22688 - SCTE Various - Quantum Lecture Insert v1 PRESS Alt

An Introduction to Quantum Computing A guide for general reading, technicians and engineers. From familiar electrical principles to qubits, quantum gates and real quantum processors.

By Dave Hodges, HFSCTE, HFCAI and Dr Anthony Basham, FSCTE

October 2026

An Introduction to Quantum Computing

An Introduction to Quantum Computing ____________________________________________________________________________________ A guide for general reading, technicians and engineers. From familiar electrical principles to qubits, quantum gates and real quantum processors. Introduction

Quantum computing remains in its early stages and is developing at an extremely rapid pace.

_______________________________________________________________________________________________ SCTE Technical Committee : Dave Hodges and Dr Anthony Basham. © 2026 Society for Broadband Professionals. All rights reserved Page 1 The components of quantum systems exhibit wave-like behaviour, which poses a fundamental challenge to classical physics concepts. Take electrons as an example: they can only be detected as discrete, point-like particles at a single unique location in space, but before an accurate measurement is performed, all their possible paths and the behaviours along these paths can be mathematically described by a spread-out wave function that can produce constructive or destructive interference just like a wave. The same holds true for photons: when they strike a sensor, they only generate independent, highly localised single-particle detection events, yet they can also display wave-like characteristics of light beams such as interference and diffraction. This combination of seemingly contradictory properties is known as wave-particle duality. From the Everyday World to the Quantum World At the macroscopic scale that humans encounter in daily life, the well-established framework of classical physics can describe the physical world around with high precision and stability. Electricians can smoothly apply Ohm’s law and Kirchhoff’s laws, and even more comprehensive electromagnetic theories and circuit analysis tools to carry out their work. This fact confirms that the macroscopic behaviour of circuits has clear certainty and predictability. Under this framework, voltage can be measured as a unique value by standard instruments, current can be calculated with mathematical precision, and the total energy of a capacitor or inductor can also be uniquely linked to these two types of physical quantities. However, once we enter the microscopic scale made up of individual atoms, subatomic electrons, and fundamental photons, the everyday intuition of classical physics can no longer explain the observed physical reality. Only the advanced mathematical framework that accompanies quantum mechanics is the suitable tool for this scale. A fundamental feature of quantum mechanics is that certain physical quantities, such as the energy of an electron bound within an atom, can take only specific allowed values. This is known as quantisation. However, not every physical quantity is restricted to discrete values; some quantum observables can have continuous ranges. This is the so-called quantisation, meaning that the related variables can only change incrementally by specific discrete units. This introductory text on quantum computing is by no means complete in covering the entirety of quantum mechanics. It has three core goals: first, to clarify why the operating mechanism of quantum computing is fundamentally different from that of conventional digital computers; second, to explain how basic quantum bits are physically realised; third, to interpret how digital computer systems communicate with complex quantum processors, exert control over them, and reliably read their output data. Classical digital computers store and process all information in a uniform, orderly manner, and all content is encoded into discrete, mutually exclusive binary values of 0 and 1. In contrast, the quantum state in a quantum computer exists as a wave function, whose amplitude and phase carry fundamental continuous properties. This wave function can also form complex multi-particle correlations that spans across space, time, and momentum, and it is highly manipulable. Before the fragile quantum state is disrupted, a series of carefully designed coordinated operations are carried out in sequence. Only when a measurement is performed does the quantum state collapse, and the output reverts to standard digital information. Quantum computers are not simply more powerful processors whose computing speed is several orders of magnitude faster than classical digital computers, but Quantum computing is an entirely distinct type of information processing, and its computational value only applies to specific scenarios. Only by customising the computing process for specific problems and leveraging the unique, counterintuitive rules of quantum mechanics can a quantum computer fulfil its potential.

An Introduction to Quantum Computing

An Introduction to Quantum Computing ____________________________________________________________________________________

Beyond the basic principles of quantum mechanics, this introduction identifies three core, quantum concepts that are critical to the field of quantum computing. The first is the superposition principle: any quantum system can exist in multiple allowed quantum states simultaneously. The second is the interference property of superposition states: superposition components with different phases can undergo quantum interference, rather than simply adding up like ordinary non-interfering signals. The third is quantum entanglement: multiple independent quantum systems can become entangled, which means they can only be described by a unified overall state, and the independent state of each subsystem cannot be separated out. In addition, physical measurement will irreversibly collapse a probabilistic multi-dimensional quantum state into a one-dimensional digital description, outputting a single identifiable result. The core nature of quantum computing is precisely to control and uses these special quantum effects, rather than only passively observing their natural occurrence.

