo criteria
The DiVincenzo criteria have been proposed as standards that constitute the five elements of producing a well-formed quantum computer (DiVincenzo, 2000). The criteria are having (1) a scalable system of well-characterized qubits, (2) qubits that can be initialized with fidelity (typically to the zero state), (3) qubits that have a long-enough coherence time for the calculation (with low error rates), (4) a universal set of quantum gates (that can be implemented in any system), and (5) the capability of measuring any specific qubit in the ending result.
There are several approaches to quantum computing (Table 3.1) (McMahon, 2018). Those with the most near-term focus are superconducting circuits, ion trapping, topological matter, and quantum photonics.
