[Paper Review] Dual-rail encoding with superconducting cavities

James D. Teoh, Patrick Winkel+16 more|arXiv (Cornell University)|Dec 22, 2022

Quantum Computing Algorithms and Architecture124 references4 citations

TL;DR

This paper proposes a dual-rail qubit encoded in the single-photon subspace of two superconducting microwave cavities, leveraging circuit-QED to detect and convert dominant photon loss errors into erasure errors. With a single transmon ancilla per qubit, the scheme enables universal gate operations, achieves a favorable error hierarchy with Pauli errors orders of magnitude smaller than erasures, and supports logical operations below surface code thresholds using current coherence times.

ABSTRACT

The design of quantum hardware that reduces and mitigates errors is essential for practical quantum error correction (QEC) and useful quantum computation. To this end, we introduce the circuit-Quantum Electrodynamics (QED) dual-rail qubit in which our physical qubit is encoded in the single-photon subspace of two superconducting microwave cavities. The dominant photon loss errors can be detected and converted into erasure errors, which are in general much easier to correct. In contrast to linear optics, a circuit-QED implementation of the dual-rail code offers unique capabilities. Using just one additional transmon ancilla per dual-rail qubit, we describe how to perform a gate-based set of universal operations that includes state preparation, logical readout, and parametrizable single and two-qubit gates. Moreover, first-order hardware errors in the cavities and the transmon can be detected and converted to erasure errors in all operations, leaving background Pauli errors that are orders of magnitude smaller. Hence, the dual-rail cavity qubit exhibits a favorable hierarchy of error rates and is expected to perform well below the relevant QEC thresholds with today's coherence times.

Motivation & Objective

• To design a hardware-efficient quantum error correction (QEC) platform that reduces error rates and improves logical fidelity.
• To mitigate dominant photon loss errors in superconducting cavities by converting them into detectable erasure errors.
• To implement universal quantum operations—including state preparation, logical readout, and parametrizable single- and two-qubit gates—using a minimal ancilla overhead.
• To achieve a favorable error hierarchy where Pauli errors are orders of magnitude smaller than erasures, enabling performance below QEC thresholds.
• To enable scalable, fault-tolerant quantum computation by leveraging the noise bias of cavity systems and ancilla-assisted error detection.

Proposed method

• Encoding the logical qubit in the single-photon subspace {|01⟩, |10⟩} of two coupled superconducting microwave cavities.
• Using a dispersively coupled transmon ancilla to perform state preparation, measurement, and gate operations via beamsplitter-type interactions.
• Implementing parametrizable single- and two-qubit gates using a controlled-Z (ZZ) interaction generated via the transmon-cavity coupling.
• Employing sideband drives to transfer a single excitation from the transmon to the cavity for fast, high-fidelity state preparation.
• Utilizing parity measurements and dynamical decoupling to detect and suppress unwanted cross-Kerr interactions between neighboring dual-rail qubits.
• Engineering the transmon-cavity coupling strength (χ ≈ 10 MHz) to enable fast two-qubit gates (~100 ns) while minimizing dephasing and Purcell effects.

Experimental results

Research questions

• RQ1 Can photon loss errors in superconducting cavities be detected and converted into erasure errors to improve QEC performance?
• RQ2 Can a universal set of logical operations be implemented with only one transmon ancilla per dual-rail qubit?
• RQ3 Does the dual-rail cavity qubit exhibit a favorable hierarchy of error rates, with Pauli errors significantly smaller than erasures?
• RQ4 Can the scheme achieve logical error rates below the surface code threshold using current coherence times?
• RQ5 How can unwanted non-linearities, such as cross-Kerr couplings, be mitigated during gate operations?

Key findings

• The dual-rail cavity qubit converts dominant photon loss errors into detectable erasure errors, which are easier to correct and have higher thresholds.
• With a single transmon ancilla per qubit, the scheme enables universal gate operations including state preparation, logical readout, and parametrizable single- and two-qubit gates.
• First-order hardware errors in cavities and transmons are detectable and converted into erasures, reducing background Pauli errors by orders of magnitude.
• The gate time for a ZZ(θ) interaction can be as fast as ~100 ns when χ ≈ 10 MHz, comparable to transmon-based two-qubit gates.
• The system achieves a favorable error hierarchy: erasures dominate, Pauli errors are orders of magnitude smaller, and leakage is minimal.
• The scheme is robust against cross-Kerr interactions between neighboring qubits, which can be canceled via dynamical decoupling or tunable couplers.