Quantum mechanics is the branch of physics that describes nature at very small scales: atoms, electrons, photons of light, atomic nuclei, and many modern materials and devices. It is one of the most successful scientific theories ever created. It explains the structure of atoms, the behaviour of light and matter, chemical bonding, magnetism, radioactivity, semiconductors, lasers, superconductors, and much else.
It is also famously strange. Quantum objects do not behave like tiny billiard balls. They can act partly like waves, exist in combinations of possible states, and show correlations that seem impossible from an everyday point of view. But quantum mechanics is not magic, mysticism, or proof that “anything can happen”. It is a precise mathematical theory with extremely accurate experimental support.
A key point for the later discussion of quantum chips such as Google’s Willow is this:
> A quantum computer does not use “external
space”, a hidden physical dimension, or another universe to perform
calculations.
> Its power comes from the mathematics of quantum states: a system of
many qubits is described by a huge abstract space called Hilbert
space, whose size grows exponentially with the number of
qubits.
That distinction matters. The “space” used in quantum computing is not extra physical room inside the chip; it is a mathematical space of possible quantum states.
By the late nineteenth century, physics seemed almost complete. Newton’s mechanics explained motion and gravity. Maxwell’s equations explained electricity, magnetism and light. Thermodynamics explained heat and engines.
In classical physics, the world was usually pictured as follows:
This picture worked brilliantly for planets, pendulums, steam engines and radio waves. But it began to fail when physicists studied atoms, light emitted by hot objects, and the interaction between light and matter.
A black body is an ideal object that absorbs and emits radiation perfectly. A hot piece of metal, for example, glows red, then yellow-white as it gets hotter. Physicists wanted to calculate the exact spectrum of light emitted by such an object.
Classical physics predicted a disastrous result: hot objects should emit infinite energy at short wavelengths, especially in the ultraviolet. This was called the ultraviolet catastrophe.
But experiments showed no such catastrophe. The emitted radiation rose to a peak and then fell off.
In 1900, Max Planck proposed a radical idea. He suggested that energy was not exchanged continuously, but in discrete packets:
\[ E = hf \]
where:
Planck did not initially think light itself necessarily came in particles. He treated quantisation partly as a mathematical trick. But the idea was revolutionary: energy at microscopic scales seemed to come in indivisible chunks.
This was the beginning of quantum theory.
The photoelectric effect occurs when light shines on a metal and causes electrons to be emitted.
Classical wave theory predicted that brighter light should give electrons more energy, because brighter light carries more energy. It also suggested that even low-frequency light should eventually knock electrons out if one waited long enough.
But experiments showed something different:
In 1905, Albert Einstein explained this by proposing that light itself comes in packets of energy, later called photons.
Each photon has energy:
\[ E = hf \]
A photon either has enough energy to knock an electron out of the metal or it does not. Making the light brighter means sending more photons, not making each photon more energetic.
Einstein won the Nobel Prize not for relativity, but for his explanation of the photoelectric effect.
This was a major step towards the modern idea that light can behave like both a wave and a particle.
Quantisation means that certain physical quantities come in discrete allowed values rather than any value whatsoever.
A useful analogy is a staircase. In ordinary classical thinking, energy is like a ramp: you can stand at any height. In quantum systems, energy is often like a staircase: only certain steps are allowed.
For example, an electron in an atom can occupy only certain energy levels. It cannot orbit the nucleus with just any energy. When it changes energy level, it absorbs or emits a photon with exactly the energy difference between the levels.
This explains why atoms emit light at specific colours. Each chemical element has its own pattern of spectral lines, like a fingerprint.
Quantum objects can show both wave-like and particle-like behaviour.
Light sometimes behaves like a wave, producing interference patterns. But it also behaves like particles, as in the photoelectric effect.
Electrons, which were once thought of simply as particles, can also behave like waves. When electrons pass through a crystal or a double-slit apparatus, they can form interference patterns.
The phrase wave–particle duality can be misleading if taken too literally. An electron is not simply a tiny ball that sometimes turns into a water wave. Rather, “particle” and “wave” are classical concepts that each capture part of the behaviour of quantum objects. Quantum entities are something deeper than either familiar picture.
A quantum system can exist in a superposition of possible states.
For example, an electron can be in a superposition of “spin up” and “spin down”. A photon can be in a superposition of two paths through an interferometer.