The Atom, the Electron and Discrete Energy

The basic composite structure of an atom consists of a dense, positively charged atomic nucleus which contains protons and neutrons inside and negatively charged electrons distributed in areas around the nucleus. The core force that sustains this structure is electrostatic attraction. It is this strong electrostatic pull that allows electrons, which have extremely small masses, to remain bound to the central nucleus whose mass is far larger than their own. We first acknowledge that universal gravitation does act on this atomic-scale system There was a view that the movement of electrons around an atomic nucleus compared to the orbital motion of planets revolving around the Sun in the solar system. This view is far from the truth about the quantum mechanical nature of atomic behaviour. Negatively charged electrons do not orbit the nucleus along fixed, tiny paths. Instead, they must be described by a complex mathematical concept called the wave function. This function can be used to accurately calculate the specific probability of each measurable physical quantity of an electron. The so-called atomic "orbital" that is often mentioned in academic circles is a three-dimensional probability distribution of electrons, and it is never a fixed trajectory like that of a planet. The electron is a fundamental particle inside an atom and can only occupy a very small number of strictly limited, specific energy states and this is completely different from the law that energy can take continuous values in the macroscopic world. Electrons bound by an atomic nucleus cannot possess arbitrary or continuous bound-state energies at all. An electron can transition between allowed energy states through interactions that transfer the required energy. For example, an atom may absorb a photon whose energy matches the difference between two allowed levels. An excited atom may subsequently release energy through photon emission or other physical processes. This fundamental correlation between discrete energy levels and precise quantum transitions is exactly the core theoretical foundation that can be reused in the advanced design and implementation of contemporary quantum computing hardware.

An Introduction to Quantum Computing

An Introduction to Quantum Computing ____________________________________________________________________________________

_______________________________________________________________________________________________ SCTE Technical Committee : Dave Hodges and Dr Anthony Basham. © 2026 Society for Broadband Professionals. All rights reserved Page 3 The labels "spin-up" and "spin-down", which appear to belong to a binary classification, are by no means merely two mutually exclusive classical tags that can only act as static counters. However, during the unmodified, unrecorded early phase before the irreversible process of measurement-induced wavefunction collapse occurs, an electron can be arranged in a quantum superposition that incorporates both basis states. This state corresponds to both spin types, combining to produce a complex number that represents both possibilities simultaneously. This quantum property allows electrons to exist in physical states defined by distinct probability amplitudes and the precise relative phase Electron Spin Beyond the familiar basic properties such as electric charge, kinetic energy, and potential energy, electrons possess an intrinsic, purely quantum-mechanical trait called "spin.". This strictly microscopic phenomenon is exclusive to quantum mechanics, and there is no accurate, direct, and intuitively perceptible counterpart for it in classical physics. When a measurement is conducted on the electron's intrinsic spin the physical record will only produce two mutually exclusive outcomes, which are referred to as spin-up and spin-down. This intrinsic property of the electron's angular momentum is bound to a related electromagnetic moment, which exhibits net dipole-like behaviour under the action of an external magnetic field. Therefore, we can synthesise precisely tuned external electromagnetic radiation to control the spin state and complete the measurement. The two distinguishable spin states of an electron, conventionally labelled spin-up and spin-down along a selected measurement axis, can serve as the computational basis states of a spin qubit. Appropriate electromagnetic control and measurement techniques allow quantum information to be prepared, manipulated and read out. Figure 1. Discrete energy levels and resonant transitions. Electrons are restricted to specific quantum energy levels within an atom. They can only move between these levels by the atom interaction in a way that allows a change in the quantum state by absorbing or emitting a photon whose energy exactly equals the difference between the two levels. This quantised behaviour produces the characteristic spectral lines of each element and forms one of the fundamental principles of quantum mechanics. The resonance phenomenon can be used to understand abstract quantum systems. A resonance system has a natural frequency and will produce a stronger response to an external input that matches this frequency. Quantum systems follow rules like those of harmonic oscillators: they have strictly defined energy level differences, which correspond to precise transition frequencies. This analogy is not completely rigorous, as the fundamental physical laws that underpin the two types of resonance differ. Even so, the similarity between the two still effectively explains why precisely controlled microwave or light energy can selectively excite a quantum system from one energy level to another.

An Introduction to Quantum Computing

An Introduction to Quantum Computing ____________________________________________________________________________________ between the two superposed states. This multi-dimensional mathematical complexity gives electron spin a unique, extremely high value for the advanced processing and manipulation of quantum information, with application potential that far outstrips the rigid limitations of traditional digital data storage systems that rely on a strict binary framework.

