Semiconductor Charge Qubit

Figure

Description

The semiconductor charge qubit encodes quantum information in the position of a single electron within a double quantum dot (DQD). The two computational basis states correspond to the electron being localized in the left dot ($|L⟩$) or the right dot ($|R⟩$), with the qubit state $|\Psi ⟩=\alpha |L⟩+\beta |R⟩$ representing a coherent superposition of charge configurations.

The double quantum dot is formed in a two-dimensional electron gas (2DEG) at a semiconductor heterointerface — typically GaAs/AlGaAs or Si/SiGe — using lithographically defined metallic gate electrodes that electrostatically confine electrons. Two quantum dots are coupled via a tunnel barrier, and the relative chemical potentials ${\mu }_L$ and ${\mu }_R$ of the dots are controlled by gate voltages $V_L$ and $V_R$. At zero detuning ($ϵ={\mu }_L-{\mu }_R=0$), the eigenstates are symmetric and antisymmetric superpositions split by twice the tunnel coupling $2t_c$.

Qubit operations are performed entirely electrically using fast voltage pulses that modulate the detuning $ϵ(t)$, driving coherent charge oscillations between the two dots. This all-electrical control is a major advantage, enabling gate times below 1 ns. However, the charge degree of freedom couples directly to electric field fluctuations (charge noise) in the solid-state environment, resulting in very short coherence times ($T_2^{\ast }\sim 1$ ns).

The semiconductor charge qubit is historically significant as the simplest semiconductor qubit and the first demonstration that artificial atoms can be formed from semiconductors with coherent quantum control. Its rapid decoherence motivated the development of spin-based encodings (Loss-DiVincenzo, singlet-triplet, exchange-only) that exploit the weaker coupling of spin to the charge noise environment.

Hamiltonian

$H=\frac{ϵ}{2}{\sigma }_z+t_c{\sigma }_x$

where:

• $ϵ={\mu }_L-{\mu }_R$ is the detuning between dot chemical potentials, controlled by gate voltages
• $t_c$ is the tunnel coupling between the two dots
• ${\sigma }_z=|L⟩⟨L|-|R⟩⟨R|$ is the charge polarization operator
• ${\sigma }_x=|L⟩⟨R|+|R⟩⟨L|$ is the tunneling operator

The energy eigenvalues are $E_{\pm }=\pm \frac{1}{2}\sqrt{{ϵ}^2+4t_c^2}$, producing a characteristic hyperbolic anticrossing with minimum splitting $2t_c$ at $ϵ=0$. At large detuning ($|ϵ|\gg t_c$), the eigenstates approach the localized charge states $|L⟩$ and $|R⟩$.

Key limitation: Charge noise enters linearly through $ϵ$ fluctuations, giving a dephasing rate ${\Gamma }_{\varphi }\propto |\partial E/\partial ϵ|$. At the sweet spot ($ϵ=0$), the first-order sensitivity vanishes ($\partial E/\partial ϵ=0$), but second-order sensitivity and the intrinsically strong charge-environment coupling still limit $T_2^{\ast }$ to the nanosecond scale.

Motivation

• Demonstrates that artificial atoms can be formed from semiconductors with all-electrical quantum control — foundational proof of concept for the entire semiconductor qubit field.
• Extremely fast gate times (<1 ns) due to direct electrical coupling, establishing the speed benchmark for semiconductor qubits.
• Simplest semiconductor qubit, providing a pedagogical and experimental stepping stone to more complex encodings.
• Compatible with semiconductor fabrication technology, motivating the search for charge-noise-insensitive encodings within the same platform.
• The short coherence times directly motivated the development of spin qubits (Loss-DiVincenzo, singlet-triplet, exchange-only) that exploit the spin degree of freedom’s weaker coupling to charge noise.

Experimental Status

First coherent manipulation — Hayashi et al. (2003):

• Demonstrated coherent charge oscillations in a GaAs/AlGaAs double quantum dot using pulsed gate voltages.
• Observed $T_2^{\ast }\sim 1$ ns, confirming the dominant role of charge noise.
• Used a quantum point contact for single-shot charge readout.

Charge qubit coherence — Petersson et al. (2010):

• Achieved quantum coherence in a one-electron semiconductor charge qubit with improved gate fidelity.
• Demonstrated $T_2^{\ast }$ of a few nanoseconds, limited by $1/f$ charge noise.
• Validated the double-quantum-dot charge qubit as a platform, while highlighting the need for spin-based approaches for longer coherence.

Key Metrics

Metric	Value	Notes	Fidelity reference
Qubit coherence $T_1$	~10 ns	Charge relaxation	Hayashi et al. 2003
Qubit coherence $T_2^{\ast }$	~1 ns	Dominated by $1/f$ charge noise	Hayashi et al. 2003
Gate time (1Q)	<1 ns	Very fast voltage pulses	—
Gate fidelity (1Q)	~90%	Limited by decoherence	Petersson et al. 2010
Readout fidelity	~95%	Quantum point contact	Petersson et al. 2010
Qubit footprint	~100–200 nm	Double quantum dot pitch	—
Operating temperature	20–100 mK	GaAs or Si heterostructure	—

References

Experimental demonstrations

• T. Hayashi, T. Fujisawa, H. D. Cheong, Y. H. Jeong, and Y. Hirayama, “Coherent Manipulation of Electronic States in a Double Quantum Dot,” Phys. Rev. Lett. 91, 226804 (2003)
• K. D. Petersson, J. R. Petta, H. Lu, and A. C. Gossard, “Quantum Coherence in a One-Electron Semiconductor Charge Qubit,” Phys. Rev. Lett. 105, 246804 (2010)

Related theory

• T. Fujisawa, T. Hayashi, R. Tomita, and Y. Hirayama, “Bidirectional counting of single electrons,” Science 312, 1634 (2006)

Linked Papers

• petersson-2010-semiconductor-charge

Related Entries

• loss-divincenzo-qubit — spin encoding in the same platform, much longer $T_2$
• singlet-triplet-qubit — two-electron spin encoding in a double quantum dot
• cooper-pair-box-charge-qubit — superconducting charge qubit analogue
• hybrid-qubit — exploits both charge and spin degrees of freedom
• silicon-spin-qubit — spin qubit in isotopically purified silicon