Deterministic Ground State Preparation via Power-Cosine Filtering of Time Evolution Operators

Abstract

The deterministic preparation of quantum many-body ground states is essential for advanced quantum simulation, yet optimal algorithms often require prohibitive hardware resources. Here, we propose a highly efficient, non-variational protocol for ground state preparation using a Power-Cosine quantum signal processing (QSP) filter. By eschewing complex block-encoding techniques, our method directly utilizes coherent time-evolution operators controlled by a single ancillary qubit. The integration of mid-circuit measurement and reset (MCMR) drastically minimizes spatial overhead, translating iterative non-unitary filtering into deep temporal coherence. We analytically demonstrate that this approach achieves exponential suppression of excited states with a circuit depth scaling of $\mathcal{O}(Δ^{-2}\log(1/ε))$, prioritizing implementational simplicity over optimal asymptotic complexity. Numerical simulations on the 1D Heisenberg XYZ model validate the theoretical soundness and shot-noise resilience of our method. Furthermore, an advantage analysis reveals that our protocol exponentially outperforms standard Trotterized Adiabatic State Preparation (TASP) at equivalent circuit depths. This single-ancilla framework provides a highly practical and deterministic pathway for many-body ground state preparation on Early Fault-Tolerant (EFT) quantum architectures.

Figures (5)

• Figure 1: Deterministic Ground State Preparation via Power-Cosine Filtering
• Figure 2: Quantum circuit representation of the Power-Cosine Filter. The system register $\mathcal{S}$ consisting of $N$ qubits is evolved under the Hamiltonian $H$ for a tuned duration $\tau$, controlled by a single ancilla qubit $\mathcal{A}$. The successful projection of the ancilla onto $\ket{0}$ applies the non-unitary filter operator $(I + e^{-iH\tau})/2$ to the system. This block is repeated $d$ times to achieve exponential suppression of excited states.
• Figure 3: Energy convergence and theoretical state fidelity of the Power-Cosine filter. The blue squares and the red triangles indicate the ideal energy expectation and state fidelity computed via exact statevector evolution, respectively. The orange circles represent the measured energy obtained from a noiseless sampler with $10,000$ shots. Error bars denote the $1\sigma$ standard error of the mean due to finite sampling. The horizontal dotted line corresponds to the exact ground state energy $E_0$.
• Figure 4: Advantage analysis comparing the state infidelity ($1 - \mathcal{F}$) of the proposed Power-Cosine QSP filter (blue squares) and the Trotterized Adiabatic State Preparation (red circles) as a function of the circuit cost. Note the logarithmic scale on the y-axis.
• Figure 5: Energy convergence of the Power-Cosine filter under the ibm_yonsei hardware noise model. The deviation from the ideal statevector trajectory (blue squares) illustrates the accumulation of gate errors and decoherence as the circuit depth (filter degree $d$) increases.