End-to-End Efficient Quantum Thermal and Ground State Preparation Made Simple

TL;DR

The paper introduces a simple, resource-efficient quantum algorithm for preparing thermal and ground states by repeatedly applying a forward-evolution quantum channel created from a system–bath interaction with a single ancilla qubit. By tuning bath initialization, coupling operators, and a Gaussian temporal envelope, the channel’s fixed point can be made arbitrarily close to the target state, with polynomial mixing-time guarantees for several physically relevant Hamiltonians. The authors develop a rigorous framework connecting the discrete channel to an effective Lindblad dynamics, derive fixed-point error bounds, and prove end-to-end runtimes that scale polynomially with system size. They also discuss concrete applications to quantum materials, chemistry on early hardware, and hardware benchmarks for dissipative engineering and error correction co-design. Overall, the work provides a theoretically rigorous, implementable pathway for end-to-end state preparation on near-term and early fault-tolerant quantum devices, with broad implications for quantum simulation of complex many-body systems.

Abstract

We propose new quantum algorithms for thermal and ground state preparation based on system-bath interactions. These algorithms require only forward evolution under a system-bath Hamiltonian in which the bath is a single reusable ancilla qubit, making them especially well-suited for early fault-tolerant quantum devices. By carefully designing the bath and interaction Hamiltonians, we prove that the fixed point of the dynamics accurately approximates the desired quantum state. Furthermore, we establish theoretical guarantees on the mixing time, and thereby providing a rigorous justification for the end-to-end efficiency of system-bath interaction models in thermal and ground state preparation, for several physically relevant systems.

Figures (1)

• Figure 1: Illustration of the quantum circuit for the proposed algorithm. The weak-coupling dynamics in \ref{['eqn:Phi_alpha']} are implemented via a second-order Trotter decomposition. The procedure requires only a single ancilla qubit. Here, $\rho_E\propto \exp(\beta \omega Z/2)$ for thermal state preparation, and $\rho_E=\ket{0}\bra{0}$ for ground state preparation. The system-bath interaction term $W_{A_S,m}(\tau/2)$ is defined in \ref{['eqn:Wnformula']} with $A_S$ randomly sampled from a set $\mathcal{A}$. For each $\omega > 0$ randomly sampled from a given distribution $g(\omega)$, the algorithm approximately generates a jump from an energy eigenstate $\ket{\psi_j}$ to another eigenstate $\ket{\psi_i}$ with Bohr frequency $\lambda_i - \lambda_j \approx \pm \omega$. That is, the change in energy of the system can be either $+\omega$ or $-\omega$. In the thermal state preparation algorithm, both energy-increasing and energy-decreasing transitions are allowed, while in the ground state preparation algorithm, only energy-decreasing transitions ($\lambda_i - \lambda_j \approx -\omega$) are permitted. The system-bath interaction block $W(\cdot)$ is explained in the Methods section.

Theorems & Definitions (46)

• Theorem 1: Informal main result
• Theorem 2
• Theorem 3
• Theorem 4: Informal
• Proposition 5
• Definition 6
• Theorem 7: Rigorous version of \ref{['thm:char_Phi_alpha']}
• proof : Proof of \ref{['thm:char_Phi_alpha_rigor']}
• Theorem 8
• proof : Proof of \ref{['thm:almost_fixed_point']}