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Loss-tolerant cross-Kerr enhancement via modulated squeezing.

Ankit Tiwari, Daniel Klaus Burgarth, Linran Fan, Saikat Guha, Christian Arenz

Published Dec 1, 2025• 1 citation
Publisher

Abstract

We develop squeezing protocols to enhance cross-Kerr interactions. We show that through alternating between squeezing along different quadratures of a single photonic mode, the cross-Kerr interaction strength can be generically amplified. As an application of the squeezing protocols, we discuss speeding up the deterministic implementation of controlled phase gates in photonic quantum computing architectures. We develop bounds that characterize how fast and strong single-mode squeezing has to be applied to achieve a desired gate error and show that the protocols can overcome photon losses. Finally, we discuss experimental realizations of the squeezing strategies in optical fibers and nanophotonic waveguides.

DOI
10.1364/oe.577300

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We develop squeezing protocols to enhance cross-Kerr interactions. We show that through alternating between squeezing along different quadratures of a single photonic mode, the cross-Kerr interaction strength can be generically amplified. As an application of the squeezing protocols, we discuss speeding up the deterministic implementation of controlled phase gates in photonic quantum computing architectures. We develop bounds that characterize how fast and strong single-mode squeezing has to be applied to achieve a desired gate error and show that the protocols can overcome photon losses. Finally, we discuss experimental realizations of the squeezing strategies in optical fibers and nanophotonic waveguides.
We develop squeezing protocols to enhance cross-Kerr interactions. We show that through alternating between squeezing along different quadratures of a single photonic mode, the cross-Kerr interaction strength can be generically amplified. As an application of the squeezing protocols, we discuss speeding up the deterministic implementation of controlled phase gates in photonic quantum computing architectures. We develop bounds that characterize how fast and strong single-mode squeezing has to be applied to achieve a desired gate error and show that the protocols can overcome photon losses. Finally, we discuss experimental realizations of the squeezing strategies in optical fibers and nanophotonic waveguides.
Phase shifts induced by the Kerr effect are usually very small at the single-photon level. We propose two circuits for enhancing the cross-Kerr phase shift by applying one- and two-mode quadrature squeezing operators. Our results are based on the vector coherent state theory and can be implemented by physical operations satisfying the commutation relations for generators of the generalized special unitary group, SU(1,1). While the proposed methods could be useful for the realization of quantum optical entangling gates based on Kerr nonlinear media at the single-photon level, they also indicate a general alternative approach to enhance higher-order nonlinearities by applying lower-order nonlinear effects.
The controlled phase gate is one of the most important logic gates in the quantum computation field. In this paper, we proposed a protocol for implementing the two-qubit controlled phase gates with the help of cross-Kerr nonlinearity, optical elements and the conventional photon detectors, which are feasible with existing experimental technology. The protocol also can be applied to implement the controlled phase gates of many different atomic and photonic degrees of freedom with successful probability of 100%, that is, our protocol is efficient and flexible.
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 analyse an experimental method for creating interesting nonclassical states by processing the entanglement generated when two large coherent states interact in a cross-Kerr medium. We specifically investigate the effects of loss and noise in every mode of the experiment, as well as the effect of ‘binning’ the post-selection outcomes. Even with these imperfections, we find an optimal set of currently achievable parameters which would allow a proof-of-principle demonstration of number squeezing in states with large mean photon number. We discuss other useful states which can be generated with the same experimental tools, including a class of states which contain coherent superpositions of differing photon numbers, e.g. good approximations to the state 12(|0⟩+|20⟩). Finally, we suggest one possible application of this state in the field of optomechanics.
Quantum computation with light, compared with other platforms, offers the unique benefit of natural high-speed operations at room temperature and large clock rate, but a big obstacle of photonics is the lack of strong nonlinearities which also makes loss-tolerant or generally fault-tolerant quantum computation (FTQC) complicated in an all-optical setup. Typical current approaches to optical FTQC that aim at building suitable large multi-qubit cluster states by linearly fusing small elementary resource states would still demand either fairly expensive initial resources or rather low loss and error rates. Here we propose reintroducing weakly nonlinear operations, such as a weak cross-Kerr interaction, to achieve small initial resource cost and high error thresholds at the same time. More specifically, we propose an approach to generate a large-scale cluster state by hybridizing Gottesman-Kitaev-Preskill (GKP) and single-photon qubits. Our approach enables us to implement FTQC based on GKP squeezing of 7.4 and 8.4 dB and a photon loss rate of 1.0 and 5.0 %, respectively. In addition, our scheme has a reduced resource cost, i.e., number of physical qubits/photons per logical qubit or initial entanglement, compared to high-threshold FTQC with optical GKP qubits or fusion-based quantum computation with encoded single-photon-qubit states, respectively. Furthermore, our approach, when assuming very low photon loss, allows to employ GKP squeezing as little as 3.8 dB, which cannot be achieved by using GKP qubits alone.