What is a qubit

A qubit is the fundamental unit of quantum information, analogous to a bit in classical computing. While a classical bit can be in a state of 0 or 1, the state of a qubit is

∣ ψ ⟩ = α ∣0 ⟩ + β ∣1 ⟩

where $α$ and $β$ are complex coefficients known as probability amplitudes. The state $∣ ψ ⟩$ is a linear combination — a superposition — of $∣0 ⟩$ and $∣1 ⟩$ , which collapses to 0 or 1 upon measurement with probabilities $∣ α ∣^{2}$ and $∣ β ∣^{2}$ respectively. By definition $∣ α ∣^{2} + ∣ β ∣^{2} = 1$ ^{Kumar et al. 2025}.

The same definition applies regardless of how the qubit is realised — a photon's polarisation, an electron's spin, an ion's hyperfine state, a transmon's two lowest energy levels. Each physical platform makes a different trade-off between coherence time, gate fidelity, and whether the qubit can travel; the rest of the page covers what those trade-offs are.

Notation primer

Bra–ket notation, due to Dirac, is shorthand for vectors and their duals. The ket $∣ ψ ⟩$ is a column vector in the complex Hilbert space $H$ ; the bra $⟨ ψ ∣$ is its conjugate-transpose, a row vector in the dual space. The two-level computational basis is just the two standard column vectors:

∣0 ⟩ = (10), ∣1 ⟩ = (01), ⟨ 0∣ = (10), ⟨ 1∣ = (01) .

For an $n$ -level system (a qudit), $∣ k ⟩$ is the column vector with a 1 in the $k$ -th slot (0-indexed) and zeros elsewhere — e.g. in a 4-level system:

∣0 ⟩ = 1000, ∣1 ⟩ = 0100, ∣2 ⟩ = 0010, ∣3 ⟩ = 0001 .

And a general ket has complex entries; its bra is the complex-conjugate row vector — for $∣ a ⟩ = α ∣0 ⟩ + β ∣1 ⟩$ , $⟨ a ∣ = (α^{*} β^{*})$ . The inner product $⟨ ϕ ∣ ψ ⟩$ is then ordinary row-times-column matrix multiplication, and it measures overlap between states. Qudits generalise this to $n > 2$ but lag qubits significantly and are not in current quantum-internet architectures ^{Kumar et al. 2025}.

The Bloch sphere

A pure single-qubit state can be represented as a point on the surface of a unit sphere — the Bloch sphere. Up to a global phase, every pure state can be written as

∣ ψ ⟩ = cos (\frac{θ}{2}) ∣0 ⟩ + e^{i φ} sin (\frac{θ}{2}) ∣1 ⟩

where $θ \in [0, π]$ and $φ \in [0, 2 π)$ are the polar and azimuthal angles. The two reference states $∣0 ⟩$ and $∣1 ⟩$ are called the computational basis — the pair of mutually exclusive outcomes a standard measurement can return, and the labels we use to write every other state as a superposition $α ∣0 ⟩ + β ∣1 ⟩$ . They sit at the poles of the sphere: $∣0 ⟩$ at the north ( $θ = 0$ ) and $∣1 ⟩$ at the south ( $θ = π$ ). Equal superpositions sit on the equator. Measuring in the computational basis means asking which of $∣0 ⟩$ and $∣1 ⟩$ did we get? — the answer is one of the two, with probabilities $∣ α ∣^{2}$ and $∣ β ∣^{2}$ . Single-qubit unitary gates correspond to rotations of the sphere; measurement is projection onto a chosen axis (the computational basis is the $z$ axis).

|ψ⟩ = cos(θ/2)|0⟩ + e^iφ sin(θ/2)|1⟩

|ψ⟩ = 1.00|0⟩ + 0|1⟩

θ 0 φ 0 F 1.00

Drag the sphere to rotate the view. Use the sliders to move the state vector, or jump to a basis state with the buttons.

