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arXiv:2308.15320 · Nature Communications

Universal control of a bosonic mode via drive-activated native cubic interactions

Axel Martin Eriksson, Théo Sépulcre, Mikael Kervinen, Timo Hillmann, Marina Kudra, Simon Dupouy, Yong Lu, Maryam Khanahmadi, Jiaying Yang, Claudia Castillo-Moreno, Per Delsing, Simone Gasparinetti

Published Mar 20, 2024• 54 citations
arXivHTMLPDF

Abstract

Linear bosonic modes offer a hardware-efficient alternative for quantum information processing but require access to some nonlinearity for universal control. The lack of nonlinearity in photonics has led to encoded measurement-based quantum computing, which relies on linear operations but requires access to resourceful ('nonlinear') quantum states, such as cubic phase states. In contrast, superconducting microwave circuits offer engineerable nonlinearities but suffer from static Kerr nonlinearity. Here, we demonstrate universal control of a bosonic mode composed of a superconducting nonlinear asymmetric inductive element (SNAIL) resonator, enabled by native nonlinearities in the SNAIL element. We suppress static nonlinearities by operating the SNAIL in the vicinity of its Kerr-free point and dynamically activate nonlinearities up to third order by fast flux pulses. We experimentally realize a universal set of generalized squeezing operations, as well as the cubic phase gate, and exploit them to deterministically prepare a cubic phase state in 60 ns. Our results initiate the experimental field of polynomial quantum computing, in the continuous-variables notion originally introduced by Lloyd and Braunstein.

