Kimin Park

Nonlinear phase gates are essential to achieve the universality of continuous-variable quantum processing and its applications. We present a deterministic protocol for generating nonlinear phase gates in trapped ion systems using simultaneous two-tone sideband drives beyond the Lamb-Dicke regime. Our approach harnesses higher-order interaction terms typically neglected or suppressed to construct nonlinear phase gates. This methodology enables high-fidelity gate engineering with a near three-fold reduction in control pulses compared to state-of-the-art theoretical proposals.

Quantum interference between interacting systems is fundamental to basic science and quantum technology, but it typically requires precise control of the interaction phases of lasers or microwave generators. Can interference be observed if those interaction phases are stable but unknown, usually prohibitive for complex state without active control? Here, we answer this question by experimentally preparing a Schrödinger-cat-like state of an internal qubit and a motional oscillator of a trapped $^{40}$Ca$^{+}$ ion, and its robustness to such uncontrolled phase. By applying alternating red and blue sideband pulses, we enforce a strict qubit-parity correlation and interference inherently insensitive to stable but unknown phases of the driving laser. For this qubit-parity interference, we use a minimal two-pulse interferometric sequence to demonstrate characteristic visibilities of $20\%$ and $40\%$, which approach the theoretical visibility limit, providing a scalable coherence witness without full state tomography for high-dimensional states.

Quantum simulations provide means to probe challenging problems within controllable quantum systems. However, implementing or simulating deep-strong nonlinear couplings between bosonic oscillators on physical platforms remains a challenge. We present a deterministic simulation technique that efficiently and accurately models nonlinear bosonic dynamics. This technique alternates between tunable Rabi and SNAP gates, both of which are available on experimental platforms such as trapped ions and superconducting circuits. Our proposed simulation method facilitates high-fidelity modeling of phenomena that emerge from higher-order bosonic interactions, with an exponential reduction in resource usage compared to other techniques. We demonstrate the potential of our technique by accurately reproducing key phenomena and other distinctive characteristics of ideal nonlinear optomechanical systems. Our technique serves as a valuable tool for simulating complex quantum interactions, simultaneously paving the way for new capabilities in quantum computing through the use of hybrid qubit-oscillator systems.

The precise determination of a displacement of a mechanical oscillator or a microwave field in a predetermined direction in phase space can be carried out with trapped ions or superconducting circuits, respectively, by coupling the oscillator with ancilla qubits. Through that coupling, the displacement information is transferred to the qubits which are then subsequently read out. However, unambiguous estimation of displacement in an unknown direction in the phase space has not been attempted in such oscillator-qubit systems. Here, we propose a hybrid oscillator-qubit interferometric setup for the unambiguous estimation of phase space displacements in an arbitrary direction, based on feasible Rabi interactions beyond the rotating-wave approximation. Using such a hybrid Rabi interferometer for quantum sensing, we show that the performance is superior to the ones attained by single-mode estimation schemes and a conventional interferometer based on Jaynes-Cummings interactions. Moreover, we find that the sensitivity of the Rabi interferometer is independent of the thermal occupation of the oscillator mode, and thus cooling it to the ground state before sensing is not required. We also perform a thorough investigation of the effect of qubit dephasing and oscillator thermalization. We find the interferometer to be fairly robust, outperforming different benchmark estimation schemes even for large dephasing and thermalization.

We present a protocol for transferring arbitrary continuous-variable quantum states into a few discrete-variable qubits and back. The protocol is deterministic and utilizes only two-mode Rabi-type interactions which are readily available in trapped-ion and superconducting circuit platforms. The inevitable errors caused by transferring an infinite-dimensional state into a finite-dimensional register are suppressed exponentially with the number of qubits. Furthermore, the encoded states exhibit robustness against noise, such as dephasing and amplitude damping, acting on the qubits. Our protocol thus provides a powerful and flexible tool for discrete-continuous hybrid quantum systems.

Squeezed states of harmonic oscillators are a central resource for continuous-variable quantum sensing, computation and communication. Here we propose a method for the generation of very good approximations to highly squeezed vacuum states with low excess anti-squeezing using only a few oscillator-qubit coupling gates through a Rabi-type interaction Hamiltonian. This interaction can be implemented with several different methods, which has previously been demonstrated in superconducting circuit and trapped-ion platforms. The protocol is compatible with other protocols manipulating quantum harmonic oscillators, thus facilitating scalable continuous-variable fault-tolerant quantum computation.

Quantum computing potentially offers exponential speed-ups over classical computing for certain tasks. A central, outstanding challenge to making quantum computing practical is to achieve fault tolerance, meaning that computations of any length or size can be realised in the presence of noise. The Gottesman-Kitaev-Preskill code is a promising approach towards fault-tolerant quantum computing, encoding logical qubits into grid states of harmonic oscillators. However, for the code to be fault tolerant, the quality of the grid states has to be extremely high. Approximate grid states have recently been realized experimentally, but their quality is still insufficient for fault tolerance. Current implementable protocols for generating grid states rely on measurements of ancillary qubits combined with either postselection or feed forward. Implementing such measurements take up significant time during which the states decohere, thus limiting their quality. Here we propose a measurement-free preparation protocol which deterministically prepares arbitrary logical grid states with a rectangular or hexagonal lattice. The protocol can be readily implemented in trapped-ion or superconducting-circuit platforms to generate high-quality grid states using only a few interactions, even with the noise levels found in current systems.