Photons as Quantum Carriers

Photons are fundamental particles of electromagnetic energy, and they are the smallest quantum indivisible unit. Their core fundamental property is that they carry no electric charge, carry energy and momentum and have no rest mass at all, the latter is a physical characteristic that makes them highly unique. Photons are quanta of electromagnetic radiation. Their energy is related to frequency by \(E=hf\), and their polarisation provides an additional degree of freedom that can be used to encode quantum information. Together, these properties explain the differences in how electromagnetic radiation of different frequencies interacts with matter. The core reason for these differences is that the vibration frequency of a photon has a strict, directly proportional mathematical relationship to its intrinsic energy. Polarisation is a core resource that combines high performance and high flexibility. As a fundamental component, it underpins the operation of optical and quantum systems. One set of orthogonal polarisation states forms the basis for building functional optical systems, while the other set is designated as the two basic states of photonic quantum bits. Relying on the complex superposition states of these two sets of basic states, a wide range of more complex quantum states can be accurately described. Thanks to their unique ability to propagate in a near-vacuum-like manner in free space and thin optical fibres, photons have become a highly promising technological carrier. They not only support long-distance quantum communication but also transmit fragile quantum information between geographically separated units of large-scale integrated systems. Although photons possess excellent properties suitable for quantum computing, major obstacles must still be overcome to use them as the core computing medium: under ordinary physical conditions, the interaction between photons is extremely weak. To achieve reliable quantum logic operations, three categories of technologies must be relied on. These are elaborately designed optical interactions, advanced measurement schemes, and precision interfaces that can connect to solid-state quantum bits. Based on these properties, photons are currently used as high-speed carriers for transmitting quantum data. For scenarios requiring long-term storage and strong local interactions, other quantum physical technologies must be adopted. Everything from a digital bit to a qubit The foundation of general-purpose computers’ ability to process all types of information is that all their computing logic is executed using a binary unit called a "bit". Each independent bit can only exist in one of two completely mutually exclusive discrete states, which are the logical values 0 or 1. These two logical states can be fully realised through physical hardware, for example via different voltage levels, stable steady charge states, the positive or negative polarity of magnetism, or any stable and easily detectable physical phenomenon. To prevent confusion between identifying 0 and 1 caused by random environmental noise or system disturbances, hardware engineers deliberately set a sufficiently large clear gap between the two inherent physical states to guarantee the accuracy of logical state identification.

An Introduction to Quantum Computing

An Introduction to Quantum Computing ____________________________________________________________________________________

Figure 2. Classical bit versus qubit: discrete logic states compared with a coherent quantum state.

Like the classical digital computer bits introduced earlier in this text, a qubit also has only two optimal reference states. Their standard written form is |0 ⟩ and |1 ⟩ , which are pronounced "ket zero" and "ket one" in speech. This set of symbols originates from Dirac notation, which is universally used across all subfields of quantum mechanics which is the mathematical notation for linear algebra and linear operators on complex vector spaces together with their dual spaces both in the finite- and infinite-dimensional. The core difference between classical information and quantum information is that a qubit can exist in a coherent quantum superposition of these two basis states. |ψ ⟩ = α|0 ⟩ + β|1 ⟩ In the simple equation above, there exist two mathematically complex probability amplitudes, α and β. The coefficients α and β are complex probability amplitudes. Their squared magnitudes determine the probabilities of measuring the computational basis states 0 and 1, while their relative phase influences how the quantum state evolves and interferes under subsequent quantum operations.

|α|² + |β|² = 1

This strict condition, known as the normalisation condition, is derived entirely from the probabilistic interpretation of quantum bits. Measurement on this fragile quantum bit that is in the computational basis, the sum of the total probabilities of measuring 0 or 1 must equal 100%. Specifically, the mathematical expression for the probability of measuring logical 0 is | α|², and the probability of measuring logical 1 is strictly defined as | β|². The quantum properties of a quantum bit disappear the moment it interacts with an external measurement device. Its coherent quantum state will inevitably collapse into a single digital discrete outcome of either 0 or 1. The unique computing power of quantum bits does not come from the final measured reading at all. Its core potential arises entirely from the fact that before that irreversible measurement takes place, a systematically performed series of complex, interconnected transformation operations on its probability amplitudes and its fragile relative phases, can be conducted with precision.

