Quantum Computing, An Easy Introduction to the Emerging Terms that Could Define the Century

The fundamental distinction between classical bits and quantum bits, or qubits, lies in the principles of classical and quantum physics. Classical bits, the basic units of information in classical computing, adhere to the binary system, existing in one of two definite states: 0 or 1. This binary nature reflects the deterministic framework of classical physics. In contrast, qubits, central to quantum computing, operate under the principles of quantum mechanics. They can exist in a superposition of states, as eloquently described by physicist John Preskill: “Quantum bits are like classical bits, but they can also be in superpositions of 0 and 1” (Preskill, 2012). This superposition allows a qubit to be in a combination of both 0 and 1 simultaneously, a feature absent in classical bits.

The concept of a qubit, derived from ‘Quantum Bit’, was first introduced to provide a quantum analogue to the classical bit. Unlike classical bits, qubits are influenced by quantum phenomena such as superposition and entanglement. Superposition, as Erwin Schrödinger first described, allows particles to be in multiple states at once, a principle that qubits embody (Schrödinger, 1935). Entanglement, another quantum property, described by Einstein as “spooky action at a distance”, enables qubits to be interconnected in such a way that the state of one qubit instantaneously influences another, regardless of distance (Einstein, Podolsky, & Rosen, 1935). This interconnectedness is a stark contrast to the independent nature of classical bits.

Quantum mechanics, a cornerstone of modern physics, fundamentally challenges our classical perceptions of the natural world. At its core, quantum mechanics describes the behavior of matter and energy at the atomic and subatomic levels, where the conventional laws of classical physics no longer apply.

The origins of quantum mechanics can be traced back to the early 20th century, with significant contributions from renowned physicists like Max Planck, Niels Bohr, Werner Heisenberg, and Erwin Schrödinger. Planck’s introduction of the quantum hypothesis in 1900, proposing that energy is quantized and emitted in discrete units called quanta, laid the groundwork for this revolutionary field (Kragh, 2000). Bohr’s model of the atom (1913) and Heisenberg’s uncertainty principle (1927) further cemented the non-intuitive nature of quantum mechanics (Jammer, 1966; Heisenberg, 1927).

Central to quantum mechanics are several key principles that defy classical intuition. The wave-particle duality, eloquently described by Richard Feynman as “nature’s great mystery,” posits that particles like electrons exhibit both wave-like and particle-like properties (Feynman, 1965). The Heisenberg Uncertainty Principle, a fundamental limit on the precision with which certain pairs of physical properties, such as position and momentum, can be known simultaneously, challenges the deterministic nature of classical physics (Heisenberg, 1927).

Another cornerstone is the concept of quantum superposition, exemplified by Schrödinger’s cat thought experiment, which illustrates how a quantum system can exist in multiple states simultaneously until it is observed (Schrodinger, 1935). Furthermore, quantum entanglement, a phenomenon Albert Einstein famously referred to as “spooky action at a distance,” describes how particles can become correlated in such a way that the state of one particle instantaneously influences the state of another, regardless of the distance separating them (Einstein, Podolsky, & Rosen, 1935).

Superposition, a cornerstone concept in quantum mechanics, represents the ability of quantum systems to exist in multiple states simultaneously, a phenomenon starkly contrasting with classical physics. This principle was first articulated in the early 20th century, emerging from the pioneering work of physicists like Erwin Schrödinger and Werner Heisenberg. Schrödinger, renowned for his eponymous wave equation, described superposition as a system existing in all possible states until it is observed. Heisenberg, through his uncertainty principle, further illuminated the intrinsic probabilistic nature of quantum states. The term ‘superposition’ itself, while not attributed to a single individual, evolved from the Latin ‘superpositio’, reflecting the overlaying of different states.

