A whisper in a noisy room is nearly indistinguishable. A conventional amplifier adds its own noise and drowns out the weak sound. A quantum amplifier works differently: it amplifies the signal while adding almost no extra noise, like a perfect ear. But even such an ear has its own problems.

Scientists built an amplifier from a superconducting loop with an array of Josephson junctions — tiny elements that operate at ultra-low temperatures. This amplifier boosts microwave signals by a factor of 20 (up to 44) over a bandwidth of about 50 MHz. But as the signal travels along the wires, even weak reflections from imperfect connections create interference. These reflections act like echoes in the mountains: the sound returns and distorts the original signal.

The authors developed a mathematical model that precisely describes how reflections affect the gain. They showed that the complex distortions in the spectrum can be explained by interference similar to that in optical resonators. Now it is possible to separate the amplifier's intrinsic properties from environmental influences and fine-tune its operation.

This approach helps create reliable quantum amplifiers for quantum computers and detectors. In quantum technologies, every bit of extra noise means loss of information. And here, the noise is almost at the limit allowed by the laws of physics.