The team obtained encoding fidelities above 0.99 for arbitrary input qubit states, even accounting for limitations imposed by Kerr nonlinearities and dissipation within the system. This advance builds upon a previously established controlled-squeezing gate [Phys. Rev. A 111, 042606 (2025)], and uses a refocusing technique to suppress unwanted effects arising from slowly varying time-dependent terms in the Hamiltonian. The work allows for the generation of more complex superpositions of squeezed states using a control qudit.

Refocusing Technique Suppresses Hamiltonian-Based Errors

The implementation of a high-fidelity conditional-squeezing gate relies on cancelling effects from slowly varying terms within the Hamiltonian, a feat achieved through a carefully orchestrated protocol. Specifically, the work demonstrates that a refocusing technique, using a symmetry inherent in the system’s bichromatic drive, effectively suppresses these time-dependent errors. Rev. A 111, 042606 (2025)]. The protocol unfolds in four distinct steps, beginning with the evolution of the qubit-resonator system under the initial Hamiltonian.

Following the application of a π pulse at time τ, the system then evolves under a transformed Hamiltonian, effectively retracing its steps. Simulations reveal that this process dramatically reduces induced phase deviations; for a 250 nanosecond protocol, the induced phase reaches 1.8 x 10^-8 radians, a substantial improvement over an uncompensated gate. This advance allows for the encoding of arbitrary qubit states into superpositions of single- and two-mode squeezed states of the resonator.

Conditional-Squeezing Gate Generalizes Controlled-Squeezing Operation

The newly demonstrated conditional-squeezing gate expands upon previously established controlled-squeezing techniques detailed in Phys. Rev. A 111, 042606 (2025). This gate achieves conditional operation by squeezing a resonator mode along a direction dictated by the state of a dispersively coupled qubit, a process reliant on suppressing unwanted effects during parametric resonance. These non-Gaussian states, generated through the conditional-squeezing operation, enable error-detectable encoding through parity measurements. The physical mechanism driving this operation involves exciting qubit-state-dependent parametric resonance within a SQUID-terminated resonator, creating the necessary squeezing effect. The encoding algorithm uses the two-mode conditional-squeezing gate.

The researchers state, “We use it as part of an encoding protocol that maps an arbitrary qubit state onto logical states that are superpositions of squeezed states, achieving numerical encoding fidelities exceeding 0.99.” The potential extends beyond current applications; the researchers envision extending this scheme to generate higher-order superpositions of squeezed states, a class of rotation-symmetric bosonic codes, using a control qudit.

Encoding Qubit States into Superpositions of Squeezed States

The ability to create superpositions of squeezed states offers a pathway toward more robust quantum information processing, and a recently implemented conditional-squeezing gate achieves encoding fidelities above 0.99 for arbitrary qubit states. The resulting encoded states, which are non-Gaussian, allow for error detection through parity measurements of the resonator. Achieving high fidelity in this encoding is limited by Kerr nonlinearities and dissipation, but the implemented gate demonstrably performs close to the ideal case under unitary evolution.

This means that the loss of a single photon immediately signals an error.

Encoding Fidelity Exceeds 0.99 with Optimized Parameters

Numerical simulations reveal a fidelity deviation of less than 4 x 10^-7 across all initial qubit states when employing the two-mode conditional-squeezing gate with refocusing. The algorithm encodes an arbitrary qubit state into a superposition of resonator states, using logical states defined as either or, as detailed in equations found in Appendix A.

The researchers state, “We show that refocusing substantially improves the encoding fidelity, which is ultimately limited by Kerr nonlinearities and dissipation in realistic implementations.”

Extending the Scheme to Multi-Mode Bosonic Codes

The underlying Hamiltonian governing the SQUID-terminated resonator mode, detailed in the Supplementary Material, reveals the oscillatory behavior of bosonic operators at frequencies dependent on the qubit state. Analysis of fidelity loss across cardinal states of the Bloch sphere, poles and equator, indicates a consistent loss of approximately 0.17%, resulting in a minimum fidelity of 0.9977 at the equator.

Photon losses within the resonator are identified as the primary source of infidelity, yet the two-mode scheme demonstrably achieves higher fidelities in shorter gate times compared to the single-mode conditional-squeezing gate. Further adaptation of the refocusing protocol, including a D-frequency drive and time-inversion scheme, is currently under investigation to address the broader class of rotation-symmetric bosonic codes.

👉 More information
🗞 High-fidelity conditional-squeezing gate in superconducting circuits via refocusing
✍️ Roman Schiaffino, Fernando C. Lombardo and Juan Pablo Paz
🧠 DOI: http://link.aps.org/doi/10.1103/mqt6-fh7c

More like this