Basic quantum mechanics principles and their application

Quantum computers use principles and theories (such as quantum field theory and group theory) to describe the quantum mechanics phenomenon. Quantum mechanics principles, such as superposition, decoherence, and entanglement, have been utilized to build processors that process and relay information at exponential speed. The following section maps the quantum computer’s evolution journey and briefly describes quantum mechanics principles.

The emerging role of quantum computing technology for next-generation businesses

For a long time, advances in digital computers at economies of scale have suppressed the development of other computing paradigms. Moore’s law (Figure 1.3) has predicted exponential growth and advancement in the microprocessor. However, the presence of a large amount of data collected over decades of computing advancements has put a limitation on computing power, storage, and communication. To overcome the limits of the current architectures, we must overcome challenges such as finite memory, self-programmable computers, large number factorization, and faster microprocessors.

Figure 1.3 – Transistor number growth according to Moore’s law

Looking at the current limitations of digital computers due to their fundamental principles and assumptions, there is a need for new computing paradigms to emerge. To solve the problems related to various domains related to climate, process automation, industry mechanizations, and autonomous systems, there is a need to overcome the current challenges. Quantum computing, molecular computing, nature-inspired algorithms, and synergistic human-machine interaction (Computer’s Special Issue September 2016 Examines “Next-Generation Computing Paradigms,” IEEE Computer Society, https://tinyurl.com/4b5wjepk) are the current areas of interest and innovation in the pursuit of overcoming the aforementioned challenges. Figure 1.4 charts the journey and impact of the quantum-computing paradigm from theoretical to practical application:

Year	Phenomenon	Effect
1905	Photoelectric effect was discovered by Albert Einstein and discovery of photon took place.	Laid the foundation to discover quantum behavior in atomic particles.
1924 to 1927	Max Born coined the term Quantum Mechanics and Heisenberg, Born, and Jordan discovered matrix mechanics.	Discovery of quantum mechanics principles, which were harnessed to produce the quantum processor.
1935	Erwin Schrödinger conceptualized and wrote his thought experiment known as Schrödinger’s cat.	The principle of quantum entanglement was discovered.
1976	Quantum information theory was proposed by Roman Stanisław Ingarden.	Quantum Information science as a discipline was formulated, which laid the foundation for quantum algorithms.
1981	Richard Feynman proposed that a quantum computer had the potential to simulate physical phenomena.	The practical application of quantum mechanics was harnessed to develop working quantum computers.
1994	Shor’s algorithm for factoring integers was discovered.	Formulated the basis of cryptography for post quantum key distribution.
1996	Grover’s algorithm was discovered.	Laid the way for storing information in database form.
2011	D-Wave offered the first quantum computing solution using quantum annealing.	Opened up the possibilities of using quantum computers for commercial purposes.
2019	Google claimed quantum supremacy.	Showed a use case of quantum supremacy that can help in better encryption.
2021	IBM unveiled the first 127-qubit quantum computer named Eagle.	Facilitated faster processing of the complex NP-hard problem.

Figure 1.4 – Journey from quantum mechanics to quantum computing

As you can see from the evolution point of view (Figure 1.4), quantum technologies are making rapid strides to overcome problems such as accurate simulation, efficient optimization, and correct pattern recognition. Once researchers can overcome the related problems that limit current users, and implement quantum technology to solve day-to-day problems, one can see how the industry-wide adoption of quantum technology can solve large-scale problems.

The next section describes some of the common terminologies and principles of quantum mechanics used in building and operating quantum computers.

From quantum mechanics to quantum computing

Deciphering the quantum mechanics principles involved in quantum computing is an uphill task for a layperson. This section describes each quantum mechanics postulate in easy-to-understand language, explaining how it is involved in the quantum computing mechanism.