A qubit can be considered in the superposition of two states |0⟩ and |1⟩. The relative components of each of those states are given by α and β. Hence the state of the superposition of the qubit is:

| φ⟩ = α|0⟩+β|1⟩

Entanglement, a term famously described by Einstein as “spooky action at a distance,” is a property where the state of one qubit is dependent on the state of another, regardless of the distance separating them (Einstein, Podolsky, & Rosen, 1935). This entanglement leads to a massive parallelism, vastly increasing the computational power of quantum computers. The practical implications of these properties are profound, as they enable quantum computers to solve certain problems much faster than their classical counterparts.

Quantum interference, a cornerstone concept in quantum mechanics, is a phenomenon that arises when two or more quantum states overlap and combine to form a new quantum state. This principle is elegantly encapsulated in Richard Feynman’s assertion that “each photon then interferes only with itself. Interference between different photons never occurs” (Feynman, Leighton, Sands, 1965). The term ‘interference’ itself, originating from the Latin ‘interferre’, meaning ‘to strike against’, aptly describes the process where waves, in this case, probability waves of quantum particles, superpose to form a resultant wave of greater or lesser amplitude.

In the realm of quantum computing, interference is a pivotal mechanism. It allows for the manipulation of qubits (quantum bits), the fundamental units of quantum information, which derive their name from the contraction of ‘quantum’ and ‘bit’. Unlike classical bits, qubits can exist in superpositions of states, embodying the principle of quantum superposition. This superposition, as described by Erwin Schrödinger, one of the founding fathers of quantum mechanics, is a fundamental characteristic of quantum systems (Schrödinger, 1935). When qubits interact, their superposed states can interfere constructively or destructively, an effect that is harnessed in quantum algorithms to perform complex computations more efficiently than classical computers.

The Bloch Sphere, a concept fundamental to the understanding of quantum mechanics and quantum computing, offers a vivid geometrical representation of the state of a two-level quantum system, such as a qubit.

The Bloch Sphere was named after the physicist Felix Bloch, who introduced it in 1946 to describe nuclear magnetic resonance (NMR) and, by extension, the state of quantum systems (Bloch, 1946). This representation is particularly valuable in visualizing the peculiarities of quantum states, including superposition and entanglement.

In the Bloch Sphere representation, a qubit state is depicted as a point on the surface of a sphere. The north and south poles of the sphere typically represent the standard basis states, often denoted as |0⟩ and |1⟩ in quantum mechanics. Any point on the sphere’s surface can be reached by rotating these basis states, which corresponds to the superposition of states in a qubit.

The sphere’s axes are crucial for understanding quantum phenomena: the x-axis often represents the real part of the superposition, the y-axis the imaginary part, and the z-axis the probability difference between the |0⟩ and |1⟩ states. This geometric representation elegantly encapsulates the principles of superposition and phase, which are central to quantum mechanics and quantum computing (Nielsen & Chuang, 2010).

The term “quantum” itself, derived from the Latin word “quantus” meaning “how much,” was first used in this context by Max Planck, a key figure in the field. Planck’s work, along with Albert Einstein’s explanation of the photoelectric effect, laid the groundwork for what would become Quantum Physics. This field radically departs from classical physics, particularly in its assertion that energy is quantized, existing in discrete units called quanta. This concept was revolutionary, challenging the continuous wave theory of light that prevailed at the time.

At the heart of Quantum Physics are principles like wave-particle duality and quantum entanglement. Wave-particle duality, a concept brought to the fore by Louis de Broglie and Werner Heisenberg, posits that every quantum entity exhibits both particle-like and wave-like properties. This duality is famously demonstrated in the double-slit experiment, which shows that particles like electrons can display interference patterns, a characteristic of waves.

The QPU is analogous to the Central Processing Unit (CPU) in classical computers, but it operates on the principles of quantum mechanics.

The operational heart of a QPU lies in its ability to perform quantum computation through qubits. Qubits are manipulated using quantum gates in a manner analogous to how classical logic gates manipulate bits. However, quantum gates operate through complex operations like superposition and entanglement.