Mixed states — states that are statistical mixtures rather than coherent superpositions — sit inside the sphere. A perfectly maximally mixed qubit (the result of complete decoherence) sits at the centre. Distance from the surface is one way of quantifying decoherence; pure-state fidelity is another.

Why two parameters, not four

$α$ and $β$ are complex, so a general $∣ ψ ⟩ = α ∣0 ⟩ + β ∣1 ⟩$ looks like it has four real degrees of freedom. Two constraints reduce that to two:

Normalisation — $∣ α ∣^{2} + ∣ β ∣^{2} = 1$ is one real equation. Three real parameters left.
Global phase is unobservable — every measurement outcome $∣ ⟨ m ∣ ψ ⟩ ∣^{2}$ is unchanged if we multiply $∣ ψ ⟩$ by any unit-modulus complex number $e^{iγ}$ . We can spend that freedom to make $α$ real and non-negative — write $α = ∣ α ∣ e^{i φ_{α}}$ and multiply by $e^{- i φ_{α}} = α^{*} /∣ α ∣$ . Two real parameters left.

Those two are precisely $θ$ and $φ$ : $∣ α ∣ = cos (θ /2)$ sets the polar angle, and the relative phase that survives — $φ = φ_{β} - φ_{α}$ — is the azimuth. Surface of a sphere, two coordinates.

Flying-qubit encodings

A flying qubit is a quantum state that travels — typically a single photon moving through optical fibre or free space. The mathematical representation is the same two-dimensional Hilbert space as any other qubit; what changes is which physical degree of freedom of the photon carries $∣0 ⟩$ and $∣1 ⟩$ . Each of the encodings below has a sweet spot in the channel and the kind of network it suits.

Polarisation

free-space

Direction of the electromagnetic field's oscillation: horizontal (H) and vertical (V) form the computational basis; diagonal (D, A) and circular (R, L) are equal superpositions on the Bloch sphere. Intuitive and used widely in free-space and short-fibre QKD. Birefringence in long fibre rotates the polarisation state and requires active compensation ^{Azuma et al. 2023}.

Active compensation has been shown to work on short metro routes: the Cisco × Qunnect Brooklyn ↔ 60 Hudson demonstration ran polarisation-entangled pairs over 17.6 km of deployed New York City fibre at >99 % fidelity using automatic polarisation controllers at every receiver, and the prior GothamQ run on the same route held 99.84 % uptime over ~15 days. Time-bin remains the default for long-haul prepare-and-measure QKD; on metro distances, polarisation is a viable option when the source produces polarisation pairs natively, not a forced choice over time-bin.

Time-bin

fibre

The photon arrives in one of two well-separated time slots — early or late. Time-bin is unaffected by fibre birefringence, making it the dominant encoding in metropolitan and long-haul QKD deployments today. The relative phase between the early and late modes is itself the resource Twin-Field QKD exploits to beat the rate-loss bound.

Frequency-bin

fibre

The photon occupies one of several discrete frequency modes (ω₁, ω₂, …). Compatible with deployed dense-wavelength-division-multiplexing (DWDM) infrastructure — quantum and classical channels can ride the same fibre on non-overlapping ITU grid slots. Useful for multiplexing many quantum channels on one fibre.

Path (spatial)

fibre

Which of two optical paths the photon takes. The default encoding inside integrated photonic chips: gates (beam splitters, phase shifters) compose cleanly, and measurement is unambiguous. As with time-bin, path-encoded photons prefer fibre over free-space transport ^{Azuma et al. 2023}.

All four encodings above are dual-rail in the broader sense — the qubit lives in two orthogonal modes (two polarisations, two time-bins, two frequency-bins, two paths), and $∣0 ⟩$ / $∣1 ⟩$ are which mode is occupied. The alternative is single-rail encoding, where the qubit lives in one mode and $∣0 ⟩$ / $∣1 ⟩$ are different states of that mode — Fock states (vacuum vs single photon), coherent / cat states, and GKP states are the standard examples. Single-rail encodings show up in continuous-variable QKD and in some bosonic error-corrected qubits but are not the focus of this series ^{Azuma et al. 2023}.

