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A quantum computer processes information by preparing qubits, transforming their states with gates, and measuring selected qubits to produce classical results. Superposition and entanglement shape the calculation, but the machine cannot simply reveal every possible answer at once. Because physical qubits are noisy, reliable large-scale computation also depends on encoding information and repeatedly detecting errors.
What happens during a quantum computation?
In the circuit model, a computation follows a sequence: initialize qubits, apply quantum gates, then measure selected qubits. The gates transform the quantum state; measurement turns part of that state into ordinary classical data, such as a string of zeroes and ones.
Qubits represent quantum states
A classical bit is either 0 or 1. A qubit can instead be in a superposition of the computational basis states, written as α|0⟩ + β|1⟩. The amplitudes α and β determine the probabilities of the possible measurement outcomes. A measurement returns a classical result; it does not print both basis values as a list, and measuring can change the state.
Superposition is not the same as a computer calculating every answer and letting you inspect them all. A quantum algorithm arranges transformations so that amplitudes can interfere: some outcomes become more likely and others less likely. The useful result comes from the algorithm’s design and the statistics of measurement outcomes.
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Gates transform states
A quantum gate is a controlled operation on one or more qubits. A circuit combines these operations in a particular order, much as a classical program combines instructions, though quantum gates act on quantum states rather than directly manipulating ordinary bits.
- Hadamard: changes basis and can put a qubit that starts in a computational-basis state into superposition.
- CNOT: acts on two qubits. Depending on their input state, it can create entanglement.
- Clifford gates: IBM Quantum Learning’s stabilizer lesson groups Hadamard, S, and CNOT among the generators of Clifford circuits. T and Toffoli are not in that set; Clifford gates alone do not provide universal quantum computation.
Entanglement links qubits
Entangled qubits have correlations that cannot be described as independent states for each qubit. A gate such as CNOT can entangle qubits when applied to a suitable input. Algorithms use these multi-qubit relationships alongside interference; measuring one or more qubits then yields outcomes whose distribution carries information about the computation.
Why does measurement not reveal every answer?
Measurement gives a classical outcome, not a readable copy of the entire quantum state. In a circuit, a chosen measurement basis determines which property is read out, and the act of measurement generally changes the state. Algorithms therefore encode a task into the circuit so that useful answers are more likely to appear in repeated measurements.
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One run may produce only one outcome. To understand the result distribution, a computation may be run repeatedly, with the same circuit and input, and the outcomes analyzed classically. The number of runs and the chance of obtaining a useful result depend on the particular algorithm and hardware; there is no general promise that a quantum computer will be faster for every task.
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Why do quantum computers need error correction?
Physical qubits are imperfect. Errors can arise during initialization, gates, measurement, or while qubits are stored. The operations used to detect and correct errors can also fail or introduce additional errors, so correction must keep pace with faults throughout a computation.
Logical qubits encode information across physical qubits
A physical qubit is a hardware component. A logical qubit is encoded information spread across multiple physical qubits using a quantum error-correcting code. This redundancy is not a way to make arbitrary copies of an unknown quantum state. Instead, the code distributes information across a correlated state so that certain errors can be detected and corrected.
Syndrome measurements detect errors without reading the logical state
A code measures error syndromes: information that helps identify whether certain errors have occurred and what correction may be needed. These measurements are designed to reveal information about errors without directly measuring the encoded logical state, which would damage the computation. Codes can correct only the errors within their capabilities; they do not remove all noise automatically.
Correction is repeated as computation proceeds. Gates and measurements on encoded information also need protection in a fault-tolerant scheme, because errors can spread through operations if they are not controlled. This makes error correction an ongoing part of the computation rather than a one-time repair afterward.
Quantum codes use different constructions
IBM Quantum Learning’s course materials introduce the nine-qubit Shor code, seven-qubit Steane code, and five-qubit code, then develop stabilizer and CSS formalisms and discuss toric and surface codes. These named code sizes describe examples, not a universal overhead or a ranking of practical performance. Which code is suitable depends on its correctable error patterns, gate implementation, physical overhead, and the hardware’s noise assumptions.
What does fault tolerance mean?
Fault tolerance is a conditional route to reliable large computations, not a claim that current quantum hardware is error-free. IBM Quantum Learning explains the threshold result this way: in theory, if noise is below a certain threshold and operations are arranged to control error propagation, arbitrarily large reliable computations are possible.
There is no single threshold number that applies to every processor. The threshold depends on assumptions about the noise, code, and operations. Nor does adding error correction necessarily improve every device: the additional physical qubits and operations have their own error risks, and a scheme must control those faults well enough for its logical information to become more reliable.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.How should you compare quantum processors?
Qubit count alone does not tell you how much useful computation a processor can perform. IBM Quantum Learning identifies qubit count, errors per layered gate (EPLG), and circuit layer operations per second (CLOPS) as metrics to consider, while cautioning that their importance depends on the application.
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| Metric | What it helps describe | What it does not establish by itself |
|---|---|---|
| Qubit count | The number of qubits reported for a processor. | How many protected logical qubits are available, or how well a particular workload will run. |
| Errors per layered gate (EPLG) | An aspect of gate quality measured across layers of operations. | A complete measure of performance across every circuit or application. |
| Circuit layer operations per second (CLOPS) | Circuit-layer throughput on a specified benchmark. | A general ranking of useful computational capability across workloads. |
For a practical comparison, match metrics to the workload and consider connectivity as well as qubit count and error behavior. Also check whether a quoted count refers to physical or logical qubits: a physical-qubit total is not the number of error-protected logical qubits.
Where can you learn more?
IBM Quantum Learning’s introductory lesson, “Lesson 02: Bits, gates, and circuits,” dated April 19, 2024, presents the circuit-model foundations of qubits, gates, superposition, measurement, and entanglement. Its “Foundations of quantum error correction” course progresses from basic codes toward fault-tolerant computation. The course lists Quantum Computation and Quantum Information by Michael Nielsen and Isaac Chuang among its further-reading references; it is an optional, substantial technical reference rather than a prerequisite for understanding the basic model.
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