In practice, QPUs are still in a nascent stage, with challenges in scalability, error rates, and maintaining qubits in a stable state (quantum coherence). Despite these challenges, significant progress has been made. Companies like IBM and Google have developed quantum processors, and research continues to advance towards more stable and powerful QPUs. The development of quantum error correction and quantum algorithms are pivotal in harnessing the full potential of quantum computing.

As you cannot buy a quantum computer easily (yet) the majority of people interact with quantum computers over the cloud. They do as most quantum computers require special conditions such as refrigeration or optical tables to run. They are not quite ready for the desktop, although it is possible to buy a desktop quantum computer for research purposes.

Rigetti have recently announced that they are selling their machines for use, although they are pretty expensive coming in at almost a million USD.

Interacting with a quantum computer is markedly different from using a classical computer. Users typically interact through a classical interface, often a regular computer, which sends instructions to the quantum processor. Programming a quantum computer involves using specialized quantum programming languages, such as Qiskit developed by IBM or Cirq by Google, which allow the creation of quantum circuits.

These circuits define sequences of quantum operations or gates, analogous to classical logic gates but exploiting quantum phenomena like superposition and entanglement (Cross et al., 2017; Quantum AI team and collaborators, 2020). The quantum state evolves through these gates, leading to an output state that, when measured, collapses to a definite classical state, providing the result of the computation.

This service-oriented model allows users to access quantum computing resources over the cloud, bypassing the need for direct ownership of highly complex and expensive quantum hardware. The concept of QCaaS is rooted in the broader trend of cloud computing, but it specifically leverages the unique capabilities of quantum computers.

The emergence of QCaaS is a testament to the rapid advancements in quantum computing and its transition from theoretical exploration to practical application. This model democratizes access to quantum computing, allowing researchers, businesses, and developers to explore quantum solutions without the prohibitive costs of building and maintaining quantum infrastructure. However, the field is still in its nascent stages, with many challenges such as error correction, qubit scalability, and algorithm development yet to be fully resolved.

A QOS, fundamentally, is the software layer that manages and controls quantum hardware, akin to how traditional operating systems like Windows or Linux operate on classical computers.

Some researchers think that building a Quantum Operating System or QOS will be key to building sustianble quantum computing. Companies such as Riverlane have been exploring the building of Quantum Operating Systems, often focussed on Quantum Error Correction.

The development of quantum operating systems is still in its infancy, with companies and research institutions experimenting with various approaches. As quantum technology evolves, these operating systems will become more sophisticated, enabling more complex quantum computations and potentially revolutionizing fields like cryptography, materials science, and complex system modeling.

Programming a quantum computer diverges significantly from classical programming. The process involves preparing qubits in a certain quantum state, manipulating these qubits through quantum gates, and finally measuring the qubits to collapse their state to a classical outcome. Quantum gates, the building blocks of quantum circuits, operate on a small number of qubits and are the quantum equivalent of classical logic gates. They manipulate qubits through operations that can be understood as rotations on the Bloch sphere, a geometrical representation of the pure state space of a two-level quantum mechanical system.

Renowned physicist Richard Feynman’s quote, “Nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical,” encapsulates the necessity of quantum computing in simulating complex quantum phenomena. Quantum programming languages, such as Q# from Microsoft and Qiskit from IBM, have been developed to facilitate the creation of quantum algorithms. These languages often require an understanding of both quantum mechanics and classical computing principles.

The evolution of quantum frameworks is equally crucial. Frameworks like Qiskit and Cirq (developed by Google) provide an environment for quantum algorithm development, simulation, and execution on actual quantum hardware. They are designed to abstract the complexities of quantum hardware, allowing programmers to focus on algorithm design. For instance, Qiskit enables the creation and manipulation of quantum circuits, translating these into instructions that can be executed on IBM’s quantum computers. The frameworks also play a vital role in error correction and optimization, essential in a field where quantum decoherence and noise are significant challenges.

