How Do Quantum Computers Work? Superposition, Interference and Error

A classical bit is either 0 or 1. A quantum bit can be in a superposition, meaning its state is described by two numbers called amplitudes, one associated with 0 and one with 1, and the probability of measuring each outcome is the square of the size of its amplitude. The crucial point is that amplitudes can be negative or complex, which classical probabilities cannot, and that is what allows interference: two routes to the same outcome can cancel. A second uniquely quantum resource is entanglement, in which two or more qubits share a joint state that cannot be described by specifying each separately, so that measuring one immediately constrains the other. A register of n qubits is described by two to the power of n amplitudes, which is why fifty qubits already require more numbers than a classical computer can hold, and why simulating such a system is hard.

The constraints that make the machine difficult all follow from how quantum states behave when touched. Measuring a superposition collapses it to a single outcome, so all the information in the other amplitudes is destroyed and can be extracted only statistically across many runs. An unknown quantum state cannot be copied, a result called the no-cloning theorem, which rules out the error correction strategy of simply keeping backup copies. And any interaction with the environment, a stray photon, a vibration, a fluctuating magnetic field, acts like a partial measurement and degrades the state, a process called decoherence which is the central engineering problem. Superconducting qubits currently hold coherence for microseconds to milliseconds, which sounds workable until you note that a useful algorithm may need billions of operations.

Quantum computers are not generally faster, and for most tasks they offer no advantage at all. The known speedups are specific:

• •Shor's algorithm, from 1994, factors large numbers in polynomial time, which would break the RSA and elliptic curve cryptography that secures most internet traffic, and is the reason governments fund the field
• •Grover's algorithm, which searches an unstructured list in roughly the square root of the number of items, a real but quadratic rather than exponential gain
• •Quantum simulation, proposed by Feynman in 1981 and the most likely early practical use, since simulating molecules and materials is exactly what classical computers do badly and what a quantum system does natively
• •Optimisation and machine learning applications, widely promoted and so far without a demonstrated advantage on a real problem
• •For the vast majority of computing, from spreadsheets to video, a quantum machine offers nothing and would be far slower

Several physical implementations compete, and none has won. Superconducting circuits, used by Google and IBM, are tiny loops of superconducting metal cooled to about fifteen millikelvin, colder than interstellar space, and are fast but short-lived. Trapped ions, used by several companies, hold individual charged atoms in electromagnetic fields and manipulate them with lasers, giving much longer coherence and much slower gates. Photonic approaches use light, neutral atoms held in optical tweezers have advanced quickly, and topological qubits, pursued by Microsoft, would in principle be intrinsically protected from noise and have proved extremely difficult to realise. Across all of them the limiting number is not the qubit count but the error rate, currently around one error in a thousand operations at best, where useful computation needs something closer to one in a billion.

The path from here runs through quantum error correction, which encodes one reliable logical qubit across many noisy physical ones, using measurements that detect errors without revealing the data. Current estimates put the overhead at roughly a thousand physical qubits per logical one for the leading scheme, which means that breaking modern cryptography would require millions of physical qubits against the low thousands that exist today. Google demonstrated in 2023 and again in 2024 that increasing the size of an error-correcting code reduces the error rate rather than increasing it, which was the key threshold result, and the field is now in the phase of scaling that up. Claims of quantum supremacy, in which a machine performs some contrived task faster than a classical supercomputer, have been made and then partly undercut by better classical algorithms each time, and they are milestones rather than applications. The practical consequence today is in cryptography, where the risk of an adversary storing encrypted traffic now and decrypting it in twenty years has driven standards bodies to publish post-quantum algorithms, which are classical and are being deployed already.

A quantum computer does not try every answer at once; it uses amplitudes that can cancel to make wrong answers interfere destructively, so a measurement is likely to yield the right one. Qubits exploit superposition and entanglement, and are limited by decoherence, the impossibility of copying an unknown state and the destructiveness of measurement. Known speedups are narrow, covering factoring, unstructured search and simulation of quantum systems, and useful machines require error correction with roughly a thousand physical qubits per logical one.