Recently, a team led by Academician Dapeng Yu at the Shenzhen International Quantum Academy (IQASZ), in collaboration with a team led by Researcher Xiaoming Sun at the Institute of Computing Technology, Chinese Academy of Sciences (ICT, CAS), reported a major advance in quantum error correction and fault-tolerant quantum computing. Using a superconducting quantum processor, the researchers implemented the Floquet-Bacon-Shor (FBS) error correction code. In addition to encoding a conventional static logical qubit, they successfully encoded a dynamical logical qubit, demonstrated the preservation and operations of two-logical-qubit states, and generated high-fidelity entanglement between the two logical qubits via a logical controlled-NOT (CNOT) gate. The work, titled “Logical Operations with a Dynamical Qubit in Floquet-Bacon-Shor Code”, was published online on November 25, 2025, in Physical Review Letters.

Figure 1. Simultaneous encoding of static and dynamical logical qubits based on the Floquet-Bacon-Shor code

Quantum computers are expected to outperform classical computers on certain complex tasks, but quantum states are inherently fragile and therefore require protection through quantum error correction. Conventional stabilizer codes—including the surface code, color code, and Bacon-Shor code—encode information redundantly across many physical qubits and repeatedly measure stabilizers to detect and suppress errors, with substantial progress demonstrated across multiple hardware platforms in recent years. However, these approaches generally store logical information in a time-invariant subspace, so the resulting logical qubits are effectively “static”.

More recently, time-dynamical quantum error correction—exemplified by Floquet codes and related extensions—has emerged as an alternative framework. By introducing periodic, low-weight parity-check measurements over time, the code structure itself evolves dynamically. This makes it possible to encode an additional dynamical logical qubit using the same physical resources, increasing encoding flexibility and potentially enhancing error correction performance—while opening a pathway toward more resource-efficient fault-tolerant quantum computing.

Figure 2. Preparation and preservation of two-qubit logical states

In this study, the researchers implemented the Floquet-Bacon-Shor (FBS) code on a 66-qubit superconducting quantum chip, using 21 qubits for the demonstration. The encoding employs a 3×3 array of data qubits surrounded by ancilla qubits. This Floquet-style implementation has distance 2 and requires only square-lattice connectivity. Unlike the conventional Bacon-Shor code, which encodes only a single static logical qubit, the FBS code retains that static logical qubit while also encoding an additional dynamical logical qubit in the gauge degrees of freedom by applying a period-4 schedule of weight-2 Pauli measurements—thereby realizing a coexisting pair of static and dynamical logical qubits within the same physical layout.

Experimentally, the team prepared all 36 two-logical-qubit Pauli eigenstates and characterized them using logical state tomography. Some states were generated with fault-tolerant preparation and showed higher encoding fidelity. With repeated rounds of stabilizer measurements for error detection and post-selection, the researchers achieved stable storage of two-logical-qubit states. For the logical states ∣−,0⟩ and ∣−,1⟩, the raw logical error rate was about 14% per round, which dropped to roughly 2.6% per round with error detection—substantially below the physical error level over the same timescale.

Figure 3. Logical gate operations on the dynamical logical qubit

During the experiments, the team also carried out a systematic study of logical-level operations, including both single-logical-qubit and two-logical-qubit gates. For the dynamical logical qubit, they inserted transversal single-qubit gates between rounds of stabilizer measurements to implement fault-tolerant logical Pauli operations. Averaged over a range of input logical states, the gate fidelities were essentially unchanged compared with the case where no gates were inserted, indicating that—within the error-detection framework—these operations introduce little to no additional logical error. The team also used ancilla qubits to implement arbitrary-angle rotations about different axes, and confirmed agreement with theory by tracking how the expectation values of logical operators vary with the applied rotation angle.

Building on these capabilities, the researchers designed and demonstrated a logical CNOT with the static logical qubit as the control and the dynamical logical qubit as the target, transforming the initial state ∣+,0⟩ into a Bell-entangled state of the two logical qubits. After error detection, the logical Bell-state fidelity reached 75.9%. Logical process tomography yielded a logical CNOT fidelity of approximately 84.1%; excluding certain input states with intrinsically lower encoding quality, the estimated gate fidelity could be as high as 93.6%. Together, these results show that implementing the Floquet-Bacon-Shor code on a superconducting quantum processor enables the joint encoding, preservation, and high-quality logical operations of static and dynamical logical qubits under quantum-error-correction protection—an important experimental step toward larger-scale, resource-efficient fault-tolerant quantum computing.

Figure 4. CNOT gate between dynamical and static logical qubits and the logical Bell state

In this work, Xuandong Sun (SIQA PhD student), Longcheng Li (master’s student at ICT, CAS; now a PhD student at the University of Cambridge), and Zhiyi Wu (PhD student, School of Physics, Peking University; visiting student at SIQA) are co-first authors. Dapeng Yu, Xiaoming Sun, Youpeng Zhong, and Ji Chu are the corresponding authors, with Academician Dapeng Yu as the last author. This research was supported by the Department of Science and Technology of Guangdong Province, the Shenzhen Science, Technology and Innovation Commission, the National Natural Science Foundation of China (NSFC), the Hefei National Laboratory, and other organizations.

Link to the paper: https://doi.org/10.1103/425n-6k9s