The concept of quantum error correction is to protect quantum information against errors due to decoherence and other quantum phenomena. Peter Shor, a renowned American mathematician and professor of applied mathematics at MIT, was one of the pioneers in this field. In 1995, Shor developed the first quantum error-correcting code, known as the Shor code, which encodes a single qubit of information into a highly entangled state of nine qubits. This code can correct for arbitrary errors in any one of the nine qubits.

The principle behind quantum error correction is somewhat counterintuitive: it involves entangling the qubit with additional qubits to form a more robust quantum state that can be monitored and corrected without directly measuring the quantum information, thus avoiding the collapse of the quantum state.

In practice, quantum error correction is a complex and resource-intensive process. It requires a significant overhead of additional qubits and sophisticated algorithms to detect and correct errors. Despite these challenges, quantum error correction is fundamental to the development of scalable and reliable quantum computers. Without it, the errors in quantum calculations would accumulate rapidly, rendering the results meaningless. The ongoing research in this field is not only deepening our understanding of quantum mechanics but also paving the way for the practical realization of quantum computing.

Quantum computers can be categorized primarily into three types: gate-based quantum computers, quantum annealers, and topological quantum computers. Gate-based quantum computers, which are the most similar to classical computers, operate using quantum logic gates to manipulate qubits. These systems, like those developed by IBM and Google, have demonstrated significant milestones, such as Google’s claim of achieving quantum supremacy in 2019 (Arute et al., 2019). Quantum annealers, on the other hand, are designed for solving optimization problems by naturally finding the lowest energy state of a system.

D-Wave Systems has been a pioneer in this field, focusing on specific computational tasks (Johnson et al., 2011). The third type, topological quantum computers, still largely theoretical, propose to use anyons, particles that are not limited to the standard fermion-boson classification, to encode information. This approach is predicted to offer greater fault tolerance, a significant challenge in quantum computing (Nayak et al., 2008).

In practice, quantum computers are not just faster versions of classical computers but are suited for particular types of problems like quantum simulations, optimization, and factoring large numbers, which have implications in cryptography. The development of quantum algorithms, such as Shor’s algorithm for factoring and Grover’s algorithm for database searching, has highlighted the potential of quantum computing to solve problems that are currently intractable for classical computers (Shor, 1997; Grover, 1996). However, challenges such as qubit coherence, error correction, and scalability remain significant hurdles.

As research progresses, the integration of quantum computing into practical applications will depend on overcoming these technical challenges and developing new algorithms tailored to the quantum paradigm.

The use cases for quantum computers are huge. And whilst there perhaps isn’t any clear agreement over quantum advantage, there are plenty of potential use cases that are being explored (just read our site). Too numerous to list, but here are just a few examples.

Quantum Simulation

The practical realization of quantum simulation involves encoding the problem into a quantum system, where qubits represent different states or particles of the simulated system. This encoding exploits the properties of superposition and entanglement, quintessential to quantum mechanics. For instance, Lloyd (1996) demonstrated how quantum algorithms could efficiently simulate the dynamics of quantum systems, a task that grows exponentially harder for classical computers as the system size increases.

The potential applications of quantum simulation are vast, ranging from understanding complex chemical reactions for drug discovery to unraveling mysteries in high-energy physics and materials science. As Georgescu et al. (2014) noted, the ability to simulate complex quantum systems could lead to breakthroughs in designing new materials and understanding biological processes at a molecular level. However, the field is not without its challenges. Current quantum computers, often referred to as Noisy Intermediate-Scale Quantum (NISQ) devices, are limited by errors and decoherence, which affect the accuracy of simulations.

For instance, Lloyd (1996) demonstrated how quantum algorithms could efficiently simulate the dynamics of quantum systems, a task that grows exponentially harder for classical computers as the system size increases. The potential applications of quantum simulation are vast, ranging from understanding complex chemical reactions for drug discovery to unraveling mysteries in high-energy physics and materials science. As Georgescu et al. (2014) noted, the ability to simulate complex quantum systems could lead to breakthroughs in designing new materials and understanding biological processes at a molecular level.