Superposition: More Than an Unknown Bit

An Introduction to Quantum Computing

An Introduction to Quantum Computing ____________________________________________________________________________________ observation capabilities to capture this information. Therefore, true quantum superposition is by no means a collection of classical information that merely waits to be revealed; the two have a fundamental difference. To formally demonstrate this core difference, a mathematical method to construct an instance of a qubit can be used in a specific state to create an illustration. |ψ ⟩ = (|0 ⟩ + |1 ⟩ ) / √2 A measurement on this quantum system, if the measurement is restricted to output only one value and uses the standard computational basis, the empirical probability of observing the measurement value 0 is exactly 50%. Similarly, the empirical probability of observing the measurement value 1, derived through calculation, yields the same result: 50%. However, before the measurement occurs, that is, before this irreversible action that locks the observer into one of the two states takes place the unmeasured quantum system exists in a well-defined superposition of the two fundamental basis states. This inherent coherence is critically important: the precise relative phase between individual quantum components can alter and affect all operations performed on the system or its ensemble, ultimately leading to entirely different experimental outcomes. The mechanical mechanism of quantum entanglement is complex. The definition of an isolated quantum bit is that it possesses a precise quantum state, with specific, entangled probability amplitudes for the two computational basis states |0 ⟩ and |1 ⟩ . To conduct research on the unique wave interference properties of quantum mechanics, it is essential to clarify the subtle but critical difference between these two descriptions. Amplitude, Phase and Quantum Interference A familiarity with basic principles of waves such as amplitude and phase can serve as an intuitive bridge for entering the field of quantum computing. A classical physics scenario when two sine signals are superimposed, if their phases are aligned, the overlapping of peaks and troughs will produce constructive interference, which greatly amplifies the output signal; if the phase difference between the two signals is 180 degrees, the signals will cancel each other out, resulting in destructive interference. Although the rigorous mathematical basis of quantum interference differs in detail from that of classical wave mechanics, the core physical importance of relative phase is almost identical in both scenarios. These are shown in figures 3 and 4.

Figure 3. Constructive interference: relative phase changes the combined result.

An Introduction to Quantum Computing

An Introduction to Quantum Computing ____________________________________________________________________________________

Two independent quantum states of quantum superposition show this concept as an example for illustration: | + ⟩ = |0 ⟩ + |1 ⟩ / √ 2; |− ⟩ = |0 ⟩ − |1 ⟩ / √ 2 If these two states are immediately measured under the standard 0/1 computational basis vectors, both will produce an even 50/50 probability distribution of outcomes, with identical chances of being measured as 0 or 1. However, despite their equivalent statistical performance in immediate measurements, these two quantum states are not identical. They have a significant difference in the relative phase between their components. If an extra quantum logic gate is added to the system before the final measurement, this phase difference will become critical: it will cause the complex probability amplitudes to interact in completely distinct ways, such that one measurement outcome is greatly strengthened, while the probability of the other outcome is systematically suppressed, or even completely eliminated. T he direct effect of quantum interference is the core premise that allows all modern quantum algorithms to be properly constructed and successfully executed. Q uantum algorithms should be a carefully design ed combinations of phases and amplitudes throughout the entire process. This causes the complex probability amplitudes tied to correct outputs to undergo constructive interference and amplify one another, while the amplitudes tied to incorrect outcomes undergo destructive interference and are suppressed to nearly zero. All computational work is completed within the quantum state that evolves internally in the system before the final measurement, and the actual results are only presented at the end of the process.

Figure 4. Constructive interference: relative phase changes the combined result

_______________________________________________________________________________________________ SCTE Technical Committee : Dave Hodges and Dr Anthony Basham. © 2026 Society for Broadband Professionals. All rights reserved Page 7 The Bloch Sphere: A Picture of One Qubit The quantum state of a single isolated qubit can be mapped onto a three - dimensional geometric model called the Bloch sphere (Figure 5). The north pole of this sphere corresponds to the qubit's ground state |0 ⟩ , while the south pole corresponds to the other ground state |1 ⟩ . The surface of the Bloch sphere represents the continuous set of possible

An Introduction to Quantum Computing

An Introduction to Quantum Computing ____________________________________________________________________________________ pure states of a single qubit, with each point defined by two angular coordinates, θ and φ. The north and south poles represent the computational basis states \(|0\ θ \) and \(|1\ φ \ ). This concrete geometric mapping not only renders obscure quantum concepts accessible to general understanding, but also fully preserves the rigor of the professional core of the theory.

Figure 5. The Bloch sphere provides a geometric representation of a single-qubit state.

