Every digital device you have ever used operates on the same fundamental principle. Information is stored and processed as bits, tiny switches that are either off or on, 0 or 1. Billions of these switches, flipping in orchestrated patterns, give rise to everything from spreadsheets to satellite navigation. This architecture has served us extraordinarily well for the better part of a century. But there are problems it cannot solve, not because our machines are too slow, but because the classical approach itself is fundamentally inadequate for certain kinds of computation.
Quantum computing offers a radically different approach. Instead of bits that must be 0 or 1, a quantum computer uses qubits, quantum bits, that exploit two phenomena at the heart of quantum mechanics: superposition and entanglement. Together, these properties allow quantum computers to explore vast spaces of possibilities in ways that no classical machine can replicate efficiently. The promise is not simply faster computers, but an entirely new category of computation.
Qubits and Superposition: Beyond 0 and 1
What a Qubit Actually Is
A classical bit is definite. Ask it for its value and you will always get a clear answer: 0 or 1. A qubit, by contrast, can exist in a superposition of both states simultaneously. This is not merely a metaphor for uncertainty or ignorance. It is a precise physical condition described by quantum mechanics, in which the qubit’s state is a combination of 0 and 1 with specific probability amplitudes. Only when the qubit is measured does it collapse into one definite value.
It is important to resist the popular oversimplification that a qubit is “both 0 and 1 at the same time.” The reality is subtler. A qubit in superposition is described by a vector in a two-dimensional complex space that encodes not just probabilities but also phases. These phases are crucial. They allow quantum computations to use interference, amplifying paths that lead to correct answers and cancelling paths that lead to wrong ones. Without interference, qubits superposition would offer no computational benefit whatsoever.
Physical Implementations
Qubits can be realised in many physical systems. IBM and Google build their quantum processors from superconducting circuits, tiny loops of metal cooled to temperatures colder than outer space, where electrical currents flow without resistance and quantum effects become observable. Other approaches use trapped ions held in electromagnetic fields, photons guided through optical circuits, or neutral atoms arranged by laser tweezers. Each platform has its own strengths in terms of coherence time, gate fidelity, and scalability, and the diversity of approaches reflects the fact that building reliable qubits remains a formidable challenge.
Entanglement as a Computational Resource
Correlations That Defy Classical Explanation
Superposition alone does not make quantum computing powerful. The second essential ingredient is entanglement, a uniquely quantum form of correlation between particles. When two qubits are entangled, measuring one instantly determines something about the state of the other, regardless of the distance between them. Einstein famously called this “spooky action at a distance.” But decades of experiment, from Alain Aspect’s pioneering tests in the 1980s to the loophole-free Bell tests of 2015, have confirmed that entanglement is real and irreducible.
In a quantum computer, entanglement allows qubits to share information in ways that create computational states impossible to represent efficiently on a classical machine. A system of n entangled qubits can exist in a superposition of 2n states simultaneously, and the correlations between qubits mean that this vast state space is genuinely exploited during computation. This is the origin of the exponential scaling that gives quantum computers their potential advantage.
Understanding Quantum Advantage
The term quantum advantage refers to the ability of a quantum computer to solve a specific problem significantly faster than any known classical algorithm. This does not mean quantum computers are universally faster. For many everyday tasks, a classical computer is perfectly adequate. The advantage appears for problems with a particular mathematical structure, where the exponential state space of entangled qubits can be harnessed through clever algorithms to find solutions that would take classical computers an impractical amount of time.
The Algorithms That Make It Matter
Shor’s Algorithm and the Threat to Cryptography
In 1994, the mathematician Peter Shor discovered a quantum algorithm that could factor large integers exponentially faster than any known classical method. This was not a minor theoretical curiosity. The security of most modern encryption, including the RSA system that protects banking transactions, government communications, and virtually all internet commerce, rests on the assumption that factoring large numbers is computationally infeasible. Shor’s algorithm, running on a sufficiently powerful quantum computer, would break that assumption entirely.
No quantum computer today is large or reliable enough to run Shor’s algorithm on cryptographically relevant numbers. But the threat is taken seriously. Governments and companies worldwide are already deploying post-quantum cryptography, encryption methods designed to resist attack by both classical and quantum computers. NIST finalised its first post-quantum cryptographic standards in 2024, a sign that the field considers the threat real even if the timeline remains uncertain.
Grover’s Algorithm and Quantum Search
Two years after Shor, Lov Grover published an algorithm that provides a quadratic speedup for unstructured search problems. Where a classical computer must check N items one by one to find a specific entry, Grover’s algorithm finds it in roughly the square root of N steps. The speedup is less dramatic than Shor’s exponential advantage, but it applies to an enormously broad class of problems, from database search to optimisation.
