Self-Restricting Noise: How Strong Noise Can Counterintuitively Protect Quantum Systems
By Nicholas LaRacuente, Postdoctoral Scholar at the University of Chicago & the Chicago Quantum Exchange.
Noise is among the most important hurdles in the way of full-scale quantum computing. Therefore, it’s crucial that we understand it as best we can so that we can counteract it. But deep study of quantum noise has demonstrated that it can work in mysterious ways.
What do I mean? As you increase the noise acting on a quantum system, you’d expect that the rate of decoherence would increase; more noise would make the system decohere faster, approaching an equilibrium state determined by the environment. Curiously, strong noise sometimes has a counterintuitive effect: it protects parts of a quantum system from itself. In a new paper, I studied and observed this self-restricting noise using IBM Quantum processors and Qiskit.
I started by using Qiskit Dynamics to simulate a four-qubit system with nearest neighbor interactions — that is, one where each qubit can only interact with its neighbor. I exposed the qubit on one end to varying levels of noise, while the other three qubits only received noise via interactions with the exposed qubit.
Then, I plotted how the relative entropy varied over time, where the relative entropy is more or less a measure of how the quantum state differs from the equilibrium state. This value is a strong way to quantify the decay of a quantum state.
At first, the observations aligned with expectations: increasing the strength of the noise experienced by the first qubit led to a quicker drop in the relative entropy and a quicker decay of the qubit. But then, two strange things happen. First, I observed a plateau — a counter example to the idea that quantum systems always decay exponentially. More surprising was what happened when I ramped the noise up to stronger levels: I observed that the overall decay rate started to slow with increasing local noise. A closer look at the relative entropy decay plotted against the noise strength reiterated the findings.
I examined an even simpler version of the system: two qubits, one exposed to noise and the other not. I compared the increasing noise to the relative entropy decay rate, now using different simulation methods to ensure I wasn’t seeing a glitch. Once again, there was little change to the relative entropy for low noise, a steep dropoff (quick decoherence) for intermediate noise, and weakening decay for the highest-noise cases.
The first observation — that relative entropy doesn’t decay exponentially as a hard-and-fast rule — is easier to explain. Clearly, noise restricted to one part of the system doesn’t instantly spread. This principle is a central tenet of quantum error correction, where we encode quantum information in an effectively distinct subsystem, allowing us to detect and correct errors before they spread to the encoded information.
But how does one explain the slower decay under stronger noise? I propose that two pieces, the generalized quantum Zeno effect (GQZE) and an adiabatic theorem, can predict our observations. The Quantum Zeno Effect is a famous quantum oddity showing that if one measures a system repeatedly and quickly, the system’s state won’t change under its own effects or under the effect of noise. The generalized version says that any sufficiently fast process that interrupts the system’s dynamics could change or suppress those dynamics, including interactions with the outside environment. As a continuous-time analog of the GQZE, an adiabatic theorem introduced by Burgarth et al. predicts that continuous, fast processes can suppress the dynamics of slower processes. When noise applied to the leftmost qubit in the chain is extremely strong, its effects resemble the repeated interruptions of the Quantum Zeno Effect. Strong noise suppresses interactions between the leftmost qubit and its neighbor via the adiabatic theorem, isolating itself. The adiabatic theorem restricts that noise from interacting with the rest of the qubits in the chain.
I performed experiments on a real IBM Quantum system, simulating interactions with a continuously parameterized quantum gate, interrupted by a completely depolarizing channel. To implement the parameterized gate, I used Qiskit’s RZXCalibrationBuilder subroutine as developed for Qiskit Pulse. To implement the completely depolarizing channel, I coupled the target qubit to two auxiliaries and then applied reset operations to both of them. An important feature for this experiment is the fast reset time of about 1 microsecond on the ibmq_santiago processor. Theory, simulation, and experiment all seem to agree well.
These results instill confidence that quantum computers will be able to overcome the effects of noise. Even before error correction kicks in, merely looking for errors repeatedly could suppress them thanks to the quantum Zeno effect. Additionally, perhaps this work can help us come up with better noise reduction methods.
Ultimately, better understanding the interplay between noise and coherent interactions is a key step toward modeling noise in more realistic systems. Subsequent work may address the buildup of noise in these realistic quantum circuits.
This work was carried out as part of the CQE IBM Postdoctoral Training Program, which selects postdoctoral candidates interested in studying the experimental or theoretical implications of scaling superconducting qubits. Learn more here.
