Continuous-time noise mitigation in analogue quantum simulation

Abstract

Analogue quantum simulators offer a promising route to explore quantum many-body dynamics beyond classical reach in the near term. However, their vulnerability to noise limits the accuracy of simulations. Here, we establish a new framework for mitigating noise in analogue quantum simulation, operating in a time-continuous manner. To our knowledge, this is the first protocol that is fully analogue and that achieves exact noise cancellation. Our method requires a small number of ancillary qubits, whose interaction with the system$-$combined with classical post-processing of joint measurement data$-$is tailored to cancel the effect of noise. Furthermore, the protocol is Hamiltonian-independent, robust to realistic ancilla noise, and avoids any discretization, preserving the continuous-time nature of the system's dynamics. This work opens a new direction for achieving high-fidelity analogue quantum simulation in the presence of noise.

Figures (4)

• Figure 1: Schematics of the noise mitigation protocol and its implementation. (a) A quantum system evolves under noisy experimental dynamics described by the Lindbladian $\mathcal{L}_\textrm{exp}$ in Eq. \ref{['experimental_lindblad_equation']} for time $t$, and then an observable $A$ is measured. (b) In the mitigation scheme, the system is coupled to one or more ancillary qubits, each prepared in the state $\ket{+}$ and evolves under the joint dissipation, described by $\mathcal{L}_\textrm{mit}$ in Eq. \ref{['lindbladian_mitigation']}. After evolving the joint system to time $t$, joint measurements of $A$ on the system and $\sigma_x$ on the ancillae are combined through classical post-processing to yield an unbiased estimation of the noise-free expectation value $\langle A(t)\rangle_\textrm{ideal}$. The joint dissipation between system and ancilla can be implemented either using (c) a stochastic Hamiltonian or (d) coupling to an additional fast-decaying ancilla.
• Figure 2: Expectation value of the total magnetization in the 2D anisotropic Heisenberg model with transverse field and $N=4$ spins. The mitigated expectation values and their standard deviations (represented by the error bars) are obtained by averaging $10^6$ samples. Partial mitigation corresponds to the correction of system noise only, ignoring ancilla noise.
• Figure 3: Normalized rate of the Loschmidt echo after quantum quench in a 1D spin Ising chain subject to the transverse field. The mitigated expectation values and their standard deviations (represented by the error bars) are obtained by averaging over $5\times10^6$ samples.
• Figure 4: Normalized power spectrum of the total magnetization for a periodically-driven spin chain. The mitigated power spectrum is computed from expectation values obtained by averaging over $10^7$ samples.