A photon can also carry multiple qubits at once by encoding in two or more of the above degrees of freedom simultaneously — known as hyperentanglement. Hyperentanglement is studied for boosted Bell-state measurement and certain repeater architectures, though managing multiple degrees of freedom adds significant complexity ^{Kumar et al. 2025}.

Stationary-qubit encodings

A stationary qubit is held in matter for the duration of computation or storage. Each platform picks two physical states and labels them $∣0 ⟩$ and $∣1 ⟩$ — mathematically still a two-level Hilbert space; only the underlying physics changes. The encoding choice determines the operating frequency, the dominant decoherence mechanism, and what kind of photon the platform can emit when it has to talk to the network. The cards below summarise the leading platforms; for the per-platform background and onward references see Ezratty's hardware survey ^{Ezratty 2025}.

Superconducting transmon

A small superconducting electrical circuit on a chip, cooled to about 15 mK so it behaves as a quantum object. The qubit's $∣0 ⟩$ and $∣1 ⟩$ are the circuit's ground and excited states, separated by ~5 GHz, and are manipulated by microwave pulses. Their short operation times (~20 ns) make them the leading platform for quantum processors ^{Meddeb 2025}. Used by Google, IBM, IQM, Rigetti, USTC.

Trapped ion (Yb⁺-171)

A single ytterbium ion confined in a vacuum chamber by electromagnetic fields. The qubit is encoded in two of the ion's internal energy levels (here the hyperfine sub-levels of the ground state), controlled by microwave and laser pulses. Trapped ions exhibit the longest coherence times of any platform — over an hour for Yb⁺-171 — making them strong candidates for quantum memories as well as computing ^{Meddeb 2025}. Used by Quantinuum, IonQ, Oxford Ionics, Universal Quantum.

Neutral atom (Rb-87)

A single rubidium atom held in place by a tightly focused laser beam — an optical tweezer. The qubit is encoded in two of the atom's hyperfine ground states, manipulated by microwave and laser pulses. Two-qubit gates briefly excite the atoms to a Rydberg state, where the Rydberg blockade prevents simultaneous excitation of nearby atoms and creates the entanglement. Used by Pasqal, QuEra, Atom Computing, Infleqtion.

NV centre (diamond)

A nitrogen atom adjacent to a missing carbon in a diamond lattice — a point defect that traps an electron. The qubit is the electron's spin, polarised and read out optically by green and red laser pulses, and manipulated by microwaves. NV centres work at room temperature with millisecond coherence in isotopically purified diamond, but their optical line is too broad and at the wrong wavelength (637 nm) for direct telecom use — quantum-network applications need wavelength conversion.

The defect electron is only half the story. Nearby ¹³C nuclear spins in the diamond lattice couple weakly to the electron via the hyperfine interaction and act as long-lived register qubits — T₂ in the seconds range, ten or more individually addressable nuclei per defect. Bradley et al. demonstrated a 10-qubit register around a single NV (one ¹⁵N, nine ¹³C) with electron-mediated gates ^{Bradley et al. 2019}. The electron is the comm qubit (talks to photons, short coherence); the nuclei are the memory qubits (no optical interface, long coherence). Without that split, an NV node would have one qubit, not ten.

SiV centre (diamond)

A silicon atom sitting at the bond centre between two adjacent vacancies in the diamond lattice — a colour-centre defect with a strong, narrow optical line at 738 nm. The qubit is the electron spin of the defect, controlled by microwaves and read out by spin-dependent fluorescence. Operates at ~4 K. The SiV's clean optical interface makes it the leading solid-state platform for quantum-network nodes — Knaut et al. demonstrated SiV-based entanglement between two nodes over a 35 km fibre loop ^{Knaut et al. 2024}.