A single qubit state | ψ ⟩ = cos( θ/2)|0 ⟩ + e^{i φ} sin( θ/2)|1 ⟩ (qubit in the vector space of the Bloch sphere) Nearly all fundamental operations acting on a single qubit can be visually represented as continuous rotations within the spheres geometric space. For this reason, the external control pulses used in quantum computing do not suddenly "set a bit" in a rigid, either-or fashion, as is the case in digital computing. Single-qubit gates can be visualised as rotations of the quantum state on the Bloch sphere. In many physical implementations, these rotations are controlled through carefully calibrated electromagnetic pulses. The amplitude, phase and duration of a pulse d etermines the rotation axis and angle. For example, a Pauli -X operation corresponds to a rotation of 180 degrees about the X- axis, up to an overall phase. The application of continuous rotations to move the quantum state repeatedly by small angles along carefully selected axes. This adjusts the state's subtle superposition, and the entire process takes place within the fully abstract space of the Bloch sphere. Leveraging this rotational property can establish direct, highly predictable mathematical links between the physical properties of an applied microwave control pulses which is amplitude, phase, total duration and the specific quantum logic operations that the system performs. The Bloch sphere serves as a simple, conceptual bridge that connects complex quantum control mechanics with well - known classical -domain phenomena, including three-dimensional vector rotation, wave phase dynamics, and the physical principles behind resonant excitation.

Quantum Gates

An Introduction to Quantum Computing

An Introduction to Quantum Computing ____________________________________________________________________________________ All conventional digital computers are built on basic logical operations such as AND, OR, XOR, and NOT. Modern digital technologies have always followed a strict set of operating rules, but the operating logic of quantum computers is completely different. It centres on special units called quantum gates: from a mathematical perspective, these gates are high-strength transformations applied to the core quantum properties of a system; from a physical perspective, they exist in reality as either ultra-precision regulatory additional devices or fields applied to each target node, or functional units realised through electromagnetic induction trigger pathways. The simplest fundamental quantum operation in quantum computing is the Pauli-X gate. Its core function closely matches that of the NOT gate in digital computing, as it can accurately flip the quantum ground states |0 ⟩ and |1 ⟩ . The time evolution of this operation can be visualised on the Bloch sphere, where it corresponds to a 180-degree rotation around the X-axis. At the same time, this gate has the property of being self-inverse in that applying it twice consecutively will return the affected qubit completely back to its initial state. In this complex quantum computing architecture, the Hadamard gate is another core and widely used operation, with the traditional notation H. When this logic gate is directly applied to the fundamental basis state |0 ⟩ , it generates a superposition state where the weights of all possible outcomes are fully equal, with the corresponding mathematical expression as follows: H|0 ⟩ = (|0 ⟩ + |1 ⟩ ) / √2 If the gate is applied to the other alternative basis state |1 ⟩ , it also produces an evenly weighted superposition state, with the only key difference being the relative phase between its components. These unique transformation properties are why the Hadamard gate is often placed at the start of complex quantum circuits, acting as a "wavemaker" to generate large-scale superposition states. It is also reused in the resonance phase later in the process, to accurately convert hidden phase information into measurable probability differences. The most core requirement for a quantum gate is that it must stably maintain the precise mathematical structure and inherent laws of quantum mechanics. All transformations of an isolated, closed quantum system are fully reversible, which is fundamentally different from most standard digital logic operations. Digital operations often permanently discard key information. For this reason, sequences of quantum gates are arranged around reversible operations, and the result is read out through a single irreversible measurement.

Multiple Qubits and Exponential State Space

_______________________________________________________________________________________________ SCTE Technical Committee : Dave Hodges and Dr Anthony Basham. © 2026 Society for Broadband Professionals. All rights reserved Page 9 While quantum gates do carry out operations by applying coherent transformations to the overall quantum state, mathematically advancing the quantum state as a complete function in a synchronous manner, the subsequent measurement process never outputs a full list of all hidden complex amplitudes. The collapse of a quantum system is a fundamental physical process that returns to digital reality, producing only one single, definite, objective outcome. For this reason, an efficient quantum algorithm must arrange its internal quantum states precisely and manipulate If quantum entanglement or quantum state superposition exists in a collection of quantum systems, the synthetic mathematical state space that can be assigned to this collection will expand rapidly. A single isolated qubit only has two independent basis states, |0 ⟩ and |1 ⟩ . When a second qubit is added, the two-qubit system has four basis states: |00 ⟩ , |01 ⟩ , |10 ⟩ , and |11 ⟩ . When extended to three qubits, the number of basis states increases to eight. Following this logic, to accurately describe any pure quantum state of a system composed of n qubits, at least 2ⁿ independent complex amplitudes are always required to fully characterise the state. Even a small 10- qubit system requires exactly 1024 complex amplitudes; a fully functional 20 -qubit system needs more than one million (1.048 million) complex amplitudes; and a usable functional state of just 50 qubits, demands approximately 1.13 quadrillion independent complex amplitudes. This exponential scaling makes direct state-vector simulation increasingly demanding for classical computers. However, the difficulty of classical simulation depends on the structure of the quantum state and operations involved, and some restricted classes of quantum systems can still be simulated efficiently.

