Abstract The cubic phase state constitutes a nonlinear resource that is essential for universal quantum computing protocols. However, constructing such non-classical states faces many challenges. In this work, we present a protocol for generating a cubic phase state with high fidelity. The protocol is based on a set of Gaussian operations assisted by a detection operation. To find the proper set of parameters that results in both high fidelity and high detection probability, we provide a numerical multiparameter optimization. We investigate a broad range of target states and study how parameter imperfections influence fidelity.
Abstract The cubic phase state constitutes a nonlinear resource that is essential for universal quantum computing protocols. However, constructing such non-classical states faces many challenges. In this work, we present a protocol for generating a cubic phase state with high fidelity. The protocol is based on a set of Gaussian operations assisted by a detection operation. To find the proper set of parameters that results in both high fidelity and high detection probability, we provide a numerical multiparameter optimization. We investigate a broad range of target states and study how parameter imperfections influence fidelity.
In continuous-variable systems, non-Gaussian resources are essential for achieving universal quantum computation that lies beyond classical simulation. Among the candidate states, the cubic phase state stands out as the simplest form of single-mode non-Gaussian resource, yet its experimental preparation still remains a great challenge. Although a variety of approximate schemes have been proposed to simulate the cubic phase state, they often fall short when deployed in concrete quantum tasks. In this work, we present a Gaussian optimization protocol that systematically refines the non-Gaussian resources, which significantly improves the performance of both magic-state-based and measurement-based quantum computation. Leveraging task-specific Gaussian operations on approximate cubic phase states, our protocol offers an experimentally feasible approach to enhance gate fidelity in magic-state-based quantum computation and reduce the variance of nonlinear quadrature measurement in measurement-based quantum computation. Building on this framework, we further propose a task-oriented non-Gaussian state preparation scheme based on superpositions in the Fock basis followed by squeezing and displacement. This strategy enables direct tailoring of resource states to specific task goals. Owing to its flexibility and generality, our framework provides a powerful and broadly applicable tool for enhancing performance across a wide range of continuous-variable quantum information protocols.
Universal quantum computation with continuous variables cannot be attained solely with a set of Gaussian operations, it requires the addition of a non-Gaussian element, at least of third order in the quadrature operators, such as the cubic phase state. In this work, we present a method to generate a quantum state in the vibrational mode of a trapped ion that exhibits characteristics compatible with the cubic phase state, such as the distinctive oscillating pattern in its Wigner function. This state emerges from the nonlinear Jaynes-Cummings interaction native to the trapped-ion model, and under the assumption of an initial coherent vibrational state with a large occupation number. Consequently, the evolved vibrational state approximates the cubic phase state with high fidelity, and we use the variance of a nonlinear combination of the quadratures to characterize it. Finally, we provide an analytical expression for its cubicity that shows the high performance of the approximate vibrational cubic phase state.
Cubic phase states provide the essential non-Gaussian resource for continuous-variable quantum computing. We show that they also offer significant potential for quantum metrology, surpassing the phase-sensing sensitivity of all Gaussian states at equal average photon number. Optimal sensitivity requires only moderate initial squeezing, and the non-Gaussian advantage remains robust against loss and detection noise. We identify optimal measurement strategies and show that several experimentally relevant preparation schemes surpass Gaussian limits, in some cases reaching the sensitivity of cubic phase states. Our results establish cubic phase states as a promising resource for quantum-enhanced precision measurements beyond Gaussian limits.
Photonic quantum computing has gained significant interest in recent years due to its potential for scaling to large numbers of qubits. A critical requirement for fault-tolerant quantum computation is the reliable generation of non-Gaussian quantum states, typically achieved using Gaussian operations and photon-number-resolving detectors. However, the probabilistic nature of quantum measurement typically results in low success rates for state preparation. Conventionally, these circuits are optimized to herald a single specific target outcome, thereby disregarding the potential utility of alternative measurement patterns generated by the same physical setup. In this work, we propose and demonstrate a multi-outcome optimization strategy that increases the overall acceptance probability by allowing a single circuit to produce useful quantum states across several measurement patterns. To evaluate this approach, we apply the framework to the generation of Gottesman-Kitaev-Preskill core states, Schrodinger cat states, binomial codes, and cubic phase states using both two-mode and three-mode Gaussian circuits. We demonstrate that the success probability can be enhanced through two distinct mechanisms: first, by simultaneously targeting a diverse set of useful resource states, and second, by aggregating degenerate outcomes to maximize the production rate of a single target state.
The generation of non-Gaussian states of bosonic systems described by continuous quantum degrees of freedom is of interest in a variety of contexts, ranging from quantum foundations to computation and communication. A crucial feature of genuine non-Gaussian states is that they cannot be described in general with a non-negative Wignerquasi-probability distribution. In particular, this feature is equivalent to contextuality and it underpins all attempts at attaining quantum computational advantage in a universal setting. In this thesis, the generation of Wigner-negative states is addressed, pursuing two approaches. First, in an optomechanical-like setting, we develop schemes to generate Wigner-negative states of two massive mechanical systems, in turn correlated such that they also feature entanglement, another genuine quantum hallmark. These schemes are based on driven-dissipative systems where dissipation is properly engineered by taking advantage of linear-and-quadratic optomechanical interactions. We address the robustness of these schemes when uncontrollable noisy channels are included in the dynamics, proving that their resilience is comparable to Gaussian schemes that have already been implemented experimentally. Second, considering in particular circuit QED systems and trapped ions, we propose a method to engineer a set of Hamiltonian evolutions that are universal in terms of single-mode state preparation. This method is based on a driven quantum Rabi model, where the desired evolution is effectively imprinted on a continuous-variable degree of freedom by its interaction with a properly driven two-level system. We demonstrate the universality of such approach by simulating the generation of multi-squeezed and other states, including the celebrated cubic-phase state. We also consider the effect of noise in realistic settings, showing in particular that in systems involving superconducting qubits, the generation of tri-squeezed states --- a universal resource for continuous-variable quantum computation which we prove to display larger Wigner negativities with respect to Fock and cubic-phase states for the same energy --- is within experimental reach.
Iterative CZ-gate-based protocol for squeezed Schrödinger cat state engineering
Squeezed optical Schrödinger cat states constitute a key resource for both fundamental tests of quantum theory and up-to-date quantum technologies. We propose a measurement-assisted gate for the generation and manipulation of the cat states. In this scheme, an ancilla in the non-Gaussian small-amplitude (in general, squeezed) Schrödinger cat state and the target oscillator initially prepared in a squeezed vacuum (or coherent) state are subjected to a quantum nondemolition (QND) entangling operation followed by projective homodyne measurement. The proposed gate enables generation of high-fidelity squeezed Schrödinger cat states with controllable size and squeezing with tunable fidelity/success-probability trade-off. We also introduce an iterative, homodyne-conditioned CZ-based protocol for cat-state amplification. The parameter regimes required to achieve the desired fidelity and the success probability are analyzed. The approach is well suited for applications in measurement-based quantum computing and hybrid quantum networks where non-Gaussian resources enhance computational and communication capabilities.