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Description
Directional amplification is a critical requirement for scalable superconducting quantum computing, yet current solutions rely on bulky, off-chip ferrite isolators that hinder integration. Here we propose a fully on-chip, directional and broadband superconducting quantum amplifier whose isolation arises intrinsically from topological properties. The setup consists of a Josephson junction array (JJA) weakly coupled to an auxiliary array of linear resonators with impedance matching conditions on its boundaries. A strong pump injected at one end of the auxiliary array propagates unidirectionally without reflections, inducing an effective pump on the JJA that simultaneously provides phase matching and activates four-wave mixing processes. The propagation phase of this pump breaks time-reversal symmetry, rendering parametric amplification intrinsically directional with backscattering exponentially suppressed — a direct manifestation of the non-trivial topology induced in the JJA. Stability is achieved by engineering local losses on all JJA sites, which can be realized either by coupling each site to an external transmission line or by incorporating on-chip resistor elements, allowing the system to dissipate excess energy from the pump.
We fully characterize the directional amplifying properties of the device through approximate quantum input-output simulations and exact semi-classical SPICE simulations. For state-of-the-art parameters, a compact device with N~10 sites achieves gains above 20 dB, bandwidths of hundreds of MHz, and reverse isolation beyond -30 dB, while operating near the quantum noise limit. Topological protection provides robustness against fabrication disorder, reducing gain ripples, and power saturation can be mitigated by diluting each JJA non-linearity into a small sub-array of M~3 Josephson junctions in series. This work establishes an alternative route toward fully on-chip quantum microwave amplifiers.