Dual-Rail Superconducting Qubit

Figure

Description

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 and photonic qubit design — converts dominant $T_1$ decay into detectable erasure errors and, in the transmon-pair implementation, enables microwave-free control via baseband pulses.

The concept originates in quantum optics (a single photon across two spatial modes is the canonical photonic qubit; see dual-rail-photonic-qubit), but the specific application to superconducting circuits was proposed by Shim & Tahan (2016), who recognized that the same encoding applied to coupled transmons yields a Hamiltonian formally identical to the semiconductor singlet-triplet qubit — with the logical splitting set by mode detuning, controllable by baseband flux/voltage pulses.

The encoding has been realized in two distinct physical platforms:

Transmon-pair (composite qubit, CQB) — Two capacitively coupled transmons with a small avoided crossing, controlled entirely by non-adiabatic baseband pulses and coherent Landau-Zener interference. No microwave drives required. First demonstrated by Campbell et al. (2020) with Clifford fidelities >99.7%.

Cavity dual-rail — Two microwave cavities (typically 3D stub cavities with photon lifetimes >1 ms) coupled by a transmon ancilla. The cavity version leverages long photon lifetimes and converts dominant photon loss into detectable erasure events. Note: the cavity implementation does use microwave drives for state preparation, beamsplitter operations, and readout — the strict “no microwave qubit drive” advantage applies primarily to the transmon-pair CQB. Demonstrated by Teoh et al. (2023, Yale/Schoelkopf) and Levine et al. (2024, AWS).

Key advantages of the dual-rail encoding:

• Erasure 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 channel into an erasure. The double-excitation state $|11⟩$ is also outside the codespace and detectable, but is reached by excitation errors (heating, gate errors), not by $T_1$ relaxation.
• Microwave-free control (CQB): In the transmon-pair implementation, all single-qubit gates are performed by baseband (DC) flux pulses that detune the two transmons, eliminating the need for microwave generators, mixers, and filters per qubit.
• Super-semi compatibility: The encoding is especially natural for variable-junction qubits (gatemons, super-semi junctions) where junction tunability replaces flux tunability.
• QEC efficiency: Erasure conversion reduces surface code overhead by 3–10× compared to standard depolarizing noise.

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 $\{|01⟩,|10⟩\}$ single-excitation 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 via flux) and $g$ is the transmon-transmon coupling. Logical $Z$ rotations come from $\Delta$ (tunable), logical $X$ rotations from $g$ (always-on exchange). This is formally identical to the singlet-triplet spin qubit Hamiltonian $H=(J/2){\sigma }_z+(g{\mu }_B\Delta B_z/2){\sigma }_x$ — the semiconductor-superconductor bridge that motivated the proposal.

Cavity dual-rail encoding

For two cavities coupled by a transmon ancilla, the beamsplitter interaction in the single-photon subspace gives the same effective Hamiltonian. The transmon mediates a parametrically activated coupling $g_{\text{BS}}(t)$ between the cavity modes, enabling controlled rotations in the logical subspace.

Motivation

• Erasure advantage: Converting $T_1$ errors (the dominant error channel in superconducting qubits) into detectable erasures dramatically improves QEC performance. Erasure errors are ~3× cheaper to correct than Pauli errors in surface codes.
• Microwave-free scaling (CQB): Eliminating microwave control lines removes a major bottleneck for scaling — no microwave generators, mixers, filters, or IQ calibration per qubit.
• Temperature tolerance: Baseband control may enable operation at higher temperatures where microwave thermal population is problematic.
• Cross-platform insight: The semiconductor-inspired encoding demonstrates that design principles from spin qubits can yield practical advantages in superconducting circuits.