Quantum Machine Learning

The term ‘quantum machine learning’ itself is a blend of ‘quantum computing’, which leverages the principles of quantum mechanics to process information, and ‘machine learning’, a subset of artificial intelligence focused on the development of algorithms that can learn from and make predictions on data.

Quantum Companies such as Xanadu are exploring how to utilize QML and have created a framework and toolset to help developers explore Quantum Machine Learning, named: PennyLane.

Quantum Optimization

Optimization problems, which involve finding the best solution from all feasible solutions, are ubiquitous in various industries, from logistics and finance to drug discovery and machine learning. Classical computers can struggle with these problems, especially when the solution space grows exponentially with the problem size. Quantum computers, however, are theoretically capable of navigating these vast solution spaces more efficiently.

This capability is largely attributed to quantum algorithms like Grover’s algorithm, which offers a quadratic speedup in searching unsorted databases (Grover, 1996). Another notable contribution is from the Quantum Approximate Optimization Algorithm (QAOA), developed by Farhi et al., which is designed for solving combinatorial optimization problems and has shown promise in outperforming classical algorithms in certain instances (Farhi et al., 2014). Companies are busy exploring how to exploit Optimization.

Quantum computers are particularly adept at solving certain types of problems that are intractable for classical computers. For instance, they hold immense potential in factoring large numbers, a task central to cryptography. Shor’s algorithm, proposed by mathematician Peter Shor in 1994, demonstrated that a quantum computer could factor numbers exponentially faster than the best-known algorithms on classical computers. This has profound implications for security and encryption. Furthermore, quantum computers are uniquely suited for simulating molecular and atomic interactions, offering new vistas in drug discovery and materials science. As Nobel laureate Richard Feynman noted, “Nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical.”

Quantum computers excel in areas where classical computers struggle. One notable example is integer factorization, which is crucial in cryptography. Shor’s algorithm, proposed by Peter Shor in 1994, demonstrated that quantum computers could factor large numbers exponentially faster than the best-known algorithms on classical computers (Shor, 1994). This has profound implications for data security. Another area is the simulation of quantum systems.

We have more details on how to start your journey into quantum computing, but below is a quick guide.

Educational Foundation in Quantum Mechanics

Begin with a solid foundation in quantum mechanics and linear algebra. These subjects are crucial for understanding how quantum computers work. Resources like MIT’s Quantum Computation lectures or IBM’s Quantum Computing course can be invaluable.

Quantum Programming Skills

Develop programming skills, particularly in languages used in quantum computing like Python. Python is widely used due to its simplicity and the availability of quantum computing libraries like Qiskit (developed by IBM) and Cirq (developed by Google).

Hands-On Experience

Engage with quantum computing platforms. Many companies, including IBM and Google, offer cloud-based quantum computing services that provide access to real quantum computers or simulators. This hands-on experience is vital for understanding the practical aspects of quantum computing.

Community Involvement

Participate in the quantum computing community. Join forums, attend conferences, and collaborate with others in the field. This community involvement is crucial for staying updated on the rapidly evolving landscape of quantum computing.

Perhaps a moot point because most quantum computers are accessed via the cloud, there is little need to buy one or own one. You can simply use time on the device and access it via the cloud. QCaaS – or Quantum Computing as a service means developers can build a quantum circuit on their browser and simply run on quantum hardware.

If you want you can buy a quantum computer today from SpinQ or Rigetti, but we’d question why you would need to.

SpinQ will sell you a desktop machine with just two Qubits for around $5,000. But for more research-oriented consumers you’ll need to dig deeper, with Rigetti’s costing $900,000 sporting 9 qubits.

To a certain degree, quantum computers are already mainstream. Unlike the behemoth computers of the past such as Mainframes, just about anyone can access a quantum computer from a computer browser. So in that regard, Quantum Computers are already here and being used by millions of people.

IBM has published that they have seen IBM Quantum Hit the Milestone of 3 Trillion Circuits Run. The IBM Quantum Computer has gone through several incarnations since its inception in 2017.