Postulate	Definition	Usage	Further Reading
Qubits	The qubit is a basic unit of quantum information stored on a two-state device encoding information in 0s and 1s) ·	Facilitates faster processing of information for complex processes like simulation and optimization.	What is a qubit? (quantuminspire.com)
Quantum State	Quantum state is the position and value of attributes (change and spin) of atomic particles obtained naturally or induced by creating physical environments (e.g. laser and heat).	Used in processing and transforming information using qubits in a controlled environment.	Superposition and entanglement (quantuminspire.com)
Quantum Superposition	It refers to a phenomenon that tells us that quantum superposition can be seen as the linear combination of quantum states.	This property makes it hard for a system to decrypt quantum communication and thus provides a safer way to transfer information.	Superposition and entanglement (quantuminspire.com)
Quantum Entanglement	Quantum entanglement refers to the linking of two particles in the same quantum state and the existence of correlation between them.	Facilitates the ability of a system to do calculations exponentially faster by more and more qubits.	Superposition and entanglement (quantuminspire.com)
Quantum Measurement	A set of mathematical operators to understand and measure the amount of information that can be recovered and processed from qubits.	Useful in understanding the complexities of quantum mechanics.	Quantum measurement splits information three ways - Physics World.
Quantum Interference	It refers to the ability of atomic particles to behave like wave particles, thus resulting in information or the collapse of qubit state thus leading to quantum coherence or dechorence.	It measures the ability of quantum computers to accurately compute and carry the information stored in them.	What is quantum mechanics? Institute for Quantum Computing (uwaterloo.ca)
No Cloning Theorem	The “no cloning theorem” is a result of quantum mechanics that forbids the creation of identical copies of an arbitrary unknown quantum state.	The no cloning theorem is a vital ingredient in quantum cryptography, as it forbids eavesdroppers fom creating copies of a transmitted quantum cryptographic key.	The no cloning theorem – Quantiki

Figure 1.5 – Quantum computing glossary

The postulates mentioned in Figure 1.5 have enabled computer scientists to migrate from classical to quantum computers. As we will see in subsequent sections, postulates such as quantum interference and the no-cloning theorem have enabled quantum technologies to come to the fore, and laid the basis for achieving faster, more efficient, and more accurate computational power. The following section will look at technologies fueling innovations in quantum computing paradigms.

Approaches to quantum innovation

In its current form, quantum computing relies on a plethora of technologies to expand its footprint. It will take years for quantum computers to fully reach their commercial potential. However, when they work in hybrid mode (in tandem with classical computers), they are expected to produce much better results than in standalone mode. Let’s have a look at the technologies that make them tick:

• Superconducting: This technology takes advantage of the superposition property of quantum physics. Information is circulated by two charged electron currents flowing in opposite directions around the superconductor, and then exchanging the info stored in the qubit while entangling each other. This technology needs the quantum computer to be operated at extremely low temperatures.
• Trapped ions: An ion is a charged atom (Ca+ or Br+). Suppose a piece of information is coded on this charged atom. The atom is transported from state 0 to state 1 by emitting an energy pulse. This charged atom will carry the information and be decoded with the help of lasers. These ions are trapped in electric fields. Information coded is interpreted using a photonic unit and then passed on using optic fibers.
• Photonics: This technology uses photons to carry information in a quantum state. Using current silicon chips, the behavior of photons is controlled, and the information is transmitted over the circuit. Due to its compatibility with existing infrastructure and chip-making capabilities, it shows promise to achieve great success.
• Quantum dots: Quantum dots are small semiconducting nanocrystals made up of elements such as silicon and cadmium. Their size ranges from 2 to 10 nm. The physical implementation of a qubit involves exchanging information via charged qubits in capacitive states. Due to its conducive conditions, photonics is less error-prone.
• Cold atoms: Cold atoms use a ploy similar to trapped ions, where atoms are cooled below 1 mK and then used as an information highway to bounce off the information. Lasers are programmed to control the quantum behavior of cold atoms, and to then leverage them to transfer data.

To understand the milestones achieved by each technology, we will take the help of DiVincenzo’s criteria. In the year 2000, David DiVincenzo proposed a wish list of the experimental characteristics of a quantum computer. DiVincenzo’s criteria have since become the main guidelines for physicists and engineers building quantum computers (Alvaro Ballon, Quantum computing with superconducting qubits, PennyLane, https://tinyurl.com/4pvpzj6a). These criteria are as follows:

• Well-characterized and scalable qubits: Numerous quantum systems seen in nature are not qubits; thus, we must develop a means to make them act as such. Moreover, we must integrate several of these systems.
• Qubit initialization: We must be able to replicate the identical state within an acceptable error margin.
• Extended coherence durations: Qubits will lose their quantum characteristics after prolonged interaction with their surroundings. We would want them to be durable enough to enable quantum processes.
• Universal set of gates: Arbitrary operations must be performed on the qubits. To do this, we need both single-qubit and two-qubit gates.
• Quantification of individual qubits: To determine the outcome of a quantum computation, it is necessary to precisely measure the end state of a predetermined set of qubits.