Quantum Simulation
Perhaps the most natural application of a quantum computer is simulating other quantum systems. Modelling molecules, materials, or chemical reactions at the quantum level is extraordinarily expensive on classical hardware because the number of quantum states grows exponentially with the number of particles. A quantum computer, being itself a quantum system, can represent these states directly. This was, in fact, the original motivation for quantum computing.
Where the Field Stands Today
Hardware Milestones
The past few years have seen remarkable progress. In December 2024, Google announced its Willow processor, a 105-qubit superconducting chip that achieved a landmark result: it demonstrated that increasing the number of qubits in an error-correcting code actually reduced the error rate, the first time this “below threshold” behaviour had been shown in a real device. Willow completed a benchmark computation in five minutes that Google estimated would take the world’s fastest classical supercomputer ten septillion years.
IBM has pursued a complementary strategy focused on both scale and quality. Its Heron processor offers 156 qubits with tunable couplers and improved gate fidelity, while the company’s roadmap targets quantum error correction at scale, aiming for fault-tolerant quantum computing by 2029. In early 2025, Microsoft entered the race with its Majorana 1 processor, which uses an entirely different qubit technology based on topological superconductors, though the results have prompted vigorous debate about the underlying physics.
Beyond superconducting circuits, companies such as IonQ and Quantinuum are developing trapped-ion quantum computers that offer exceptionally high gate fidelities and long coherence times. Photonic approaches, pursued by firms like Xanadu and PsiQuantum, promise room-temperature operation and natural compatibility with optical communication networks.
The Error Correction Challenge
For all this progress, the central obstacle remains the same: errors. Qubits are extraordinarily fragile. Thermal fluctuations, stray electromagnetic fields, even cosmic rays can cause a qubit to lose its quantum state, a process called decoherence. Current quantum computers are described as “noisy intermediate-scale quantum” (NISQ) devices, meaning they can perform short computations but accumulate errors too quickly for long, complex algorithms like Shor’s factoring of cryptographically relevant numbers.
Quantum error correction addresses this by encoding a single logical qubit across many physical qubits, using redundancy to detect and correct errors without disturbing the quantum information. Current schemes require hundreds or even thousands of physical qubits per logical qubit. Making this practical is widely regarded as the defining engineering challenge of the field.
A Lineage of Visionary Thinking
From Turing to Feynman
The intellectual roots of quantum computing reach back further than one might expect. In 1936, Alan Turing published his foundational paper on computable numbers, defining the abstract machine that bears his name and establishing the theoretical limits of classical computation. Every classical computer ever built is, in essence, a physical realisation of Turing’s idea. His work did not merely describe computation; it defined what computation means.
Nearly half a century later, in 1981, the physicist Richard Feynman posed a deceptively simple question at a conference at MIT: can a classical computer efficiently simulate a quantum mechanical system? His answer was no. The exponential growth of quantum states makes faithful simulation intractable on any classical machine. Feynman’s proposal was direct: to simulate quantum physics, build a computer that is itself quantum mechanical. This insight, rooted in Turing’s framework but transcending its classical boundaries, launched the field of quantum computing.
The path from Feynman’s vision to today’s processors required breakthroughs in physics, materials science, and engineering, along with the theoretical work of David Deutsch, who formalised the universal quantum computer in 1985, and Shor and Grover, whose algorithms showed that quantum computers could solve real problems faster than classical ones.
The Foundations Made Tangible
Quantum computing sits at the intersection of ideas that transformed twentieth-century science, from Planck’s radical hypothesis in 1900 to the theory of computation that Turing developed in the 1930s. Understanding where this technology comes from means returning to the original sources, the papers and minds that built the foundations.
For those who wish to engage directly with Turing’s intellect, our collector’s edition of Alan Turing’s Treatise on the Enigma presents one of the most brilliant documents in the history of cryptography and computation, a work that reveals the mind behind the machine. The quantum side of the story begins with Planck, whose courage to break with classical physics made everything that followed possible. Our edition of Max Planck’s three foundational publications brings those landmark papers to life in a design worthy of their significance. And for a broader view of the human story behind the science, Portraying Science gathers the faces and stories of the men and women who shaped our understanding of the physical world.
Quantum computing explained in full requires grappling with ideas that defy everyday intuition: superposition, entanglement, interference, and error correction. The technology is not yet mature. The machines are noisy and the engineering challenges are immense. But the trajectory is unmistakable. From Feynman’s provocation in 1981 to Google’s below-threshold error correction in 2024, the field has moved from theoretical speculation to experimental reality. The question is no longer whether quantum computers will work, but when they will work well enough to transform cryptography, chemistry, materials science, and fields we have not yet imagined. The foundations laid by Turing, Planck, and the quantum pioneers are now being built upon at extraordinary speed.
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