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A gated quantum dot is an electron island confined in all spatial directions, weakly coupled by tunnel barriers to source and drain and tuned by a plunger gate. Small capacitance makes charge addition costly, while confinement resolves orbital levels. In the constant-interaction model,The charging contribution to successive addition potentials is $e^2/C_{\Sigma }$; the often used charging-energy scale $E_C=e^2/(2C_{\Sigma })$ differs by a factor of two. Orbital spacing and spin filling add further structure.

For weak coupling, $k_{B}T$ and lifetime broadening must be smaller than the relevant addition energies to see Coulomb blockade. Sequential tunnelling proceeds when an addition level is inside the source-drain bias window and the appropriate charge states are accessible. A gate sweep gives conductance peaks near charge degeneracies and low conductance between them. A bias-versus-gate map shows Coulomb diamonds, with excited-state lines when additional levels enter the window. Their slopes and sizes depend on source, drain and gate capacitances and the bias convention. Cotunnelling gives higher-order transport inside nominally blocked regions; stronger coupling and many-body effects can invalidate the simple sequential picture.

Coherent dot states as a qubit. A single-electron spin has basis $|0⟩=|\uparrow ⟩$, $|1⟩=|\downarrow ⟩$ in a magnetic field, split by $E_Z=|g^{\ast }|{\mu }_{B}B$. A qubit is a controllable coherent state $a|\uparrow ⟩+b|\downarrow ⟩$, not just a pair of classical current levels. Initialize through spin-selective loading or relaxation; resonant magnetic or spin-orbit-assisted electrical driving produces rotations. Adjacent occupied dots can couple through a gate-controlled exchange interaction. In the weak-tunnel symmetric Hubbard limit,Local spin rotations combined with a suitable exchange entangling operation provide universal control in the ideal spin-qubit proposal. Gate pulses must avoid unwanted orbital excitation and leakage, and complete coherent operations before dephasing destroys the information.^[ref]

For measurement, place the reservoir electrochemical potential between Zeeman levels so that only one spin state can tunnel out, or use Pauli spin blockade in a double dot. A nearby quantum point contact or single-electron transistor detects the resulting charge change. Such spin-to-charge conversion makes transport useful for reading a spin even when the stored information is not itself a net current.^[ref]

A double dot can alternatively encode a charge qubit in left/right occupation, with Hamiltonian $H=(\epsilon {\sigma }_z+2t_c{\sigma }_x)/2$. It allows electrical control and charge sensing, but couples strongly to charge noise. Spin qubits also suffer hyperfine, electrical and spin-orbit-related noise, as well as relaxation and readout errors. An observed Coulomb diamond alone establishes charging physics, not initialization, coherent control or a functioning qubit.

An electrostatically defined quantum dot uses depletion gates to confine a small island laterally in a two-dimensional electron gas. Two narrow barriers allow weak tunnelling to source and drain; a plunger gate tunes the island's electrochemical levels, and additional gates can form a double quantum dot. Adjusting the gates resolves successive charge states and eventually reaches the single-electron regime. An electrical dot is defined by confinement and tunnel coupling, not simply by the drawn metal area.

In a constant interaction model,Here $Q_g$ is gate-induced charge and $C_{\Sigma }$ total island capacitance. Successive additions cost $E_{\mathrm{add}}=e^2/C_{\Sigma }+{ϵ}_{N+1}-{ϵ}_N$, with spin, exchange and correlations modifying the orbital term. Coulomb blockade appears when no allowed charge transition lies in the source–drain energy window. Gate sweeps give charge steps and transport peaks; finite-bias Coulomb diamonds constrain charging and orbital energies under a stated bias convention. Resolved single-electron operation requires thermal and tunnel broadening smaller than the relevant addition energies.

Quantum-dot charge sensing avoids relying on a measurable current through a nearly isolated dot. A nearby quantum point contact biased on a sensitive conductance slope, or a single-electron transistor, responds capacitively when one electron enters or leaves the dot. A time trace of sensor current can therefore distinguish $N$ from $N-1$ and resolve individual tunnelling events. The sensor measures charge; a spin-dependent step is needed to measure spin.

For one electron, Zeeman splitting gives a lower and a higher spin level separated by $E_Z=|g^{\ast }|{\mu }_B|B|$. In energy-selective spin readout, initialize an empty dot and pulse both levels below the reservoir chemical potential to load one electron. Then move to a readout configurationAn electron in the higher state can tunnel out, temporarily leaving the dot empty, after which a lower-state electron can refill it. An electron initially in the lower state remains trapped. The charge sensor records a pulse for the first outcome and no escape pulse for the second. This is spin-to-charge conversion; it measures the spin projection along the field through a state-dependent tunnelling probability. A primary single-shot experiment uses this conversion with a quantum-point-contact charge detector.^[ref]

The readout window must be long enough to detect escape but short compared with excited-spin relaxation:Detector bandwidth must also resolve the empty-state dwell time before refilling. Thermal activation, relaxation before escape, missed fast events and sensor backaction cause errors. Since the excited electron can leave and be replaced, this simple sequence does not preserve an arbitrary initial spin state.

For coupled dots, label charge occupation by $(n_L,n_R)$. Gate-controlled detuning can make $(1,1)$ and $(0,2)$ accessible. Two electrons in the lowest orbital of one dot must form a singlet state; a triplet state requires a different orbital or another higher-energy configuration. Choose a measurement window where the $(0,2)$ singlet is available but the $(0,2)$ triplet is not. Thenunder spin-conserving tunnelling. The second process is forbidden by spin symmetry and the Pauli exclusion principle, producing Pauli spin blockade. Charge sensing distinguishes transfer from a blocked $(1,1)$ state. This measures singlet versus triplet content; without a reference spin or additional control it is not a measurement of each electron's absolute spin direction separately.

The exchange interaction in a double quantum dot provides control of these states. In an effective spin description,For a symmetric weak-tunnelling two-site model with onsite charging cost $U$, $J\simeq 4t_c^2/U$. Gates change tunnel coupling $t_c$ and detuning, allowing preparation and evolution followed by a charge-conversion measurement. Spin mixing from local magnetic-field differences or spin-orbit effects can lift blockade, so the sensing interval must be chosen before unwanted relaxation obscures the initial state. Single-dot readout uses spin-dependent escape; double-dot readout can use spin-dependent charge transfer. In both cases the measurable signal is a resolved charge change.