A simple analogy is a musical chord. A single note is one frequency; a chord is a combination of several notes at once. Similarly, a quantum state can be a combination of several possible outcomes.
But the analogy has limits. A superposition is not merely our ignorance about which state the system is “really” in. It can produce measurable effects, such as interference, that would not occur if the system simply had one definite hidden classical state.
Quantum mechanics does not usually predict exactly what result a single measurement will give. Instead, it predicts probabilities.
For example, it might say there is a 70% chance of finding an electron in one region and a 30% chance of finding it elsewhere.
This does not mean the theory is vague. Quantum probabilities are calculated with extraordinary precision. In fact, quantum electrodynamics, the quantum theory of light and electrons, has produced some of the most accurate predictions in all science.
The wavefunction is the mathematical object that represents the quantum state of a system.
It contains all the information quantum mechanics allows us to know about the system. From it, we can calculate probabilities for possible measurement outcomes.
The wavefunction is often written using the Greek letter psi:
\[ \psi \]
For a single particle, the wavefunction can be used to calculate the probability of finding the particle in different places. Where the wavefunction has a large magnitude, the particle is more likely to be found.
However, the wavefunction is not necessarily a physical wave like a ripple on water. In many cases, especially for systems of many particles, it lives in an abstract mathematical space rather than ordinary three-dimensional space.
This becomes very important in quantum computing.
Measurement is one of the deepest puzzles in quantum mechanics.
Before measurement, a system may be described as a superposition of several possible outcomes. When measured, we obtain one definite result.
For example, an electron in a superposition of spin up and spin down is measured and found to be either up or down.
The standard calculation says that probabilities come from the wavefunction. But what exactly counts as a measurement? Does the wavefunction physically collapse? Is collapse merely an update in our knowledge? Does the measuring device become entangled with the system?
These questions lead to the measurement problem, which we shall return to later.
The Heisenberg uncertainty principle says that certain pairs of properties cannot both be known with unlimited precision at the same time.
The most famous pair is position and momentum.
Momentum is related to mass and velocity. Roughly speaking, it tells us how much motion something has.
The uncertainty principle is often written:
\[ \Delta x \Delta p \geq \frac{\hbar}{2} \]
This means that the more precisely we know a particle’s position, the less precisely we can know its momentum, and vice versa.
This is not just a limitation of our instruments. It is a feature of nature as described by quantum mechanics.
A helpful analogy is sound. A short, sharp click is localised in time but contains a wide range of frequencies. A pure musical tone has a well-defined frequency but must last for some time, so it is not sharply localised. Similarly, a quantum wave that is sharply localised in position must be built from many different momenta.
Entanglement occurs when two or more quantum systems are described by a shared state, such that the properties of each part cannot be fully described independently of the whole.
Imagine two particles prepared so that if one is measured spin up, the other will be spin down, even if they are far apart. Quantum mechanics predicts correlations stronger than any allowed by ordinary classical hidden-variable theories.
Entanglement does not allow faster-than-light communication. You cannot use it to send a controllable message instantly. But it does reveal that nature is not built from independent local properties in the simple way Einstein hoped.
Entanglement is not mystical “cosmic connection”. It is a precise physical and mathematical relationship between quantum systems, confirmed by many experiments.
As discussed, Max Planck introduced quantised energy in 1900 to solve black-body radiation. His constant, \(h\), became one of the central constants of nature.
Planck’s idea was conservative in intention but revolutionary in consequence.
In 1905, Einstein used the quantum idea to explain the photoelectric effect. He argued that light energy comes in localised packets.
Einstein also contributed to the theory of specific heats and stimulated emission, the latter becoming important for lasers.
Ironically, although Einstein helped found quantum theory, he later became one of its sharpest critics. He disliked the idea that probability was fundamental, famously saying:
> “God does not play dice.”
This was not a religious argument so much as an objection to the idea that nature is fundamentally indeterministic.
In 1913, Niels Bohr proposed a model of the atom in which electrons occupy certain allowed orbits around the nucleus. Electrons could jump between these orbits by absorbing or emitting photons.
Bohr’s model explained the spectrum of hydrogen remarkably well. It was not the final theory, but it introduced key ideas:
Bohr later became a central figure in the interpretation of quantum mechanics, especially the Copenhagen interpretation.
In 1924, Louis de Broglie proposed that if light waves can behave like particles, perhaps particles such as electrons can behave like waves.
