Quantum Computing Error Rate Reduced by 6.8% Using Soft Information, Researchers Find

Researchers from QuTech, Kavli Institute of Nanoscience at Delft University of Technology, Riverlane, Delft Institute of Applied Mathematics, and the University of Sheffield have demonstrated the benefits of incorporating soft information into the decoding process of a superconducting logical qubit. The team used a 3×3 data qubit array to encode each of the 16 computational states that make up the logical state 0L and protect them against bitflip errors. Their results showed a reduction of up to 6.8% in the extracted logical error rate with the use of soft information, which could lead to significant improvements in the performance of quantum computing systems.

What is the Significance of Reducing the Error Rate of a Superconducting Logical Qubit?

Quantum error correction is a critical aspect of quantum computing that allows for the preservation of logical qubits with a lower logical error rate than the physical error rate. The performance of this process depends on the decoding method used. Traditional error decoding approaches often rely on the binarization or hardening of readout data, which can ignore valuable information embedded in the analog soft readout signal.

A team of researchers from QuTech and Kavli Institute of Nanoscience at Delft University of Technology, Riverlane, Delft Institute of Applied Mathematics, and the Department of Physics and Astronomy at the University of Sheffield have presented experimental results that showcase the advantages of incorporating soft information into the decoding process of a distance three (d=3) bitflip surface code with transmons. The team used a 3×3 data qubit array to encode each of the 16 computational states that make up the logical state 0L and protect them against bitflip errors by performing repeated Z-basis stabilizer measurements.

The researchers employed two decoding strategies: minimum weight perfect matching and a recurrent neural network. Their results showed a reduction of up to 6.8% in the extracted logical error rate with the use of soft information. This approach is widely applicable, independent of the physical qubit platform, and could reduce the readout duration further, minimizing logical error rates.

How Has Quantum Error Correction Progressed Over the Years?

Over recent years, small-scale quantum error correction experiments have made significant progress. This includes fault-tolerant logical qubit initialization and measurement, correction of both bit and phase-flip errors in a distance-three (d=3) code, magic state distillation beyond breakeven fidelity, suppression of logical errors by scaling a surface code from d=3 to d=5, and demonstration of logical gates.

The performance of these logical qubit experiments across various qubit platforms is dependent on the fidelity of physical quantum operations, the chosen quantum error correction codes and circuits, and the classical decoders used to process quantum error correction readout data. Common error decoding approaches with access to analog information often rely on digitized binary qubit readout data as input to the decoder. The process of converting analog to binary outcomes inevitably leads to a loss of information that reduces decoder performance.

What is the Advantage of Using Soft Information in Quantum Error Correction?

Incorporating analog soft information in the decoding of quantum error correction experiments can potentially improve the threshold by 25% compared to decoding with hard binary information. This advantage has been demonstrated on simulated data with neural network decoders. Soft information decoding has also been realized for a single physical qubit measured via an ancilla in a spin-qubit system and for a superconducting-based quantum error correction experiment with a simple error model assuming uniform qubit quality.

The incorporation of soft information with variable qubit fidelity can theoretically provide further benefit when decoding experimental data. However, this can be challenging as additional noise sources, such as leakage and other non-Markovian effects, add complexity. Therefore, the advantage of decoding with soft information is not guaranteed.

How Was Soft Information Used in the Decoding Process of the Experiment?

In the experiment conducted by the researchers, soft information was used in the decoding process of experimental data obtained from a bitflip d=3 code in a 17-qubit device using flux-tunable transmons with fixed coupling. Unlike a typical d=3 surface code with both X and Z stabilizers, the researchers repeatedly measured Z-basis stabilizers and protected against bitflip errors throughout varying quantum error correction rounds.

This approach allowed the researchers to avoid problematic two-qubit gates between specific pairs of qubits that occur due to strong interactions of the qubits with two-level system (TLS) defects. The researchers encoded and stabilized each of the 16 computational basis states that occur in the superposition of the 0L state and approximated its performance by averaging across these states. They employed two decoding strategies to extract a logical fidelity: a minimum weight perfect matching decoder and a recurrent neural network decoder.

What Were the Results of the Experiment?

For each decoding strategy, the researchers compared the performance across two variants: one with soft information and one without. With soft information, the extracted logical error rates were reduced by 6.8% and 5% for the minimum weight perfect matching and neural network decoders, respectively.

In the d=3 code used in the experiment, the 0L state is defined as the uniform superposition of the 16 data qubit computational states. These computational states are eigenstates of the Z-basis stabilizers and the logical operator ZL of the surface code with eigenvalue. Therefore, they can be used to protect a logical qubit from single bitflip errors.

The results of this experiment demonstrate the potential of using soft information in the decoding process of quantum error correction, which could lead to significant improvements in the performance of quantum computing systems.