Fault-tolerant GKP Gates Achieve Arbitrarily Small Logical Rate with On-Demand Noise Biasing

Quantum computers promise revolutionary computational power, but building stable and reliable qubits remains a significant challenge. Minh T. P. Nguyen and Mackenzie H. Shaw, both from Delft University of Technology, now demonstrate a pathway towards more robust quantum computation using a specific type of qubit encoded in light, known as the Gottesman-Kitaev-Preskill (GKP) code. Their research addresses a critical limitation of GKP qubits, the difficulty of implementing certain essential quantum operations without introducing errors, and they achieve this by developing a method to actively control the noise affecting the qubit during these operations. This on-demand noise biasing technique allows for arbitrarily precise gate control, and the team’s analysis, supported by detailed simulations, shows that high-fidelity quantum gates are achievable with realistic levels of quantum control, representing a substantial step towards practical, fault-tolerant quantum computing with bosonic codes.

The central goal is to develop robust and efficient methods for encoding, manipulating, and decoding quantum information, protecting it from noise affecting real-world hardware. Researchers are deeply concerned with the practical implementation of these codes, not just theoretical feasibility. GKP codes encode qubits into continuous-variable degrees of freedom, like the position and momentum of a harmonic oscillator, offering advantages in error thresholds and code distance. Superconducting qubits are a leading platform for building these quantum computers, and the focus is on implementing GKP codes within this technology. Scientists are particularly interested in finding minimal polynomials that achieve the desired gate operation with minimal resource overhead, emphasizing careful characterization of noise and optimization of code parameters.

GKP Qubit Control via Noise Biasing

Scientists have developed a novel method for implementing a logical T gate within the Gottesman-Kitaev-Preskill (GKP) error correcting code, achieving fault tolerance and improved performance. Researchers demonstrated that this biasing can be achieved using a standard GKP syndrome extraction circuit, effectively switching between a non-biased code suitable for Clifford gates and a biased code optimized for T gates. The team’s methodology involves precisely controlling the noise profile of the GKP codestate before and after applying the T gate, ensuring optimal performance.

Through rigorous mathematical proof and numerical investigation, scientists demonstrated that the logical error rate of the T gate can be made arbitrarily small as the quality of the GKP codestates increases, achieving average gate fidelities exceeding 99% with 12 dB of GKP squeezing without relying on post-selection techniques. Furthermore, the study pioneered a formalism for finding optimal unitary representations of logical diagonal gates within the Clifford hierarchy, utilizing “polynomial phase stabilizers,” providing a powerful algebraic tool for analyzing non-Clifford gates in bosonic quantum codes. This work addresses a fundamental challenge in implementing logical quantum gates, demonstrating that the logical error rate can be made arbitrarily small as the quality of the GKP codestates improves. The team proposes a circuit that allows for precise control over noise biasing, enabling the codestate to be adjusted before a gate operation and returned to its original state afterward. Experiments reveal that the cubic phase gate can achieve average gate fidelities exceeding 90% with 12 dB of GKP squeezing, without the need for post-selection techniques. The researchers developed a formalism for finding optimal representations of logical gates, utilizing “polynomial phase stabilizers” whose exponents are polynomial functions of quadrature operators, providing a powerful algebraic tool for analyzing complex quantum operations. This framework extends naturally to multi-qubit gates and number-phase bosonic codes.