Experimental Status

Transmon-pair CQB — Campbell et al. (2020):

• Two capacitively coupled transmons with small avoided crossing (gap < $k_{B}T$)
• Control: solely baseband pulses + Landau-Zener interference
• Average Clifford fidelity: >99.7% (randomized benchmarking)
• Coupled CQB-CQB operations demonstrated
• No microwave generators/mixers/filters needed

Cavity dual-rail — Teoh et al. (2023, Yale/Schoelkopf):

• Logical qubit in $|01⟩$/$|10⟩$ of two 3D stub superconducting cavities
• Photon lifetime: >1 ms
• Erasure:Pauli error ratio strongly biased (>10:1)
• QND parity measurement via transmon ancilla

Cavity dual-rail — Levine et al. (2024, AWS):

• Erasure detection rate: >99% of $T_1$ errors detected
• Effective $T_1$ (undetected): ~10× improvement over bare transmon
• First demonstration of erasure conversion in superconducting circuits

Erasure-detected logical measurements — Chou et al. (2024, Yale):

• Logical state preparation and measurement errors at the 0.01% level ($\sim 10^{-4}$)
• Over 99% of cavity decay events detected as erasures
• Confirmed error hierarchy: decay errors ~0.2%/μs, phase errors 6× less, bit flips ≥140× less
• First confirmation of the error hierarchy needed for efficient erasure code concatenation

Two-qubit gates — Mehta et al. (2025, Yale):

• Bias-preserving and error-detectable two-qubit entangling operations
• Demonstrated in dual-rail cavity system

Multi-qubit entanglement — Huang et al. (2026):

• Logical multi-qubit entanglement with dual-rail superconducting qubits
• Published in Nature Physics

Key Metrics

Metric	Value	Notes	Fidelity reference
Clifford fidelity (CQB)	>99.7%	Baseband-only control, Landau-Zener	Campbell et al. 2020
SPAM error (cavity)	~10⁻⁴ (0.01%)	Erasure-detected logical measurement	Chou et al. 2024
Cavity $T_1$	>1 ms	3D stub cavities	Teoh et al. 2023
Erasure detection rate	>99%	Dominant $T_1$ errors detected	Levine et al. 2024
Effective $T_1$ (undetected)	~10× bare	After erasure post-selection	Levine et al. 2024
Decay error rate	~0.2%/μs	Dominant error channel	Chou et al. 2024
Phase error rate	~6× lower than decay	Confirmed error hierarchy	Chou et al. 2024
Bit flip rate	≥140× lower than decay	Strongly suppressed	Chou et al. 2024

Scaling Considerations

• Microwave-free advantage (CQB): Eliminates 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. The confirmed error hierarchy (decay ≫ phase ≫ bit flip) enables efficient concatenation with tailored erasure codes.

References

Original proposal

• Y.-P. Shim and C. Tahan, “Semiconductor-inspired design principles for superconducting quantum computing,” Nature Commun. 7, 11059 (2016) — arXiv:1507.07923

Composite qubit (transmon-pair)

• D. L. Campbell et al., “Universal non-adiabatic control of small-gap superconducting qubits,” PRX 10, 041051 (2020) — arXiv:2003.13154

Cavity dual-rail

• J. D. Teoh et al., “Dual-rail encoding with superconducting cavities,” PNAS 120, e2221736120 (2023) — arXiv:2212.12077
• H. Levine et al., “Demonstrating a long-coherence dual-rail erasure qubit using tunable transmons,” PRX 14, 011051 (2024) — arXiv:2307.08737

Erasure-detected logical operations

• K. S. Chou et al., “Demonstrating a superconducting dual-rail cavity qubit with erasure-detected logical measurements,” Nature Phys. (2024) — arXiv:2307.03169
• N. Mehta et al., “Bias-preserving and error-detectable entangling operations in a superconducting dual-rail system,” arXiv:2503.10935 (2025)

Multi-qubit entanglement

• W. Huang et al., “Logical multi-qubit entanglement with dual-rail superconducting qubits,” Nature Phys. (2026)

Related photonic dual-rail

• E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46 (2001) — KLM protocol using dual-rail photonic encoding

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 — photonic ancestor encoding
• erasure-qubit — general erasure qubit concept
• transmon — physical qubit used in both implementations
• gatemon — natural super-semi variant for CQB
• singlet-triplet-qubit — semiconductor analog (formally identical Hamiltonian)
• circuit-qed — architecture for cavity dual-rail
• microwave-photonic-qubit — single-rail microwave photon encoding