He suggested that a particle with momentum \(p\) has wavelength:
\[ \lambda = \frac{h}{p} \]
This was an astonishing idea, but it was soon confirmed experimentally by electron diffraction.
De Broglie’s matter waves helped inspire Schrödinger’s wave mechanics.
In 1925, Werner Heisenberg developed one of the first complete forms of quantum mechanics, known as matrix mechanics.
Heisenberg focused only on observable quantities, such as the frequencies and intensities of light emitted by atoms, rather than trying to picture electron orbits.
The mathematics involved arrays of numbers called matrices. A strange feature of matrices is that multiplication can depend on order:
\[ AB \neq BA \]
This non-commutativity became central to quantum mechanics. It is closely related to the uncertainty principle.
Heisenberg later formulated the uncertainty principle in 1927.
In 1926, Erwin Schrödinger developed a different-looking version of quantum mechanics: wave mechanics.
His famous equation describes how the wavefunction changes over time:
\[ i\hbar \frac{\partial \psi}{\partial t} = \hat{H}\psi \]
This is the Schrödinger equation. It plays a role in quantum mechanics somewhat like Newton’s laws play in classical mechanics.
Schrödinger’s approach was more visually intuitive than Heisenberg’s matrix mechanics. It pictured electrons as described by waves. Soon it was shown that Schrödinger’s wave mechanics and Heisenberg’s matrix mechanics were mathematically equivalent.
Max Born gave the wavefunction its modern probabilistic interpretation.
He proposed that the square of the wavefunction’s magnitude gives the probability of finding a particle in a particular state or location.
This was a profound change. Schrödinger had hoped the wavefunction might describe a real spread-out physical wave. Born showed that it should be understood, at least operationally, as a probability amplitude.
A probability amplitude is not itself a probability. It can be positive, negative or even complex-valued. Probabilities are obtained from amplitudes by taking their squared magnitude.
The fact that amplitudes can add and cancel is what produces quantum interference.
Wolfgang Pauli introduced the exclusion principle, which states that no two identical fermions can occupy the same quantum state.
Electrons are fermions. Pauli’s exclusion principle explains the structure of the periodic table. It is why electrons in atoms fill shells rather than all collapsing into the lowest energy state.
It is also crucial for the stability of matter. Without the exclusion principle, ordinary matter would not have its familiar structure.
Spin was another key development. Particles such as electrons have an intrinsic angular momentum called spin. It is not literally a tiny ball spinning on its axis, but it behaves mathematically like angular momentum and gives particles magnetic properties.
Paul Dirac united quantum mechanics with special relativity for the electron.
His equation predicted the existence of antimatter. In particular, it implied a particle like the electron but with positive charge: the positron. The positron was discovered experimentally in 1932.
Dirac also helped lay foundations for quantum field theory and introduced elegant mathematical notation still used today.
During the 1920s, Niels Bohr, Werner Heisenberg and others developed what became known as the Copenhagen interpretation.
It is not a single rigid doctrine, but it commonly includes ideas such as:
The Copenhagen view became the practical working philosophy for many physicists. However, it left some people dissatisfied because it did not fully explain what physically happens during measurement.
Quantum mechanics initially dealt with particles and waves in fixed numbers. But nature allows particles to be created and destroyed. Light can create electron-positron pairs; particles can emit and absorb photons.
To handle this, physicists developed quantum field theory.
In quantum field theory, fields are the fundamental entities. Particles are excitations, or “quanta”, of fields.
For example:
This framework combines quantum mechanics with special relativity and underlies the Standard Model of particle physics.
Quantum electrodynamics, or QED, is the quantum field theory of light and charged particles, especially electrons and photons.
It describes how electrons emit and absorb photons and how electromagnetic forces arise from these interactions.
QED is astonishingly accurate. Some of its predictions agree with experiment to more than ten decimal places.
Richard Feynman was one of the most important physicists of the twentieth century and a brilliant communicator of quantum ideas.
Feynman developed a formulation of quantum mechanics called the path integral approach.
In classical mechanics, a particle travels along one definite path. In Feynman’s quantum picture, to calculate the probability of a process, we consider all possible paths the particle could take. Each path contributes a probability amplitude. These amplitudes interfere with one another.
This does not mean a particle is literally wandering through every path in the everyday sense. Rather, the mathematics requires summing contributions from all possible histories.