SiV uses the same comm/memory split as NV but with a different isotope. Knaut's nodes pair the SiV electron spin (comm) with an adjacent ²⁹Si nuclear spin (memory) — T₂ ≥ 1 s with dynamical decoupling. Nuclear-spin registers are not a standalone qubit modality — they have no direct optical interface, so a defect electron has to mediate every gate and every herald — but they are why defect platforms scale past a single qubit per node.

Quantum dot (silicon spin)

Quantum dots are nanoscale semiconductor structures that confine single electrons; in the silicon flavour, gate electrodes patterned on a silicon chip form the trap ^{Meddeb 2025}. The qubit is the electron's spin (up vs down in an applied magnetic field), driven by microwave pulses. Coherence is exceptional in isotopically purified silicon-28 because the nuclear-spin background that normally dephases the electron is absent. Built on CMOS manufacturing, so potentially scalable to industrial densities. Quantum dots also play a separate role as single-photon sources for photonic networks (Quandela and others); that's a source component, not a stationary qubit — covered in the spectrum and transduction subjects.

Topological (Majorana)

A pair of Majorana zero modes at the ends of a topological superconducting nanowire — bound states with no individual location, only a shared fermion parity. The qubit is that parity (even or odd), and gates are performed by braiding the modes around each other rather than driving energy transitions. The non-local encoding gives theoretical protection against local noise. Pursued primarily by Microsoft; the least mature of the listed platforms, with the first plausible Majorana-mode demonstrations published in 2023–25.

Atomic ensemble

A cloud of $N$ atoms — a warm vapour cell, a cold atomic gas, or a rare-earth-ion-doped crystal — operated as a single collective qubit. The qubit is encoded in a delocalised spin-wave excitation shared symmetrically across the ensemble: $∣0 ⟩$ is all atoms in their ground state, $∣1 ⟩$ is a single quantum of excitation distributed across them. Used primarily as a quantum memory in DLCZ-style repeater protocols and Atomic-Frequency-Comb schemes; the collective enhancement gives strong coupling to single photons ^{Sangouard et al. 2011}.

Inside a single quantum processor or repeater node, stationary qubits are typically assigned distinct functional roles: computational qubits run the gates, ancilla qubits assist error correction and measurement, storage qubits hold state with extended coherence, and communication (or interface) qubits couple to flying qubits to generate the photons that carry entanglement out of the node ^{RFC 9340}.

Indistinguishability — what makes these quantum, not classical

Both flying and stationary encodings share a requirement that is easy to miss. An encoding produces a real qubit only when the carrier is indistinguishable in every degree of freedom apart from the one carrying the bit. If anything else tags the outcome, the superposition collapses to a classical mixture.

Time-bin is a useful worked example. A time-bin photon must arrive with the same frequency, polarisation, and pulse shape in both the early and the late slot. If the early slot is slightly redder than the late slot, that frequency difference tags which-slot the photon ended up in — a hidden which-slot label. The state is now a classical mixture (early or late, we just don't know which), not a genuine superposition $α ∣ early ⟩ + β ∣ late ⟩$ . The same logic governs every flying encoding. Dual-rail: the two paths must be matched in every other property, or the path is readable without measurement. Frequency-bin: pulse shapes at $ω_{1}$ and $ω_{2}$ must be matched in time and polarisation.

Photon-source quality is therefore a network-level concern. The Hong-Ou-Mandel dip — the bunching of two indistinguishable photons on a beam splitter — is the standard test for it. Heralded entanglement and entanglement swapping (covered in later subjects) both rely on a beam splitter erasing which-photon-came-from-where information; if the photons are distinguishable in any DOF, the erasure fails and the protocol degrades to classical correlation.