An Introduction to Quantum Computing

An Introduction to Quantum Computing ____________________________________________________________________________________ them carefully, to ensure that the final required physical quantities can be stably reproduced from the statistical distribution of measurement results. The larger technical and theoretical barriers may not lie in building a physical system with an extremely large state space. The challenge is to maintain effective control over this high-dimensional state space with extremely high precision. The core goal is to protect inherently fragile physical effects such as quantum interference and quantum entanglement, so that they can meet the requirements needed to achieve real, usable, and implementable quantum computational advantage. Quantum Entanglement Quantum entanglement is the phenomenon in which the quantum state of each particle in a group cannot be described independently of the state of the others, even when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical physics and quantum physics. These entangled particles must be described as a single unified whole. It is not only a unique core feature of modern quantum mechanics, but also a key computational resource that quantum algorithms can leverage. For example, the mathematically expressed standard form of a maximally entangled two-qubit state: |Φ + ⟩ = |00⟩ +|11⟩ √2 When both qubits are measured in the computational basis, the outcomes 00 and 11 each occur with a probability of 50% in the ideal case. The individual outcomes are random, but their correlation reflects the entangled nature of the joint quantum state.

Figure 6. A Hadamard gate followed by CNOT creates a standard entangled Bell pair.

An Introduction to Quantum Computing

An Introduction to Quantum Computing ____________________________________________________________________________________ Quantum entanglement produces extremely strong statistical correlations that no digital hidden variable model can replicate, and at the same time, it cannot carry any usable active information to achieve faster-than-light transmission. From the specific perspective of applied quantum computing, the role of quantum entanglement is critically important: it allows all information encoded in a large multi-qubit register to dynamically exist in complex non-local dependencies between the states of correlated qubits that are far apart, rather than being confined only to isolated individual qubits. This collective information processing capability is the core foundation required to implement computing algorithms, quantum simulation, and quantum error correction protocols.

How Entanglement Can Be Created.

_______________________________________________________________________________________________ SCTE Technical Committee : Dave Hodges and Dr Anthony Basham. © 2026 Society for Broadband Professionals. All rights reserved Page 11 A qubit is a state, not a specific component. There is no single thing that can be unambiguously referred to as "the qubit". A qubit is never a single piece of hardware; it is fundamentally defined as a two-level quantum information system, which can only be physically implemented and realised by relying on a controllable physical degree of freedom within a larger system. Building on this foundation, competing technical architectures can have completely different physical systems as their basic building blocks. The primary reason for this is that each technical approach has a unique, precise trade-off space across five key properties. These are the level of control precision, the length of quantum coherence time, the level of interconnectivity between different qubits, the complexity of large-scale manufacturing, and the environmental requirements for physical operation. This concept is the core idea, and it can be demonstrated by a simple, quantum circuit equipped with only two basic logic gates. To start the preparation process, several qubits need to be prepared, only two are needed as a starting point. Carefully initialising them to the most basic unentangled reference state, mathematically denoted as the |00 ⟩ state. After completing this first phase of the preparation process, the corresponding quantum operation should be performed on the target qubit, which is the first physical working qubit to apply to a Hadamard gate. Once this operation is finished, the first qubit immediately enters an equal-weight superposition of all possible states. At the same time, the second qubit remains completely unaffected and stays in its original |0 ⟩ state. As a result, the joint quantum state of these two systems evolves accordingly and can be precisely described by a clear mathematical expression. (|00 ⟩ + |10 ⟩ ) / √2 Next, the conditional two-qubit operation should be introduced and that must be implemented in the next step of the quantum computing workflow the controlled-NOT gate (CNOT). The first qubit specified in the previous text can be designated as the control qubit, and the following second qubit as the target qubit. The operating logic of this operation changes based on the value of the control qubit. If the control qubit’s value is 0, no operation is executed on the target qubit, and it maintains its original state at all times; if the control qubit’s value is 1, the quantum state of the target qubit undergoes a fundamental flip. Additionally, because the control qubit can simultaneously hold two potential values and exists in a fragile superposition state, executing this operation for one possible state directly affects the other. Therefore, the mathematical methods must be used to describe the combined state of all possible scenarios. (|00 ⟩ + |11 ⟩ ) / √2 It is at this precise juncture during the quantum operation process that it can be said the two qubits are entangled and must be described by a joint quantum state. This entanglement is not necessarily permanent; subsequent quantum operations can modify or remove it. The qubits remain physically distinct systems, even while sharing an entangled state. It must be recognised that what exhibits this deep level of entanglement is entirely the abstract quantum state itself. The physical devices that carry these qubits never merge at the physical level, nor are they permanently connected. In fact, in many practical implementation scenarios, almost immediately after this highly unusual quantum entanglement is established, these physical devices can be separated by billions of kilometres in principle.