Figure 1.6 helps evaluate the promises and drawbacks of each kind of quantum technology based on DiVincenzo’s criteria:

	Superconducting	Trapped Ions	Photonics	Quantum Dots	Cold atoms
Well-characterized and scalable qubit	Achieved	Achieved	Achieved	Achieved	Achieved
Qubit initialization	Achieved	Achieved	Achieved	Achieved	Achieved
Extended coherence durations	99.6%	99.9%	99.9%	99%	99%
Universal set of gates	10-50 ns	1-50 us	1 ns	1-10 ns	100 ns
Quantification of individual qubits	Achieved	Achieved	Achieved	Achieved	Achieved

Figure 1.6 – DiVincenzo’s criteria

On various parameters, technologies such as superconducting and trapped ions are showing the most promise in overcoming the challenges of quantum technology. While supergiants such as IBM and Google are betting on such technology to develop their quantum computers, new-age start-up technologies, including IQM and Rigetti, are exploring others that are more compatible with the current infrastructure.

In the next section, we will detail the applications and technologies associated with the quantum computing ecosystem.

Quantum computing value chain

Quantum computing technology is still in its infancy. If we have to draw parallels from a technology point of view, in 1975, most of the investors were investing in hardware firms such as IBM, HP, and later Apple, to make sure that people would be able to migrate from mainframe to personal computers. Once the value from hardware had been derived, they started paying attention to software, and firms such as Microsoft came into prominence. According to a report published by BCG, 80% of the funds available are flowing toward hardware companies such as IonQ, ColdQuanta, and Pascal. Key engineering challenges that need to be overcome are scalability, stability, and operations.

Several companies and start-ups are investing in quantum computing. Countries such as the USA ($2 billion), China ($1 billion), Canada ($1 billion), the UK (£1 billion), Germany (€2 billion), France (€1.8 billion), Russia ($790 million), and Japan ($270 million) have pledged huge amounts to achieve quantum supremacy. It has been speculated that quantum solutions, including quantum sensors, quantum communication, and quantum internet, need huge investments to help countries in achieving quantum supremacy. McKinsey has pegged the number of quantum computing start-ups at 200. Also, according to PitchBook (market data analyst), global investment in quantum technologies has increased from $93.5 million in 2015 to $1.02 billion in 2021. A few well-known start-ups that have attracted huge investments recently are Arqit, Quantum eMotion, Quantinuum, Rigetti, D-Wave, and IonQ.

Figure 1.7 shows the potential application of quantum technologies in different fields based on the types of problems solved by quantum computers:

Figure 1.7 – Application of quantum computing

The following technologies are helping companies to create the value chain for end users in the quantum realm:

• Quantum computing: Quantum computing refers to developing software and hardware technologies using quantum mechanics principles.
• Quantum key distribution (QKD): QKD, or quantum cryptography, provides a secure way for banks and other institutions to exchange encryption keys. It uses principles of quantum mechanics to secure the communication channels.
• Quantum software and quantum clouds: Quantum software, or programming languages such as Qiskit, provide a medium for end users to interface with system hardware and perform complex computing operations including simulation, optimization, and pattern recognition.

Figure 1.8 – Quantum technology

• Post-quantum encryption: One of the key research areas that have prompted countries to invest billions of dollars is the hunch that current encryption software will be susceptible to quantum algorithms. They need algorithms that can secure these channels further.
• Quantum sensors and atomic clocks: These terms refer to the development of laser and trapped-ion technologies to control the atomic behavior of molecules. This has prompted researchers to develop use cases where next-gen technologies such as quantum sensors will be useful in the early detection of natural calamities, including tsunamis and earthquakes.
• Quantum materials: Quantum materials refers to the cluster of world-class technologies that help capture and manipulate elements’ quantum properties for industrial usage.
• Quantum memories and other quantum components: These devices carry information in qubit form via photons. It is complex technology that is still under development and is expected to overcome the memory barriers defined by current limitations.

As observed in Figure 1.8, the quantum computing ecosystem is vast. It has multiple facets such as quantum materials, memories, and sensors, empowering the user to collect and analyze data more effectively.

In the following section, we will look at the companies powering the revolution in quantum technologies.