A useful analogy is wave interference in water. Ripples from different routes can reinforce or cancel. In quantum mechanics, probability amplitudes do something similar.
The path integral is especially powerful in quantum field theory.
Feynman also introduced Feynman diagrams, pictorial tools for calculating particle interactions.
For example, a diagram might show two electrons exchanging a photon. The diagram is not a literal photograph of tiny particles colliding. It is a compact representation of mathematical terms in a calculation.
Feynman diagrams became essential in particle physics because they make complicated calculations more manageable.
In the early 1980s, Feynman argued that ordinary classical computers struggle to simulate quantum systems efficiently because quantum states grow exponentially in complexity.
He suggested that to simulate quantum physics naturally, one should use a controllable quantum system.
This idea helped inspire the field of quantum computing and quantum simulation.
Feynman’s insight was simple but profound:
> Nature is quantum, so perhaps the best way to simulate nature is with a quantum machine.
Quantum mechanics works extraordinarily well, but what does it mean? Several puzzles remain debated.
The Schrödinger equation describes smooth, deterministic evolution of the wavefunction. But measurement seems to produce a definite outcome randomly.
So there appears to be a tension:
This is the measurement problem.
Different interpretations of quantum mechanics respond to it differently.
Schrödinger invented his famous cat thought experiment in 1935 to show how strange quantum superposition becomes if applied to everyday objects.
Imagine a cat in a sealed box with a radioactive atom, a detector, and a mechanism that releases poison if the atom decays. If the atom is in a superposition of decayed and not decayed, does that mean the cat is in a superposition of alive and dead?
Schrödinger’s point was not that cats really wander around half-alive in ordinary experience. He wanted to expose the difficulty of connecting microscopic quantum superpositions with definite macroscopic outcomes.
Today, physicists understand that decoherence plays a major role. Large objects interact constantly with their environments, causing quantum interference between macroscopically different states to become effectively unobservable. Decoherence helps explain why the world appears classical, though many argue it does not by itself completely solve the measurement problem.
In 1935, Einstein, Boris Podolsky and Nathan Rosen published a famous paper arguing that quantum mechanics was incomplete.
The EPR argument considered entangled particles. Measuring one particle seemed to allow instant knowledge of the state of the other, even if far away.
Einstein objected to what he called “spooky action at a distance”. He believed that physical properties should be local and real:
EPR argued that quantum mechanics must be missing hidden variables: deeper facts that determine outcomes.
In 1964, John Bell made a remarkable discovery. He showed that the debate could be tested experimentally.
Bell derived inequalities that any local hidden-variable theory must obey. Quantum mechanics predicts that entangled particles can violate these inequalities.
Experiments have repeatedly shown violations of Bell inequalities, agreeing with quantum mechanics.
Important experiments were performed by John Clauser, Alain Aspect, Anton Zeilinger and many others. Modern tests have closed major loopholes.
The conclusion is subtle but profound:
> Nature cannot be explained by any simple theory in which measurement outcomes are determined by pre-existing local properties.
This does not mean useful information travels faster than light. It means the classical idea of local realism cannot be maintained in its simplest form.
No single interpretation is universally accepted. Here are some major ones.
The Copenhagen approach treats the wavefunction as a tool for predicting measurement outcomes. It emphasises the role of measurement and the limits of classical concepts.
Strength: practical and historically influential.
Weakness: unclear about exactly what counts as a measurement.
The many-worlds interpretation, associated with Hugh Everett, says the wavefunction never collapses. Instead, all possible outcomes occur in different branches of the universal wavefunction.
When you measure a quantum system, you become entangled with it, and different versions of you see different outcomes.
Strength: keeps the Schrödinger equation universal and avoids
collapse.
Weakness: raises difficult questions about probability and the ontology
of branches.
Pilot-wave theory, associated with Louis de Broglie and David Bohm, says particles have definite positions guided by a real wavefunction.
It is deterministic but non-local.
Strength: gives a clear picture of particles following definite
trajectories.
Weakness: requires non-local influences and is harder to reconcile
elegantly with relativity and quantum field theory.
Objective collapse theories propose that wavefunction collapse is a real physical process that happens spontaneously, especially for large systems.
Strength: directly addresses why macroscopic objects have definite
states.
Weakness: requires modifying standard quantum mechanics and awaits
decisive experimental confirmation.