DOI
10.1038/s41467-024-46507-1

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Linear bosonic modes offer a hardware-efficient alternative for quantum information processing but require access to some nonlinearity for universal control. The lack of nonlinearity in photonics has led to encoded measurement-based quantum computing, which relies on linear operations but requires access to resourceful ('nonlinear') quantum states, such as cubic phase states. In contrast, superconducting microwave circuits offer engineerable nonlinearities but suffer from static Kerr nonlinearity. Here, we demonstrate universal control of a bosonic mode composed of a superconducting nonlinear asymmetric inductive element (SNAIL) resonator, enabled by native nonlinearities in the SNAIL element. We suppress static nonlinearities by operating the SNAIL in the vicinity of its Kerr-free point and dynamically activate nonlinearities up to third order by fast flux pulses. We experimentally realize a universal set of generalized squeezing operations, as well as the cubic phase gate, and exploit them to deterministically prepare a cubic phase state in 60 ns. Our results initiate the experimental field of polynomial quantum computing, in the continuous-variables notion originally introduced by Lloyd and Braunstein.
Bosonic codes encoded in superconducting cavities offer a hardware-efficient path to fault tolerance by exploiting the infinite dimensionality of a single harmonic oscillator. However, the non-linear mixing elements required for autonomous stabilization introduce parasitic self-Kerr interactions that induce deterministic dephasing and limit coherence times. We introduce a control framework based on resonant Kerr-cancellation dynamics using a Superconducting Nonlinear Asymmetric Inductive Element (SNAIL). By tuning the external magnetic flux to a symmetry-protected sweet spot, we eliminate the fourth-order non-linearity while maintaining the third-order mixing required for confinement. We derive an analytical stability threshold χaa<0.1κconf\chi_{aa} < 0.1 \kappa_{conf}χaa​<0.1κconf​ necessary to restore the exponential suppression of bit-flip errors. Analysis of spectroscopic data confirms that operating below this threshold eliminates the phase-space shearing observed in previous experiments. This protocol establishes the physical conditions required to surpass the break-even point in continuous variable quantum information.
Continuous-variable quantum information processing with mechanical oscillators requires a uni- versal gate set, including a genuine non-Gaussian evolution. While circuit quantum acoustodynamics (cQAD) experiments have realized bilinear and quartic (four-wave mixing) operations by coupling mechanical modes to transmon qubits, the intrinsic Kerr nonlinearity of these devices precludes access to odd-order effective Hamiltonians such as trisqueezing. Here we propose a cQAD architec- ture in which a mechanical mode, hosted in a high-overtone bulk acoustic-wave resonator (HBAR), is coupled to a superconducting nonlinear asymmetric inductive element (SNAIL). By combining the cubic nonlinearity of the SNAIL with parametric flux driving, we engineer a three-wave mixing interaction that generates trisqueezed mechanical states, producing the characteristic triangular, star-shaped Wigner function with negative regions indicative of non-Gaussianity. We derive the effective trisqueezing Hamiltonian from the full circuit model, identify the drive frequencies and flux modulation required to isolate the desired interaction from competing terms, and quantify the achievable coupling strengths for parameters compatible with current fabrication capabilities. Our results establish a hardware-efficient route to non-Gaussian resource generation in mechanical quantum systems, extending the toolbox of cQAD toward universal continuous-variable quantum computation and enhanced quantum-limited sensing.
We propose a deterministic, measurement-free implementation of a cubic phase gate for continuous-variable quantum information processing. In our scheme, the applications of displacement and squeezing operations allow us to engineer the effective evolution of the quantum state propagating through an optical Kerr nonlinearity. Under appropriate conditions, we show that the input state evolves according to a cubic phase Hamiltonian, and we find that the cubic phase gate error decreases inverse quartically with the amount of quadrature squeezing, even in the presence of linear loss. We also show how our scheme can be adapted to deterministically generate a nonclassical approximate cubic phase state with high fidelity using a ratio of native nonlinearity to linear loss of only 10^{-4}, indicating that our approach may be experimentally viable in the near term even on all-optical platforms, e.g., using quantum solitons in pulsed nonlinear nanophotonics.
We provide an explicit construction of a universal gate set for continuous-variable quantum computation with microwave circuits. Such a universal set has been first proposed in quantum-optical setups, but its experimental implementation has remained elusive in that domain due to the difficulties in engineering strong nonlinearities. Here, we show that a realistic three-wave mixing microwave architecture based on the superconducting nonlinear asymmetric inductive element [Frattini et al., Appl. Phys. Lett. 110, 222603 (2017)APPLAB0003-695110.1063/1.4984142] allows us to overcome this difficulty. As an application, we show that this architecture allows for the generation of a cubic phase state with an experimentally feasible procedure. This work highlights a practical advantage of microwave circuits with respect to optical systems for the purpose of engineering non-Gaussian states and opens the quest for continuous-variable algorithms based on few repetitions of elementary gates from the continuous-variable universal set.
The rich dynamics and large Hilbert space of quantum harmonic oscillators make them natural candidates for hardware-efficient and error-correctable quantum information processing. However, implementing direct entangling operations between oscillators remains an outstanding challenge. Existing strategies typically rely on parametrically activating interactions that populate the excited states of a nonlinear element, which introduces additional dissipation channels and potential leakage from the encoded manifold. Here, we engineer a Raman-assisted cross-Kerr interaction between microwave photons hosted in two superconducting cavities. Crucially, this dynamics does not excite the mediating nonlinear coupler, thereby suppressing coupler induced decoherence and leakage out of the bosonic code space. We use this direct nonlinear coupling to implement a controlled-phase gate within the single- and two-photon subspaces of two oscillators, deterministically generating entanglement between them. Finally, we use these engineered dynamics to implement a photon-number parity check on a storage cavity via purely bosonic interactions with an ancillary cavity, demonstrating an enhancement in the storage lifetime. Our work provides a promising pathway toward engineering robust operations that act entirely within a protected bosonic code space and realizing fault-tolerant quantum information processing with bosonic elements.
Continuous variable (CV) quantum computation offers an alternative to qubit-based computing by exploiting the infinite-dimensional Hilbert space of bosonic modes. Despite recent progress, superconducting platforms have yet to demonstrate a scalable architecture capable of universal computation. Here, we design and numerically simulate a two-layer superconducting architecture that implements all five interactions of the universal CV gate set (rotation, displacement, squeezing, Kerr, and beam splitter) within experimentally accessible regimes. To this end, we employ a DC-SQUID as the bosonic mode, a fluxonium qubit to mediate nonlinear interactions, and two ancillary qubits that enable Gaussian and multi-mode operations. By tuning fluxes and frequencies, we achieve high fidelities (≥98%\geq 98\%≥98%) across all gates within state-of-the-art parameter ranges. The modular nature of the design allows straightforward scaling, establishing a feasible pathway toward high-fidelity, universal CV quantum computation based on superconducting circuits.