An Introduction to Quantum Computing

An Introduction to Quantum Computing ____________________________________________________________________________________ Currently, the global quantum computing field has developed a diverse set of experimental and commercialised technological portfolios, covering multiple hardware. These range from superconducting circuits that have entered the pre-commercialisation stage, to semiconductor-substrate isolated electron spin qubits, artificial quantum dots, electromagnetically trapped ions, and neutral atoms that enable high-precision and high-density manipulation. All of these have accumulated years of experimental foundations and further to the cutting-edge, exploratory photonic systems. Regardless of the physical platform chosen, all technologies address the same set of core operational challenges: reliably generating distinguishable quantum ground states, preparing quantum superposition states, executing precision logical operations, coupling or decoupling qubits as needed, protecting quantum states from decoherence, and accurately measuring the final computational results. During the 1920’s and 30’s the basic physical principles and the underlying quantum-mechanical logic of quantum systems had been defined. However, to turn practical, usable devices into a reality, the core engineering challenges standing in the way remain severe in not only to design a scalable, high-efficiency qubit architecture, but more critically, to physically build an integrated, fully functional system. This system must integrate a large number of qubits that can be precisely controlled, incorporate supporting technologies from multiple fields including digital electronic engineering, ultracold cryogenic physics, precision laser optics, and electromagnetic radio frequency control, and also be equipped with dynamic calibration and signal coupling processes that connect, via transduction and feedback, to a digital processing system managed by dedicated software. Quantum Dots and Electron-Spin Qubits Quantum dots are a class of nanostructured semiconductor devices, whose core property is the ability to confine charge carriers within an extremely small spatial volume. This spatial compression generates sharp quantised excitations that can simulate the natural energy levels of atoms. To realise quantum dots, carefully designed architectures and precision manufacturing processes are required. Quantum dots can hold a precisely fixed, artificially selected number of electrons with extremely high accuracy, and the spin of this electron can serve as a natural qubit. Within the operational framework of spin qubits, two orthogonal spins can be selected that can be arranged along any quantisation axis as independent, exclusive logical ground states to support the implementation of complex quantum computing. To realize this architecture, three core types of technology must be integrated. First, a complex gate configuration is used to complete the boundary definition and fine-tuning of the quantum dot operating points; second, a customized external magnetic field combined with broadband microwave frequency control is employed to actively regulate the electron spin state; finally, through a purpose-designed ultra-high-sensitivity measurement structure, fragile quantum spin information is converted into a measurable electrostatic charge signal. The core reason that semiconductor quantum dots have attracted attention from both academic research circles and the industrial sector lies in their unique value. They can not only support the completely new next generation quantum information processing but are also compatible with the mature mass production processes that the digital semiconductor industry has refined and accumulated over decades. However, this integrated development path faces a key challenge: the physical size of quantum dots is extremely small, making them highly vulnerable to interference from the external environment. Many minor variables can destroy the quantum coherence that underpins device performance, including fluctuations in material composition that cannot be detected by standard microscopes, deviations in structural boundaries between material layers, randomly occurring uncontrolled parasitic charge traps, and small variations in the applied voltages used for computational control and voltage shielding. The combination of these outstanding sets of physical properties means that the original concept of nanoscale quantum dots as "artificial atoms" remains a reliable research framework that combines extremely high practicality and precision to this day. Heat-activated atoms naturally possess discrete, quantised energy levels, a feature that matches the properties of all quantum dots. However, the core difference of quantum dots is that their sizes can be nearly perfectly replicated, and the confinement potentials they carry can be regulated with extreme precision through electrical means.

Superconductivity and Cooper Pairs

An Introduction to Quantum Computing

An Introduction to Quantum Computing ____________________________________________________________________________________ Another relevant technical strategy centres on constructing precisely engineered superconducting circuits. The resistance of ordinary metallic conductors is inherently tied to chaotic scattering processes that dissipate energy. But if specific superconducting materials are deliberately cooled to a low temperature below their critical transition temperature, a remarkable change occurs, electrons inside the material strongly couple to form a highly coherent collective quantum state, which allows electric current to flow smoothly and stably with zero direct-current resistance. To start with the core concept of conventional superconductivity to clarify that electrons spontaneously form strongly correlated pairs, namely Cooper pairs. This is a special pairing generated by dynamic interactions. When conditions permit, the atom lattice framework with historical dependence participates in this process, and ultimately many Cooper pairs enter a highly collaborative, deeply coherent superconducting state. This coherence allows quantum behaviours, which were originally restricted to the microscopic scale, to be observed in circuit scenarios that are sufficiently large, constrained by multiple mechanical, and electrical factors, and can be reliably manufactured through standard digital engineering processes. This is precisely the most critical reason why superconductivity has become an indispensable core foundation in the global research and development process of mainstream cutting-edge quantum computing architectures. The Josephson Junction Josephson junctions are the most fundamental and core components in the rapidly developing field of superconducting quantum electronics. Their structure is very simple because they consist of two separate superconducting regions, with only an extremely thin non-conductive insulating layer between them. From the perspective of digital circuit theory, this insulating layer would completely block direct current from passing through the junction. However, from the perspective of quantum mechanics, if the insulating layer is not too thick, bound electron pairs known as Cooper pairs can directly pass through this potential barrier via the quantum tunnelling effect.

