Many optimally scaling quantum simulation algorithms employ controlled time evolution of the Hamiltonian, which is typically the major bottleneck for their efficient implementation. This work establishes a compression protocol for encoding the controlled time evolution operator of translationally invariant local Hamiltonians into a quantum circuit. It achieves a near-optimal in time $t$ scaling for circuit depth $\mathcal{O}\left[t\text{polylog}\right(tN/\epsilon \left)\right]$, while reducing the control overhead from a multiplicative to an additive factor. We report that this compression protocol enables the implementation of iterative quantum phase estimation with as few as 414 controlled-not gates for a frustrated quantum spin system on a $6\times 6$ triangular lattice and delivers ground-state energy errors below 1% (with $\pm 1.5$% variation, calculated with a hardware noise-aware pipeline) on a $4\times 4$ triangular lattice using the noisy emulator of the Quantinuum H2 trapped ion device.

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• Quantum algorithms & computation
• Quantum circuits
• Quantum computation
• Quantum information processing
• Quantum information theory
• Quantum simulation