Stationary qubits face the same constraint, but in a milder form. Inside a single processor or repeater node, qubits don't need to be indistinguishable — they sit at known locations and are addressed individually. The constraint bites at the photonic interface: when two distant matter qubits interfere their emitted photons to herald entanglement, those photons must be indistinguishable, which means the emitters themselves must match in transition frequency, linewidth, and timing. Trapped ions and neutral atoms of the same isotope are quantum-mechanically identical particles, so their emissions are naturally well-matched. Solid-state defects (NV, SiV, quantum dots, Si spin) sit in slightly different local strain environments and emit at slightly different frequencies — bringing two emitters onto resonance requires active per-qubit tuning (DC Stark shifts, strain control). This is one reason why platforms that are excellent for local computation can still be difficult for networking, and why the same indistinguishability budget reappears in subjects on memories and repeaters.

DiVincenzo's criteria

DiVincenzo (2000) set out five criteria that a physical system must satisfy to qualify as a viable platform for quantum computation ^{DiVincenzo 2000}:

A scalable physical system with well-characterised qubits (a clean two-level subspace, identifiable across many copies).
The ability to initialise the qubit register to a simple fiducial state, such as $∣0 \dots 0 ⟩$ .
Long relevant decoherence times — much longer than the gate-operation time (typically ~10⁴× longer is the working threshold).
A universal set of quantum gates: arbitrary single-qubit unitaries plus at least one entangling two-qubit gate.
High-fidelity qubit-specific measurement in the computational basis.

DiVincenzo added two further criteria for quantum networking — that the platform must be able to interconvert between stationary and flying qubits, and there must be a means of faithful transmission of flying qubits between specified locations.

Why this matters for networks

Two computers built on different qubit modalities almost certainly emit at different optical frequencies and use different photon encodings. A superconducting transmon needs ~5 GHz microwave; a Yb⁺ ion's natural transition is at 369 nm; an NV centre's zero-phonon line is at 637 nm; deployed telecom fibre carries ~1550 nm. None of these match each other, and a usable inter-node link has to bridge the gap.

Bridging the gap involves two distinct pieces of engineering. First, transduction or quantum frequency conversion shifts the photon's wavelength while preserving its quantum state. Second, encoding translation converts between photonic encodings — for example, mapping a dual-rail qubit emerging from a photonic-computing chip onto a polarisation qubit for free-space transmission, then back again at the receiver. Both are active research areas.

Once a flying qubit reaches the destination it has to be re-stored, which means the receiving platform must support a communication qubit that couples its native stationary encoding to the incoming photon's encoding. Heterogeneous endpoints don't link by laying fibre between them; they link by agreeing on the photon's encoding and wavelength, plus the conversion steps to get there ^{RFC 9340}.

Physical and logical qubits

Today's commercial hardware operates physical qubits — the actual superconducting circuit, trapped ion, or photon — with finite coherence times, imperfect gates, and continuous interaction with the environment that erodes the state. A logical qubit is an error-corrected unit built from many physical qubits via a quantum-error-correction code, designed so that errors in the underlying physical qubits can be detected and corrected without measuring the logical state directly ^{Kumar et al. 2025}.

Surface codes — the most-studied family today — historically needed on the order of 1000 physical qubits per logical qubit at currently-achievable physical-qubit error rates. The overhead has fallen sharply over the past two years. Quantum LDPC codes are the recent advance: Bravyi et al.'s 2024 bivariate-bicycle code (IBM) encodes 12 logical qubits in 288 physical (~24:1) with error suppression on par with the surface code's ~250:1 ^{Bravyi et al. 2024}. More recently, the Zhao et al. 2026 ultra-high-rate codes on reconfigurable neutral-atom arrays reach encoding rates above 50 % — about 2:1 in physical-to-logical terms ^{Zhao et al. 2026}. Bosonic codes (cat, GKP) are a different family that protects fewer logical qubits per cavity but at much lower overhead per cavity. The number to cite is no longer "1000:1" — it depends on the code and the platform, and the trend is downward.

For the per-vendor product and roadmap roster — what's shipping today, what's on each vendor's public roadmap, and the physical / logical / modality numbers for each — see Companies › QC systems and roadmaps. That page is the one that tracks vendor facts, so the roster lives there.