• Peter Shor – Currently at MIT, Shor revolutionized quantum computing with his algorithm for factoring integers, impacting the field of cryptography.
• David Deutsch – A physicist at Oxford University, Deutsch is a pioneer in the field, having developed the concept of a universal quantum computer.
• Seth Lloyd – At MIT, Lloyd proposed the first feasible design for a quantum computer, contributing significantly to its theoretical foundation.
• John Preskill – A theoretical physicist at Caltech, Preskill has made substantial contributions to quantum information theory and coined the term “quantum supremacy.”
• Charles Bennett – A physicist at IBM, Bennett’s work in quantum information theory, especially quantum teleportation, has been foundational.
• Gilles Brassard – A computer scientist at the University of Montreal, Brassard co-developed the BB84 quantum cryptography protocol.
• Lov Grover – Known for the Grover’s algorithm, he is a prominent figure in quantum computing at Bell Labs.
• Scott Aaronson – A theoretical computer scientist, Aaronson is known for his work on quantum computational complexity and is currently at the University of Texas at Austin.
• Artur Ekert – A professor at the University of Oxford, Ekert has made significant contributions to quantum cryptography.
• Ike Chuang – A physicist and electrical engineer, Chuang is known for his work in the experimental realization of quantum computing.

• Andrew Steane – A physicist at Oxford, Steane developed important quantum error correction codes.
• Raymond Laflamme – At the University of Waterloo, Laflamme’s work focuses on quantum error correction and quantum algorithms.
• John Martinis – A physicist who has significantly advanced the development of superconducting qubits.
• Michelle Simmons – At the University of New South Wales, Simmons is recognized for her work in quantum computing and atomic electronics.
• Leo Kouwenhoven – Known for his work on Majorana fermions, Kouwenhoven’s research has implications for topological quantum computing.
• Robert Schoelkopf – A physicist at Yale, Schoelkopf has been instrumental in the development of superconducting qubits.
• Lene Hau – A physicist at Harvard, Hau is known for her groundbreaking work in slowing down light, with potential applications in quantum computing.
• Krysta Svore – A leading researcher at Microsoft, Svore’s work focuses on quantum algorithm design and the development of quantum software.
• Monika Schleier-Smith – At Stanford University, Schleier-Smith’s research in quantum optics and quantum information science is paving new paths in the field.
• Jay Gambetta – A physicist at IBM, Gambetta is known for his work in quantum information processing and quantum computing systems.

There are thousands, literally thousands. Keeping up with them can be a challenge. There is a huge list over at Mega List of Quantum Companies. You’ll find companies such as IBM, Google, and Microsoft are all pursuing Quantum strategies and developing quantum computers.

We have covered a variety of companies across the globe including 20 companies in the UK. But of course, there are thousands around the globe with new ones emerging every day from stealth.

No.

This is a common misconception. Quantum Computers can only do certain tasks more efficiently than classical computers.

Researchers think that certain quantum algorithms perform faster than classical ones. But Only certain ones such as Shor or Grover. There is a Quantum Zoo of Quantum Algorithms.

Quantum computing, often perceived as a concept bordering on science fiction, is a rapidly evolving field grounded in well-established physical principles. The term ‘quantum computer’ refers to a device that utilizes the principles of quantum mechanics to process information.

Quantum computers are not merely theoretical constructs but are being actively developed and refined. Companies like IBM and Google have made substantial progress in this field. Google’s quantum computer, Sycamore, famously achieved ‘quantum supremacy’ in 2019 by performing a specific task in 200 seconds that would take a state-of-the-art supercomputer approximately 10,000 years to complete.

The potential of quantum computing to revolutionize fields like cryptography, material science, and complex system simulation is immense, but the path to realizing these applications is fraught with scientific and engineering challenges.

Just like any nascent industry, there is plenty of hype around. Do check the claims of companies and always put any achievements in context.

In the face of “quantum hype,” it is crucial to maintain a balance between optimism and realism.