Quantum mechanics is not merely philosophical. Much of modern technology depends on it.
A semiconductor is a material whose electrical conductivity can be controlled. Silicon is the most famous example.
Quantum mechanics explains the energy bands in solids: ranges of energy that electrons may or may not occupy. By adding tiny amounts of impurities, called doping, engineers can control how electrons move.
The transistor uses this behaviour to switch or amplify electrical signals. Transistors are the building blocks of computer chips, phones, radios, cars, satellites and almost all modern electronics.
Without quantum mechanics, there would be no modern digital world.
A laser produces coherent light: light waves with a well-defined frequency and phase.
Lasers rely on quantum transitions between energy levels and on stimulated emission, an idea Einstein introduced.
They are used in:
Light-emitting diodes, or LEDs, emit light when electrons and holes recombine in a semiconductor.
The colour of the LED depends on the quantum energy gap in the material.
LEDs are efficient, durable and now central to lighting, displays and optical communications.
Magnetic resonance imaging, or MRI, uses the quantum spin of atomic nuclei, especially hydrogen nuclei in water molecules.
In a strong magnetic field, nuclear spins have different energy states. Radio waves can flip these spins, and the emitted signals are used to form detailed images of the body.
MRI is a medical technology built directly on quantum physics.
Atomic clocks use the precise frequency of quantum transitions in atoms, often caesium or rubidium.
The Global Positioning System, GPS, depends on extremely accurate timing. GPS also requires Einstein’s relativity, but quantum mechanics provides the atomic clocks that make such timing possible.
Electrons have wave-like properties. Because their wavelengths can be much shorter than visible light, electron microscopes can image much smaller structures than optical microscopes.
This allows scientists to see viruses, nanostructures and atomic-scale materials.
A superconductor carries electric current with zero electrical resistance below a critical temperature.
Quantum mechanics explains superconductivity through collective behaviour of electrons, often forming pairs called Cooper pairs.
Superconductors are used in MRI machines, particle accelerators, sensitive magnetometers and many quantum computers.
Quantum sensors exploit superposition, entanglement or delicate quantum transitions to measure physical quantities with extreme precision.
They can measure:
Examples include atomic interferometers, nitrogen-vacancy centres in diamond, superconducting quantum interference devices, and advanced atomic clocks.
Quantum computing uses quantum systems to process information in ways that can outperform classical computers for certain tasks.
It is not simply a faster version of ordinary computing. A quantum computer is not better at everything. It is powerful for particular problems where superposition, entanglement and interference can be organised to produce useful results.
A classical computer uses bits.
A bit has one of two values:
Everything a classical computer does — text, images, videos, calculations — is ultimately represented by long strings of 0s and 1s.
A qubit, or quantum bit, is the basic unit of quantum information.
A qubit can be measured as:
But before measurement, it can be in a superposition of 0 and 1:
\[ \alpha |0\rangle + \beta |1\rangle \]
Here:
This does not mean a qubit is just “both 0 and 1” in a simple classical sense. It means it has a quantum state that can produce interference effects.
One qubit needs two amplitudes to describe its state.
Two qubits need four amplitudes:
\[ |00\rangle, |01\rangle, |10\rangle, |11\rangle \]
Three qubits need eight amplitudes.
In general, \(n\) qubits require \(2^n\) amplitudes to describe their most general state.
So:
This is why simulating a large quantum computer on a classical computer becomes extremely difficult.
But be careful: this does not mean a quantum computer simply tries every answer and then reads them all out. Measurement gives only one outcome. The art of quantum algorithm design is to make wrong answers cancel out and useful answers reinforce.
Quantum amplitudes can add or cancel.
If two paths lead to the same outcome, their amplitudes may reinforce each other, making that outcome more likely. Or they may cancel, making it less likely.
Quantum algorithms use this principle deliberately.
A good analogy is noise-cancelling headphones. They use waves arranged so that unwanted sound is cancelled. Quantum algorithms arrange probability amplitudes so that wrong answers tend to cancel and right answers become more likely.
The analogy breaks down because quantum amplitudes are abstract mathematical quantities, not ordinary sound waves in air.
Entanglement allows qubits to share a state that cannot be broken down into independent states of each qubit.
This is one reason quantum computers can represent complex correlations efficiently.
Entanglement is especially important in:
However, entanglement alone is not enough. A useful quantum computer also needs accurate control, low noise, good algorithms and error correction.
