October 30, 2024 | ZHIYAN DING, BOWEN LI, AND LIN LIN
This paper presents efficient quantum Gibbs samplers that satisfy the Kubo-Martin-Schwinger (KMS) detailed balance condition. The key idea is to construct Lindblad dynamics that ensure the Gibbs state is a fixed point of the dynamics, enabling efficient sampling on quantum computers. The proposed samplers use a finite set of jump operators, which allows for greater design flexibility and simpler implementation compared to previous methods. The KMS detailed balance condition is a weaker requirement than the GNS detailed balance condition, making it more suitable for efficient quantum simulation. The paper shows that the KMS detailed balance condition can be satisfied by constructing a Lindbladian with a specific form, which ensures that the Gibbs state is a fixed point of the dynamics. The proposed quantum Gibbs samplers have a comparable quantum simulation cost to previous methods but with greater flexibility and simpler implementation. The paper also discusses the implications of the KMS detailed balance condition for quantum Gibbs sampling and highlights the importance of the KMS condition in ensuring the convergence of the dynamics to the Gibbs state. The results demonstrate that the KMS detailed balance condition is a powerful tool for designing efficient quantum Gibbs samplers that can be implemented on quantum computers.This paper presents efficient quantum Gibbs samplers that satisfy the Kubo-Martin-Schwinger (KMS) detailed balance condition. The key idea is to construct Lindblad dynamics that ensure the Gibbs state is a fixed point of the dynamics, enabling efficient sampling on quantum computers. The proposed samplers use a finite set of jump operators, which allows for greater design flexibility and simpler implementation compared to previous methods. The KMS detailed balance condition is a weaker requirement than the GNS detailed balance condition, making it more suitable for efficient quantum simulation. The paper shows that the KMS detailed balance condition can be satisfied by constructing a Lindbladian with a specific form, which ensures that the Gibbs state is a fixed point of the dynamics. The proposed quantum Gibbs samplers have a comparable quantum simulation cost to previous methods but with greater flexibility and simpler implementation. The paper also discusses the implications of the KMS detailed balance condition for quantum Gibbs sampling and highlights the importance of the KMS condition in ensuring the convergence of the dynamics to the Gibbs state. The results demonstrate that the KMS detailed balance condition is a powerful tool for designing efficient quantum Gibbs samplers that can be implemented on quantum computers.