Demonstration of quantum error correction and universal gate set on a binomial bosonic logical qubit (1805.09072v1)

Abstract: Logical qubit encoding and quantum error correction (QEC) have been experimentally demonstrated in various physical systems with multiple physical qubits, however, logical operations are challenging due to the necessary nonlocal operations. Alternatively, logical qubits with bosonic-mode-encoding are of particular interest because their QEC protection is hardware efficient, but gate operations on QEC protected logical qubits remain elusive. Here, we experimentally demonstrate full control on a single logical qubit with a binomial bosonic code, including encoding, decoding, repetitive QEC, and high-fidelity (97.0% process fidelity on average) universal quantum gate set on the logical qubit. The protected logical qubit has shown 2.8 times longer lifetime than the uncorrected one. A Ramsey experiment on a protected logical qubit is demonstrated for the first time with two times longer coherence than the unprotected one. Our experiment represents an important step towards fault-tolerant quantum computation based on bosonic encoding.

• The paper achieves quantum error correction that extends the logical qubit lifetime by 2.8 times over unprotected qubits.
• The paper implements a universal gate set with 97.0% average fidelity, enabling complete logical operations within a cQED architecture.
• The paper employs a binomial bosonic code with iterative error detection, providing a scalable step towards fault-tolerant quantum computing.

Overview of Quantum Error Correction and Universal Gate Set on a Binomial Bosonic Logical Qubit

This paper presents a significant development in the field of quantum information processing, particularly in the area of quantum error correction (QEC) and logical qubit operations in bosonic systems. The authors experimentally demonstrate the complete control of a single logical qubit realized via a binomial bosonic code, incorporating encoding, decoding, repetitive QEC, and implementing a high-fidelity (97.0% process fidelity) universal quantum gate set. This work is conducted within a superconducting circuit quantum electrodynamics (cQED) architecture, utilizing a transmon qubit coupled to a bosonic mode in a 3D cavity.

Key Results

1. Quantum Error Correction: The paper achieves a QEC that extends the lifetime of the logical qubit by a factor of 2.8 compared to its uncorrected equivalent, closing in on the break-even point for quantum error correction. The bosonic logical qubit demonstrates a lifetime significantly longer than the unprotected versions, illustrating the efficacy of the implemented QEC strategy.
2. Universal Gate Set: The authors successfully demonstrate a universal set of quantum gates on the logical qubit with an average process fidelity of 97.0%. This includes the realization of complete logical operations within the code space, facilitated by high-fidelity Clifford gates on the bosonic logical qubit.
3. Ramsey Experiment: Notably, the paper reports a Ramsey experiment conducted on the QEC-protected logical qubit, showing a coherence time that is double that of the unprotected one. This highlights the potential of QEC-enhanced quantum metrology using bosonic logical qubits.

Methodological Innovations

The experiment employs a binomial coding scheme that is particularly advantageous due to its hardware efficiency and ability to correct photon loss errors. The bosonic mode encoding allows for tracking of single dominant error channels, making it compatible with the available technological resources. The authors utilize an iterative error correction approach that employs a two-layer detection strategy to optimize QEC performance, which is crucial considering the limited coherence times of ancillary transmon qubits.

Implications

The demonstrated techniques point towards scalable, fault-tolerant quantum computing based on bosonic codes. The ability to perform high-fidelity quantum gates on protected logical qubits bridges a critical gap in the practical realization of quantum algorithms. This work positions the use of bosonic modes as a promising avenue for future quantum processors, which could also support implementations of fault-tolerant logical qubit networks or quantum repeater systems.

Future Directions

Progressing from this work, several paths stand out. These include increasing the coherence times of ancillary qubits, implementing more sophisticated error-correction strategies that could further extend logical qubit lifetimes beyond their break-even points, and exploring interactions between multiple logical qubits encoded in different bosonic modes. Enhancing the fidelity and robustness of these processes will be key to unlocking more complex quantum computing and communication paradigms.

This research contributes foundational insights into bosonic error correction and logical gates, facilitating a major step towards robust, fault-tolerant quantum computation with bosonic systems. Future studies may explore the scalability and integration of such bosonic systems into larger quantum architectures, fundamentally altering the landscape of quantum computing.