Abstract The stabilisation of quantum manifolds is at the heart of error-protected quantum information storage and manipulation. Nonlinear driven-dissipative processes achieve such stabilisation in a hardware efficient manner. Josephson circuits with parametric pump drives implement these nonlinear interactions. In this article, we propose a scheme to engineer a four-photon drive and dissipation on a harmonic oscillator by cascading experimentally demonstrated two-photon processes. This would stabilise a four-dimensional degenerate manifold in a superconducting resonator. We analyse the performance of the scheme using numerical simulations of a realisable system with experimentally achievable parameters.
Abstract The stabilisation of quantum manifolds is at the heart of error-protected quantum information storage and manipulation. Nonlinear driven-dissipative processes achieve such stabilisation in a hardware efficient manner. Josephson circuits with parametric pump drives implement these nonlinear interactions. In this article, we propose a scheme to engineer a four-photon drive and dissipation on a harmonic oscillator by cascading experimentally demonstrated two-photon processes. This would stabilise a four-dimensional degenerate manifold in a superconducting resonator. We analyse the performance of the scheme using numerical simulations of a realisable system with experimentally achievable parameters.
Abstract 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 necessarily populate the excited states of a nonlinear coupler, introducing additional dissipation channels and potential leakage outside the encoded manifold. Here, we present a fundamentally different approach to generate nonlinear coupling between bosonic modes: a Raman-assisted cross-Kerr interaction between microwave photons hosted in two superconducting cavities, which does not populate the mediating coupler. Crucially, this dynamics preserves the bosonic code space throughout, which is essential for fault-tolerant bosonic quantum computation. We demonstrate that the engineered cross-Kerr can be used to directly implement controlled-phase gates between two oscillators encoded in the single- and two-photon subspaces. Further, we apply the engineered dynamics to implement code-space-preserving parity checks using one of the oscillators as an ancillary mode, demonstrating an all-bosonic syndrome extraction that extends the effective lifetime of a storage oscillator. This work establishes a qualitatively different strategy for bosonic control, providing a pathway toward fault-tolerant quantum information processing with purely bosonic gates and syndrome measurements.
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.
We consider quantum dynamics of a parametrically driven anharmonic oscillator (PDAO) at a few-photon level. In this scheme the oscillatory mode is excited through the degenerate down-conversion process. This scheme could be experimentally realized in superconducting solid-state devices based on the nonlinearity of the Josephson junction or in cooled nano-mechanical oscillators. We investigate PDAO in the strong quantum regime that means strong Kerr-nonlinearity of the mode with respect to the mode’s dissipation for two cases of excitations: by a monochromatic driving field or by a train of Gaussian pulses. We demonstrate production of the nonclassical oscillatory states with two-fold symmetry in phase-space which are approximately close to the lower pure Fock states. Production of the superposition of the Fock states for time-intervals exceeding the characteristic time of decoherence and dissipation is also shown.
We propose a scheme to dissipatively stabilize superpositions of squeezed coherent states for single- and two-resonator modes in superconducting circuits, where a superconducting qubit is coupled to a single or two parametrically driven transmission-line resonators with different circuit designs. A modulated magnetic flux applied to the qubit can periodically break the inversion symmetry of the qubit and induce both the parametrically enhanced transverse and longitudinal couplings to the resonators, resulting in strong nonlinear two-photon interactions between the qubit and the resonators and enabling the scheme to be implemented in a relatively weak coupling regime. With an additional microwave drive applied to the qubit, the dissipation of the qubit used as a resource can help drive the resonators into the desired superpositions of squeezed coherent states at a steady state with high speed. Numerical simulations show that the target states with high fidelity and highly nonlinear properties can be created for a long time even in the presence of photon leakage out of the resonators. The scheme can be generalized to other quantum platforms and may have potential applications in the field of quantum information processing and the improvement of estimation precision in quantum metrology.
Parametric oscillations are well studied phenomena, with applications in amplification, quantum optics, and quantum information processing. They can occur as a parameter of a system, such as the resonant frequency, is being modulated or “pumped” by an external field. A nonlinearity of the system can then transfer power from the pumping frequency to two frequencies called signal and idler. When the signal falls within a resonance, and when the pump amplitude exceeds an instability threshold, parametric oscillations occur. When signal and idler fall within the same resonance, the pumping is called degenerate.Due to somewhat different implementations, in combination with rich nonlinear physics, the details of the parametric oscillations can differ in different systems. In this work, we expand on the research done on parametric oscillations using a superconducting microwave resonator with a tunable boundary condition. Previously, a degenerate Josephson parametric oscillator (JPO) has been demonstrated by modulation of this boundary condition at twice the resonator's resonant frequency. We further use the JPO to implement a novel read-out method for a superconducting qubit. Moreover, we demonstrate a different, nondegenerate regime of the JPO, which we denote the NJPO, by modulating the frequency at the sum of two resonant frequencies of a multimode resonator.Both the JPO qubit read-out and the NJPO have applications within quantum information processing. The perhaps most promising platform for quantum information processing is represented by the circuit-QED architecture with superconducting resonators and artificial atoms, where the two lowest atomic levels represent the qubit. We make these circuits using lithographic techniques, and control and measure them at low temperature using microwaves. The qubit's state is fragile and difficult to read out with high fidelity. To this end, we have developed a method based on the JPO, in which the qubit state is mapped onto a zero-amplitude or a large-amplitude state of the JPO. We achieved a large contrast (185±15 photons), therefore eliminating the need for a following quantum-limited parametric amplifier. Our readout fidelity was 81.5 %, and by carefully modeling we can distinguish fidelity loss from the qubit and the readout, respectively. This analysis displays an actual readout fidelity of 98.7 %.An alternative model for quantum computing is based on continuous variables, and uses harmonic oscillators instead of qubits. Entangled states, which can be used as quantum resources, can then be created, for example, by two-mode squeezing of the oscillator ground state. The state of the NJPO produces correlated oscillations in its two modes, which might be useful for continuous-variable quantum computing. In this work we fully characterize the classical properties of the NJPO, and show good quantitative agreement with a theoretical model.
Out-of-equilibrium driven nonlinear oscillators have attracted interest as a platform for tailoring Floquet Hamiltonian spectra and stabilizing quantum states for quantum information. However, it is usually ignored that the necessary parametric drive can amplify environmental fluctuations limiting applications. In this work, we capture this effect by computing the effective Lindbladian of a Kerr parametric oscillator beyond the rotating wave approximation. We find that the relevant dissipators depend strongly on the nonlinearity and the mean-photon number in the oscillator. In particular, we address recent measurements of the logical lifetime on a Schr\"odinger's-cat qubit stabilized by a parametric drive, thereby providing an explanation for the observed three-order-of-magnitude discrepancy between experimental data and an ordinary Lindblad treatment. Our systematic approach paves the path to treat dissipative effects in Floquet-engineered nonlinear quantum systems.