Figure 7. Josephson junction and the basic transmon concept.

An Introduction to Quantum Computing

An Introduction to Quantum Computing ____________________________________________________________________________________ an extremely high frequency. These quantum phenomena establish a unique, direct electrical connection between abstract quantum phases and the measurable responses of electronic circuits. In the design of functional quantum computing architectures, intrinsic nonlinearity is a critical core property, if not an essential one. A linear LC resonator studied in a research paper recently has quantum energy levels that are completely flat and uniformly spaced, and the transitions between all adjacent energy levels occur at the same resonant frequency. In principle, it is nearly impossible to precisely and selectively manipulate only the lowest two quantum states; the system will unavoidably be excited to higher, unintended energy levels. In contrast, adding a Josephson junction to an originally linear microwave circuit introduces strong nonlinearity, which creates significant unevenness in the spacing between adjacent energy levels. Leveraging this anharmonicity, can reliably allow selection of two well-isolated energy levels to define the computational ground state |0 ⟩ and first excited state |1 ⟩ following the standard convention. The transmon qubit, see figure 7, is one of the most widely used, mature, and successful quantum architectures in the current field of quantum computing, and all its designs are supported by solid fundamental physical principles. Its core structure combines the nonlinear characteristics of a Josephson junction with a matching capacitor to build a stable quantum circuit. It can have its quantum transitions manipulated using microwave pulses with precisely selected frequency, amplitude, phase, and duration to achieve the controllable rotation of quantum states required for computation. This is an excellent entry point for understanding quantum hardware. It functions like a superconducting resonant circuit with a built-in intentional nonlinear element (the Josephson junction), has calculable quantised energy levels, and can also be precisely controlled via external microwaves. _______________________________________________________________________________________________ SCTE Technical Committee : Dave Hodges and Dr Anthony Basham. © 2026 Society for Broadband Professionals. All rights reserved Page 14 In the scenario of superconducting quantum architectures microwave resonators are core, indispensable components for implementing quantum measurements. A resonator with finely tuned parameters can achieve physical and electromagnetic coupling with the target qubit. The internal state of the qubit will precisely trigger a sensitive change in the resonator’s resonance characteristics that depends solely on the quantum state. The main control system repeatedly sends specific microwave readout pulses to the system, and by analysing the amplitude and phase shift of the returned signal, it can determine whether the qubit is most likely in the ground state |0 ⟩ or the excited state |1 ⟩ . In this way, the original fragile and easily disturbed quantum state is converted, at the interface node connecting the quantum processor and conventional digital electronic devices, into a stable, processable conventional radio frequency measurement problem. Controlling and Detecting Quantum States Quantum computing architecture must complete three core tasks which are accurately initialise qubits to a known starting state, execute computations through precise operations, and perform measurement and readout. The physical methods to achieve these three tasks are entirely tied to the underlying hardware technology adopted. Traditional superconducting qubits rely on complex microwave control schemes and low-loss microwave cavities to carry out the above operations. By contrast, ion trap and neutral atom platforms require ultra-precise, stable laser systems to achieve the same level of control and isolation. For this reason, solid-state spin qubits depend on a complex combination of applied gate voltages, finely tuned magnetic fields, and precisely arranged microwave excitation for active control. On the other hand, photonic quantum systems rely entirely on a series of specialised optical components paired with high-sensitivity single-photon detectors to process and read out encoded quantum data. Starting with the precision spin measurement process, the universal core principle in the field of quantum measurement can be found. Almost all quantum measurements convert the extremely weak, hard-to-observe physical properties at the microscopic level into electrical or optical signals that can be easily obtained at the macroscopic level. The classical Stern–Gerlach experiment has long verified this logic. In that experiment, when the intrinsic magnetic moment of a single atom passes through a non-uniform magnetic field, it produces a discrete spatial displacement of the atomic beam, which confirms the feasibility of this conversion mechanism. Today's equipment integrates ultra-stable optical cavities, strongly coupled nanoscale quantum dots, ultra-sensitive charge sensors, and radio frequency measurement technologies, and is already capable of identifying and repairing a single damaged quantum state.

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