Single-period Floquet Control Achieves High-Fidelity Bosonic Codes with Lattice Gates

Bosonic codes offer a compelling pathway towards achieving fault-tolerant quantum computation, yet current methods for their control often require lengthy and complex procedures. Tangyou Huang from Chalmers University of Technology, alongside Lei Du and Lingzhen Guo from Tianjin University, have addressed this challenge with a novel approach to manipulating these codes. Their research introduces a deterministic Floquet method capable of synthesising arbitrary unitaries within a single driving period, significantly reducing the time and complexity of existing protocols. This breakthrough enables the creation of practical pseudorandom unitaries in continuous-variable systems and facilitates the implementation of high-fidelity single-qubit logical gates using lattice gates, paving the way for more efficient quantum circuits. By fully utilising the inherent nonlinearity of Josephson junctions, the team demonstrates a powerful technique for advancing bosonic quantum computation.

The analytical construction of bosonic codes typically relies on slow adiabatic ramps requiring thousands of driving periods, a limitation circumvented by this new method. This innovative approach introduces an analytical and deterministic Floquet method capable of directly synthesising arbitrary unitaries within a single period, dramatically accelerating the process and paving the way for faster and more scalable continuous-variable quantum computing.

Researchers prepare various prototypical bosonic codes starting from the vacuum state and implement single-qubit logical gates with high fidelities utilising quantum lattice gates. These gates harness the full intrinsic nonlinearity of Josephson junctions, decomposing complex quantum circuits into a series of efficient, primitive operations suitable for continuous-variable computation. Central to this work is the development of a noncommutative Floquet engineering technique, building upon the Floquet theorem which describes the stroboscopic evolution of time-periodic Hamiltonians.

Scientists designed a time-periodic potential to synthesize a desired Floquet Hamiltonian within a cavity, effectively realizing an arbitrary unitary operation on a d-dimensional subspace of the cavity mode. The method relies on identifying a Hermitian generator such that the target unitary operator can be expressed as an exponential function, where a scaling factor is applied. Validation involved generating gate ensembles with fidelity statistics mirroring those of Haar-random unitaries, confirming the quality of the synthesized operations.

Experiments began with the preparation of prototypical bosonic codes directly from vacuum states, leveraging quantum lattice gates to implement single-qubit logical gates. An optimal pulse engineering technique was implemented to prepare binomial, cat, and Gottesman-Kitaev-Preskill codes directly from vacuum, achieving remarkably low state infidelities below 10−5. The study culminated in the demonstration of high-fidelity logical gates for these codes, achieving average gate errors on the order of 10−4, a performance improvement exceeding three orders of magnitude compared to existing adiabatic protocols.

Single-Period Floquet Synthesis of Unitaries

Bosonic codes offer a promising pathway towards fault-tolerant quantum computation, and this study addresses a significant limitation of existing Floquet protocols: their reliance on exceedingly slow adiabatic ramps. Researchers engineered a novel analytical and deterministic Floquet method capable of directly synthesizing arbitrary unitaries within a single period, dramatically accelerating the process. The team developed a technique to generate phase-space unitary ensembles that accurately reproduce Haar-random statistics, enabling the creation of practical pseudorandom unitaries essential for continuous-variable systems.

Floquet Synthesis Achieves Haar-Random Unitaries in Bosonic Codes

Scientists have developed a novel Floquet method for synthesizing unitaries within a single period, representing a significant advancement in bosonic code development. The research team achieved the creation of phase-space unitary ensembles that faithfully reproduce Haar-random statistics, enabling the generation of practical pseudorandom unitaries in continuous-variable systems. Data shows that this quantum logical gate approach serves as a practical generator of pseudo-random unitaries, crucial for robust quantum computation. The study validated this approach by successfully preparing binomial, cat, and GKP codes from vacuum states.

Measurements confirm that this approach enables single-qubit logical gate operations on the code space, with arbitrary target unitaries synthesized via quantum lattice gates for each of the three bosonic codes. To quantify performance, the team benchmarked single-qubit gates using the average gate fidelity, and optimal pulse engineering was developed to mitigate errors under specific hardware constraints. Results demonstrate that the infidelity decreases rapidly as the number of driving periods increases, eventually saturating around 10−6.

Further analysis involved sampling target single-qubit logical gates, revealing statistical stability. The elementary gates , Hadamard, phase, and π/8 , were all realized with gate errors ≲ 10−4 using optimal control, comparable to state-of-the-art superconducting single-qubit gate performance.

Floquet Protocol Enables Fast Bosonic Code Control

This work introduces a new analytical Floquet protocol for bosonic codes, achieving the direct synthesis of arbitrary unitaries within a single period, a significant improvement over existing methods. Researchers demonstrated high-fidelity preparation of Haar-distributed quantum states and assessed controllability using quantum lattice gates, successfully implementing single-qubit logical gates with errors comparable to state-of-the-art superconducting qubits. This advancement bypasses the need for slow adiabatic ramps and complex variational searches previously required for bosonic code manipulation.

The demonstrated ability to prepare binomial, cat, and GKP codewords, alongside universal single-qubit logical gates, establishes a hardware-compatible and efficient pathway towards universal continuous-variable quantum computation. Authors acknowledge limitations related to coherent control errors and decoherence, though further analysis suggests the short operation times inherent in their approach offer substantial robustness. Future research directions include extending the framework to two-qubit logical gates and exploring applications in areas such as quantum reservoir computing and quantum t-designs.