Singlet-Triplet Qubit

Description

This qubit is encoded in the Sz=0 subspace of two exchange-coupled electronic spins. These two spins are trapped inside quantum dots realized by electronic gates on the surface of a semiconductor, usually Si or GaAs, and are subject to a magnetic field gradient. The singlet state, (|up down>-|down up>)/sqrt(2), and the triplet state, (|up down>+|down up>)/sqrt(2), are the logical |0> and |1> states. Single-qubit gates are realized by tuning the exchange coupling between the two spins, which is done in experiments by changing the voltage on the electronic gate separating the two dots. The magnetic field gradient is required in order to perform rotations about axes other than the logical z axis.

These qubits may be coupled in one of two ways. One method is capacitive coupling, which uses the difference in dipole moment between the logical |0> and |1> states in order to couple qubits via dipole-dipole interaction. Another is exchange coupling, in which the exchange interaction between one of the spins in one qubit (say, the right-hand spin) and one of the spins in the other qubit (say, the left-hand spin) is used to couple the qubits.

Figure

Motivation

The most attractive property of the singlet-triplet qubit is the fact that both single- and two-qubit gates can be implemented entirely electronically, allowing for fast gates. After the single-spin Loss-DiVincenzo qubit, this is the next-simplest realization of a qubit possible using electronic spins in semiconductor-based quantum dots.

References

• https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.89.147902

Linked Papers

• petta-2005-singlet-triplet

Related Entries

• loss-divincenzo-qubit
• exchange-only-qubit
• rx-qubit
• aeon-qubit

Seed Metadata

• date_published: 2002-09-17

Physics

Logical qubit encoded in the singlet-triplet subspace of two electron spins in a double quantum dot:

$|0_L⟩=|S⟩=\frac{1}{\sqrt{2}}(|\uparrow \downarrow ⟩-|\downarrow \uparrow ⟩),|1_L⟩=|T_0⟩=\frac{1}{\sqrt{2}}(|\uparrow \downarrow ⟩+|\downarrow \uparrow ⟩)$

Both states have total $m_s=0$, providing first-order insensitivity to uniform magnetic field fluctuations. Control: exchange interaction $J$ (gate voltage) rotates around $\hat{z}$ of the logical Bloch sphere; magnetic field gradient $\Delta B_z$ between dots rotates around $\hat{x}$.

Related Qubits

• loss-divincenzo-qubit — single-spin ancestor
• exchange-only-qubit — three-spin descendant (no gradient needed)
• aeon-qubit — always-on variant

Key Metrics

Metric	Value	Notes	Fidelity reference
Qubit coherence $T_1$	>1 s	Spin relaxation in GaAs/Si	Petta et al. 2005
Qubit coherence $T_2$	1–200 μs	Limited by nuclear spin bath (GaAs) or charge noise	Bluhm et al. 2011
Gate fidelity (1Q)	99–99.9%	Exchange + gradient control	Nichol et al. 2017
Gate fidelity (2Q)	90–99%	Capacitive or exchange-mediated	Nichol et al. 2017
Gate time (1Q)	1–100 ns	Exchange pulse (Z) or gradient (X)	—
Gate time (2Q)	10–200 ns	Inter-double-dot coupling	—
Readout fidelity	95–99%	Pauli spin blockade + charge sensor	Barthel et al. 2009
Qubit footprint	~100–200 nm pitch	Two dots per logical qubit	—
Operating temperature	20 mK–100 mK	GaAs or Si/SiGe	—
Connectivity	Nearest-neighbor	Between adjacent double dots	—