A quantum gate is an operation applied to one or more qubits. It changes their quantum state.
Examples include:
A sequence of quantum gates forms a quantum circuit.
At the end, the qubits are measured, producing classical bits as output.
Quantum states are fragile. If a qubit interacts with its environment: stray heat, vibration, electromagnetic noise, defects in materials. Its delicate quantum information can leak away.
This process is called decoherence.
Decoherence turns quantum behaviour into something more classical and destroys the interference needed for quantum computation.
Preventing and correcting decoherence is one of the central engineering challenges of quantum computing.
Classical computers use error correction too. For example, information can be copied and checked.
Quantum error correction is harder because:
Quantum error correction solves this by spreading the information of one logical qubit across many physical qubits. The system measures error patterns indirectly, without measuring the protected quantum information itself.
A major approach is the surface code, which arranges qubits in a grid and repeatedly checks for local error syndromes.
A fully useful fault-tolerant quantum computer may need many physical qubits for each reliable logical qubit.
Quantum computers are not universally faster. They offer advantages for particular types of problems.
Shor’s algorithm can factor large numbers efficiently on a sufficiently powerful fault-tolerant quantum computer.
This matters because much modern cryptography, such as RSA, relies on factoring being hard for classical computers.
Current quantum computers are not yet large and reliable enough to break modern encryption, but this is a long-term security concern.
Grover’s algorithm gives a quadratic speed-up for unstructured search.
If a classical search takes roughly \(N\) steps, Grover’s algorithm can do it in roughly \(\sqrt{N}\) steps.
That is useful, but it is not an exponential speed-up.
Quantum computers may be especially valuable for simulating molecules, chemical reactions and materials.
This is because molecules are themselves quantum systems. Classical computers struggle to simulate large quantum systems exactly because the state space grows exponentially.
Potential applications include:
Some quantum approaches may help with optimisation problems, such as scheduling, logistics or portfolio design.
However, this area is complex. Quantum advantage for broad practical optimisation is not yet firmly established.
This was Feynman’s original vision: use quantum systems to simulate other quantum systems.
Quantum simulation may become one of the earliest genuinely useful applications of quantum computing.
A quantum chip is a device that contains physical systems used as qubits.
Different technologies can be used:
Google’s quantum processors, including Sycamore and Willow, use superconducting circuits.
These are tiny electrical circuits cooled to extremely low temperatures. At such temperatures, they behave quantum mechanically and can act like artificial atoms.
In superconducting quantum computers, qubits are usually made from circuits containing Josephson junctions.
A Josephson junction consists of two superconductors separated by a thin insulating barrier. Quantum tunnelling allows pairs of electrons to cross the barrier in a controlled way.
The resulting circuit has discrete energy levels, like an atom. Two of those levels can be used as the qubit’s \(|0\rangle\) and \(|1\rangle\) states.
These circuits are controlled with microwave pulses. Carefully shaped pulses implement quantum gates.
No.
This is a common misunderstanding, and it is worth addressing carefully.
A small chip does not send information into external space, another dimension, a parallel universe, or a hidden physical realm.
Instead, the quantum state of its qubits is described by a mathematical structure called Hilbert space.
For \(n\) qubits, the number of basis states is \(2^n\). So a chip with 100 qubits has a state described by amplitudes over an astronomically large number of possible basis states.
This is sometimes described loosely as the quantum computer “exploring many possibilities at once”. But that phrase can mislead.
A more accurate statement is:
> A quantum computer evolves a complex pattern of probability amplitudes across a very large Hilbert space, using quantum gates arranged so that interference increases the probability of useful answers.
The Hilbert space is not physical space. It is like the space of all possible configurations.
An analogy: a chess position can be described as a point in a huge abstract “space” of possible chess positions. That does not mean the chessboard physically contains billions of boards. It means the mathematical description has many possibilities.
Similarly, a quantum chip can be physically small while its quantum state requires an enormous mathematical description.
A quantum algorithm typically works like this:
Initialisation
Qubits are prepared in a known starting state, often all 0s.
Superposition
Gates place qubits into combinations of many basis states.
Entanglement
Multi-qubit gates create correlations that cannot be represented as
independent qubits.
Controlled evolution
Gates manipulate phases and amplitudes according to the problem
structure.
Interference
Wrong or unwanted answers are made less likely by destructive
interference. Useful answers are made more likely by constructive
interference.
