Constant-Depth Quantum Imaginary Time Evolution Using Dynamic Fan-out Circuits

Abstract

Dynamic quantum circuits combine mid-circuit measurement with classical feed-forward, enabling circuit constructions with reduced entangling-gate depth. Here, we investigate their use in Quantum Imaginary Time Evolution (QITE), where circuit depth and parameter growth limit practical implementations of ground-state preparation. For dense classical optimization Hamiltonians, we introduce a reduced-parameter QITE ansatz that restricts entanglement generation via a small set of control qubits, enabling each QITE layer to be implemented with constant two-qubit gate depth using fan-out-based dynamic circuits. In noiseless simulations of exact cover and set partitioning instances, the reduced ansatz yields a higher success probability than standard QITE approaches. We implement unitary, dynamic fan-out, and semi-classical adaptive variants on IBM superconducting hardware. The semi-classical variant performs favorably to the unitary implementation, while the fully dynamic construction exposes the trade-offs between entangling-depth reduction and measurement and feed-forward overhead associated to dynamic circuit implementations. Using a fidelity threshold of 0.5 relative to the noiseless QITE ansatz, we show that dynamic fan-out based QITE would outperform unitary implementations on current devices when the measurement and two-qubit gate errors are reduced by 65% and the feedback latency is halved.

Figures (13)

• Figure 1: (a) Single layer of the QITE ansatz. (b) Implementation of a constant‑depth parameterized multi‑qubit rotation using two fan-out gates baumer_measurement-based_2024 and $k=1$.
• Figure 2: Circuit layer of the semi-classical approach with $k=1$. This simplification of Fig. \ref{['fig:quantum_circuits']} is possible when qubit $k$ only has diagonal operations after the last fan-out gate. The double lines denote the flow of classical information.
• Figure 3: Mean success probabilities for difficult exact cover instances ($M=125$, $\Delta\tau=0.004$) across different variants of P2A. Error bars indicate the variance, $\sigma^2$ over instances. "Reduced ZY" refers to the set $\mathcal{S}_{\mathrm{red}}$, and "Compressed ZY" is when compressing the circuit. "Compressed XY" is when utilizing $XY$ rotations instead of $ZY$. "Complete" is the original ansatz P2A. "Universal reduced" is the set of Eq. \ref{['eq:diagonal_qite_universal_generators']}.
• Figure 4: Mean success probabilities of the reduced parameter QITE on the difficult set partitioning instances using $\Delta\tau = 8\times10^{-5}, M = 100$. The results are compared to QAOA and VQE results from Svensson_2023_Hybridcacao_2024_the The shaded area gives the variance, $\sigma^2$, which is notably low for QITE.
• Figure 5: Expectation value of the problem Hamiltonian for a 20-qubit exact cover instance obtained from noiseless simulation and from unitary (with and without semi-classical simplification) and dynamic circuit hardware implementations, using $M=20$ and $\Delta\tau=0.005$. The lines start at iteration $m=1$ of QITE, as all methods yield zero expectation value before the first iteration. The dashed red line indicates the ground-state energy. The crosses indicate samples taken at iteration $m=20$, corresponding to the measured overlap with the ground state.