Dual-Rail Superconducting Qubit

The dual-rail superconducting qubit encodes quantum information in the single-excitation subspace of two coupled superconducting modes: $|0_L⟩=|01⟩$ and $|1_L⟩=|10⟩$. This encoding — borrowed from semiconductor spin-qubit design — enables microwave-free control via baseband pulses, intrinsic leakage detection, and conversion of dominant $T_1$ decay into detectable erasure errors. The concept has been realized in two forms: transmon pairs (composite qubit) and cavity pairs (cavity dual-rail).

Figure

Description

Photonic ancestry

The dual-rail encoding itself originates in quantum optics: a single photon across two spatial modes ($|01⟩$/$|10⟩$) has been the canonical photonic qubit since the late 1990s (see dual-rail-photonic-qubit). The key insight of Shim & Tahan (2016) was recognizing that the same encoding applied to superconducting modes unlocks microwave-free control — because the logical splitting is the mode detuning, controllable by baseband flux/voltage pulses. The SC dual-rail is thus a cross-platform translation of a photonic concept through semiconductor physics.

Semiconductor-inspired origin

The dual-rail SC qubit was proposed by Shim et al. (2016) as a direct translation of semiconductor encoded qubit principles into superconducting circuits. In semiconductor spin qubits, two spins encode one logical qubit in $|01⟩$/$|10⟩$ because individual spins lack tunable frequencies. Superconducting qubits have tunable frequencies, making this encoding optional — but it brings profound advantages:

• Microwave-free control: The logical qubit splitting is the difference frequency of the two physical qubits, which can be tuned to zero. All single-qubit gates are performed by baseband (DC) flux pulses that detune the two qubits, driving coherent oscillations between $|01⟩$ and $|10⟩$. No microwave drives needed.
• Leakage detection: The encoded subspace $\{|01⟩,|10⟩\}$ has exactly one excitation. Any $T_1$ decay produces $|00⟩$, which is outside the codespace and detectable — converting the dominant error into an erasure.
• Super-semi compatibility: The encoding is especially natural for variable-junction qubits (gatemons, super-semi junctions) where junction tunability replaces flux tunability.

Composite qubit (CQB)

Campbell, Kannan, et al. (2020) demonstrated a composite qubit formed from two capacitively coupled transmons with a small avoided crossing (smaller than temperature). Controlled entirely by non-adiabatic baseband pulses and coherent Landau-Zener interference, achieving Clifford fidelities >99.7% without any microwave drives.

Cavity dual-rail

Teoh et al. (2023, Yale/Schoelkopf) and Levine et al. (2024, AWS) encode the qubit in $|01⟩$/$|10⟩$ of two microwave cavities coupled by a transmon ancilla. The cavity version leverages the long photon lifetimes (>1 ms in 3D stub cavities) and converts dominant photon loss into detectable erasure events. Chou et al. (2024) demonstrated erasure-detected logical measurements with error rates at parts-per-$10^5$.

Hamiltonian

Transmon-pair encoding:

$H=\frac{{\omega }_1}{2}{\sigma }_z^{(1)}+\frac{{\omega }_2}{2}{\sigma }_z^{(2)}+g({\sigma }_{+}^{(1)}{\sigma }_{-}^{(2)}+\text{h.c.})$

In the $\{|01⟩,|10⟩\}$ subspace, this reduces to:

$H_{\text{encoded}}=\frac{\Delta }{2}{\tau }_z+g{\tau }_x$

where $\Delta ={\omega }_1-{\omega }_2$ is the detuning (baseband-controllable) and $g$ is the coupling. Logical $X$ rotations come from $g$ (always-on), logical $Z$ rotations from $\Delta$ (tunable via flux). This is formally identical to a singlet-triplet spin qubit Hamiltonian — the semiconductor-superconductor bridge.

Performance Metrics

Metric	Value	Notes	Fidelity reference
Clifford fidelity (CQB)	99.7%	Baseband-only control, Landau-Zener	campbell-2020-composite-qubit
SPAM error (cavity)	~10⁻⁵	Erasure-detected, Yale 2024	teoh-2023-dual-rail-cavity
Cavity T₁	>1 ms	3D stub cavities	teoh-2023-dual-rail-cavity
Erasure detection rate	>99%	Dominant T₁ errors detected	levine-2024-dual-rail-erasure
Effective T₁ (undetected)	~10× bare	After erasure post-selection	levine-2024-dual-rail-erasure

Scaling Considerations

• Microwave-free advantage: Eliminates need for microwave generators, mixers, and filters per qubit — major simplification for large-scale systems.
• Temperature tolerance: Baseband control may enable operation at higher temperatures where microwave thermal population is problematic.
• Super-semi synergy: Gate-voltage-tunable junctions (gatemons) are a natural fit: detuning is controlled by gate voltages rather than flux, avoiding flux noise entirely.
• QEC integration: Erasure conversion reduces surface code overhead by 3–10× compared to standard depolarizing noise.

Linked Papers

• shim-2016-semiconductor-inspired
• campbell-2020-composite-qubit
• teoh-2023-dual-rail-cavity
• levine-2024-dual-rail-erasure

Related Entries

• dual-rail-photonic-qubit
• erasure-qubit
• transmon
• gatemon
• singlet-triplet-qubit
• circuit-qed