Measurement
The final quantum state is measured, producing classical bits.
Repetition and statistics
Because measurement is probabilistic, the circuit is often run many
times to build up a distribution of outcomes.
The central trick is not merely having many possibilities. It is arranging interference so that the right possibilities become easier to observe.
Quantum computers are extraordinarily delicate machines.
Superconducting qubits must be cooled to temperatures close to absolute zero, often around millikelvin temperatures.
This is colder than outer space.
The cooling is done using dilution refrigerators. Such systems are large, complex and expensive.
Qubits must be protected from:
Even tiny disturbances can cause errors.
Each qubit and each gate must be carefully calibrated.
The microwave pulses used to control qubits need the right frequency, timing, shape and amplitude.
In a large processor, calibration becomes a major challenge because qubits can influence one another.
Gate fidelity measures how accurately a quantum gate performs its intended operation.
Useful quantum computing requires extremely high gate fidelities. Small errors accumulate quickly across many gates.
At the end of a calculation, the qubits must be measured accurately.
Readout itself can introduce errors, and it must be fast enough to support error correction.
Qubits lose quantum information over time. The time over which they remain useful is called their coherence time.
Quantum gates must be performed much faster than decoherence destroys the computation.
Large-scale useful quantum computers will need error correction. This requires many physical qubits to create fewer but more reliable logical qubits.
A central milestone is showing that as you increase the size of an error-correcting code, the logical error rate goes down. That is essential for scalable quantum computing.
Google announced its Willow quantum chip as a major step in superconducting quantum computing.
Publicly reported features include:
These are significant scientific and engineering achievements.
However, one should avoid hype.
Willow is not a general-purpose quantum computer capable of solving everyday industrial problems. It has not broken modern encryption, revolutionised drug discovery, or replaced classical supercomputers.
Its importance is more specific:
Claims about classical computers taking enormous times to reproduce a sampling task should be understood in context. Such comparisons depend on the exact task, assumptions about classical algorithms, and available hardware. They do not mean the chip is faster than classical computers for all useful calculations.
Because quantum mechanics is strange, it is often misrepresented.
It does not imply that:
Quantum mechanics is subtle, but it is not a licence for mysticism. It is a rigorous physical theory with clear mathematical rules and experimentally testable predictions.
A helpful summary is this:
Classical physics describes the world in terms of definite properties: a ball is here, moving at this speed, following that path.
Quantum mechanics describes the world in terms of possible measurement outcomes and probability amplitudes. These amplitudes can combine, interfere and become entangled.
When we measure, we get definite results. But the route to those results is governed by quantum rules that are unlike everyday intuition.
The strange part is conceptual. The powerful part is practical.
Quantum mechanics explains why atoms are stable, why matter has structure, why light is emitted in specific colours, and why modern electronics work. It also gives us new forms of computation and sensing.
Quantum mechanics arose because classical physics could not explain phenomena such as black-body radiation, the photoelectric effect and atomic spectra. Planck introduced quantised energy; Einstein proposed photons; Bohr developed a quantum atom; de Broglie suggested matter waves; Heisenberg and Schrödinger built full quantum mechanics; Born gave the wavefunction its probabilistic meaning; Pauli, Dirac and others extended the theory; and Feynman transformed quantum theory through path integrals, QED, Feynman diagrams and the idea of quantum simulation.
Its core ideas include quantisation, superposition, wave–particle duality, uncertainty, probability, measurement and entanglement. These ideas are conceptually challenging but experimentally very well supported.
Quantum mechanics underpins technologies such as transistors, lasers, LEDs, MRI, atomic clocks, GPS timing, electron microscopes, superconductors and quantum sensors.
Quantum computers use qubits, which can exist in superpositions and become entangled. A small chip can correspond to an enormous quantum state space because \(n\) qubits are described by \(2^n\) basis states. But this is not “external space” or another dimension; it is an abstract Hilbert space. Quantum algorithms use gates and interference to amplify useful answers and suppress wrong ones.
Chips such as Google’s Willow are impressive engineering achievements, especially in superconducting qubits and quantum error correction, but they remain steps towards future fault-tolerant quantum computers rather than finished universal machines.
Quantum mechanics is therefore both strange and powerful: strange because it challenges everyday ideas of reality, and powerful because it explains matter and enables much of modern technology.