Can Quantum Computers Handle Chaos? New Diagnostic Tool Emerges

As the quest for scalable and reliable quantum computing continues to unfold, a pressing concern has emerged: can quantum computers handle chaos? The development of quantum computing hardware is facing a significant challenge, with current-day processors operating outside the range of classical simulation. This raises concerns about the resilience of quantum information hardware against chaotic instabilities. In this article, we delve into the world of classical chaos and explore how it can be used as a diagnostic tool to mitigate these issues.

Can Quantum Computers Handle Chaos?

The development of quantum computing hardware is facing a significant challenge. Current-day quantum processors, comprising 50-100 qubits, already operate outside the range of quantum simulation on classical computers. This raises concerns about the resilience of quantum information hardware against chaotic instabilities. In this article, we will explore how classical chaos can be used as a diagnostic tool for mitigating this problem.

Classical chaos is a well-studied phenomenon in physics, where small changes in initial conditions lead to drastically different outcomes. The mathematical pendulum is a classic example of deterministic classical chaos. When excited to energies large enough that the nonlinearity of the pendulum potential becomes sizable, a transition from integrable harmonic motion to chaotic dynamics generically takes place.

In the world of quantum physics, the mathematical pendulum finds a prominent realization as the transmon superconducting qubit. The gravitational potential is defined by a Josephson junction and the kinetic energy by a microcapacitor. This system exhibits nonlinear behavior, which can lead to chaotic dynamics when excited to high energies.

Classical Chaos in Quantum Computers

The simulation of classical limits can be a potent diagnostic tool for the resilience of quantum information hardware against chaotic instabilities. In this paper, we demonstrate that classical and quantum simulations lead to similar stability metrics, such as classical Lyapunov exponents vs quantum wave function participation ratios. However, the big advantage of classical simulation is that it can be pushed to large systems comprising up to thousands of qubits.

Researchers exhibit the utility of this classical toolbox by simulating all current IBM transmon chips, including the 433-qubit processor of the Osprey generation as well as devices with 1121 qubits (Condor generation). For realistic system parameters, we find a systematic increase of Lyapunov exponents with system size, suggesting that larger layouts require added efforts in information protection.

Mitigating Chaos in Quantum Computers

The development of quantum computing hardware is facing the challenge that current-day quantum processors already operate outside the range of quantum simulation on classical computers. This raises concerns about the resilience of quantum information hardware against chaotic instabilities. In this paper, we demonstrate that the simulation of classical limits can be a potent diagnostic tool for mitigating this problem.

As a testbed for our approach, we consider the transmon qubit processor, a computing platform in which the coupling of large numbers of nonlinear quantum oscillators may trigger destabilizing chaotic resonances. We find that classical and quantum simulations lead to similar stability metrics, such as classical Lyapunov exponents vs quantum wave function participation ratios.

Classical simulation can be a powerful tool for understanding the behavior of quantum systems. In this paper, we demonstrate that classical and quantum simulations lead to similar stability metrics, such as classical Lyapunov exponents vs quantum wave function participation ratios. However, the big advantage of classical simulation is that it can be pushed to large systems comprising up to thousands of qubits.

In conclusion, classical chaos can be used as a diagnostic tool for mitigating the problem of chaotic instabilities in quantum computers. The simulation of classical limits can provide valuable insights into the behavior of quantum systems and help to identify potential issues before they arise. By pushing the boundaries of classical simulation, we can gain a deeper understanding of the complex dynamics that govern quantum computing hardware.