Noise-Induced Thermalization in Quantum Systems

TL;DR

This work reframes noise in the NISQ era as a potential asset by leveraging the Eigenstate Thermalization Hypothesis to accelerate Gibbs-state preparation. By interleaving controlled shocks with Hamiltonian dynamics on a spin-1/2 chain, both classical and quantum simulations show faster convergence to local Gibbs states and even induce thermalization in otherwise integrable systems. The authors analyze how noise promotes information propagation and entanglement, derive scaling trends with noise frequency and system size, and establish practical guidelines for implementing the protocol on real devices. The findings suggest a practical pathway to harness noise for quantum advantage before full fault tolerance is achieved, with broad applicability across quantum simulation and quantum machine learning tasks.

Abstract

In the current Noisy Intermediate-Scale Quantum era, noise is widely regarded as the primary obstacle to achieving fault-tolerant quantum computation. However, certain stages of the quantum computing pipeline can, in fact, benefit from this noise. In this work, we exploit the Eigenstate Thermalization Hypothesis to show that noise generically accelerates a fundamental task in quantum computing -- the preparation of Gibbs states. We demonstrate this behavior using classical and quantum simulations with Haar-random and phase-flip noise, respectively, on a spin-1/2 chain with a local Hamiltonian. Our non-integrable model sees ~3.5x faster thermalization in the presence of noise, while our integrable model, which would not otherwise thermalize, reaches a thermal state due to noise. Since certifying a local Gibbs state is relatively easy on a quantum computer, our approach provides a new practical solution to a key problem in quantum computing. More broadly, these results establish a new paradigm in which noise can be harnessed on quantum computers, enabling practical advantages before the years of fault-tolerance.

Figures (9)

• Figure 1: Spectrum of the Hamiltonian in Eq. \ref{['spin_hamiltonian']}: We see that the spectrum is bounded on both sides. The red dotted line indicates the energy and the corresponding $\beta^*$ of the arbitrarily chosen initial state. The density of states is calculated using the Kernel Density Function using a gaussian kernel and is scaled by the number of energy levels.
• Figure 2: Interleaved noise protocol implemented on a quantum circuit: The circuit implements the Hamiltonian \ref{['spin_hamiltonian']} using noisy $R_{XX}$ (denoted in red), and noisy $R_{ZZ}$ gates by decomposing the time-evolution operator $e^{-iHt}$, under Suzuki trotterization, into gates native to the underlying architecture (here, it is decomposed into $R_{XX}, \text{ and }R_{ZZ}$ gates but the choice of gates does not change the result). Within one trotter step, each of these gates trigger a phase-flip noise with some probability and drive subsystems of a NISQ device toward a Gibbs state. For illustrative purposes, the first three qubits are initialized to $\ket{1}$. The choice of such an initial state does not significantly change the acceleration, but merely changes the target inverse temperature $\beta$ of the Gibbs state the system eventually converges to.
• Figure 3: Comparison between noisy and plain evolutions toward a Gibbs state: In (a) we study the relative entropy between the noisy evolution (solid) and the Gibbs state, and compare the same with that of the plain evolution (dotted) with the same Gibbs state. We see that the both the evolutions overlap in the beginning and diverge once the noise is applied. The former accelerates thermalization as witnessed by (i) higher decay rate as shown in the inset, and (ii) sustained closeness of solid lines vs dotted lines, and sustained energy of the state at long times. In (b) we look at the ability of noise to introduce non-integrability in an integrable system and aid thermalization. The dotted lines observe recurrences during its evolution and indicate that the system does not thermalize. However, the solid lines observe a sustained decay and converge to a thermal state. The insets depict a condensed representation of the spin chain, where three noisy spins are highlighted in red. The configurations shown correspond to two randomly selected examples for illustrative purposes.
• Figure 4: Phase-flip noise vs Haar random unitary noise: The main plot shows that the trace distances decay at the same rate for both phase-flip noises at all probabilities and the Haar-random unitary noise. This is reinforced in the inset where the corresponding values of $\kappa$ lie very close to each other but are higher than the plain-evolved dynamics. The second inset illustrates a condensed lattice of spins with red spin denoting the noisy space and the dotted box describes the test space.
• Figure 5: Growth of mutual information in noiseless and noisy protocols: (a) Shows the dynamics of correlations of noise subspaces (violet spins) $N_1 \in [L-1, L-2, L-3], N_2 \in [0,1,2]$ placed at equal distances from the test subspace, $T$ (dotted). We see that the noise accelerates correlation propagation as compared to that due to coherent transport (violet spins replaced with green spins). The initial sharp rise of the red line is likely due to the overlap of $N_1$ with the initial state. (b) Dynamics of correlations of noise applied at unequal distances with $T \in [0,1,2]$. We see the correlations from $N_1 \in [L/4 -1, L/4, L/4+1]$ reach $T$ earlier than from $N_2 \in [L-1, L-2, L-3]$ and observe a larger increase in the mutual information. (c) A part of $N$, $T$ overlap and we see a faster growth in correlations and greater plateau of correlations from the overlapping space. Finally, in (d) we apply a cascade of shocks on $N\in[L-1, L-2, L-3]$ and observe that the velocity of information propagation to $T\in[0,1,2]$ does not change significantly. This is likely because a non-integrable system thermalizes by itself and consequently, a single noise application readily saturates the bound on velocity.