A Variational Quantum Algorithm for Preparing Quantum Gibbs States
A Variational Quantum Algorithm for Preparing Quantum Gibbs States
复制标题
一种制备量子吉布斯态的变分量子算法
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
N. Wiebe
中科院分区：
文献类型：
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作者：
Anirban Narayan Chowdhury;G. Low;N. Wiebe
吉布斯分布的制备是量子计算的重要任务。在某些类型的量子模拟中，这是必要的第一步，对于量子玻尔兹曼训练等量子算法也是必不可少的。尽管如此，由于需要内存开销，大多数制备热态的方法在近期量子计算机上实现是不切实际的。在这里，我们提出了一种基于最小化量子系统自由能的变分方法来制备吉布斯态。关键的洞察力，使这一实际是使用傅立叶级数近似的对数，允许自由能的熵成分的估计通过一系列更简单的测量，可以结合在一起，使用经典的后处理。我们进一步表明，如果对可编程量子电路的变分参数的初始猜测足够接近全局最优，则该方法在恒定误差内有效地生成高温吉布斯态。最后，我们在数值上检验了这一过程，并使用Trotterized绝热态制备作为一种分析，证明了我们的方法对五量子位哈密顿量的可行性。
Preparation of Gibbs distributions is an important task for quantum computation. It is a necessary first step in some types of quantum simulations and further is essential for quantum algorithms such as quantum Boltzmann training. Despite this, most methods for preparing thermal states are impractical to implement on near-term quantum computers because of the memory overheads required. Here we present a variational approach to preparing Gibbs states that is based on minimizing the free energy of a quantum system. The key insight that makes this practical is the use of Fourier series approximations to the logarithm that allows the entropy component of the free-energy to be estimated through a sequence of simpler measurements that can be combined together using classical post processing. We further show that this approach is efficient for generating high-temperature Gibbs states, within constant error, if the initial guess for the variational parameters for the programmable quantum circuit are sufficiently close to a global optima. Finally, we examine the procedure numerically and show the viability of our approach for five-qubit Hamiltonians using Trotterized adiabatic state preparation as an ansatz.
影响因子：
19.6
作者：
Motta, Mario;Sun, Chong;Chan, Garnet Kin-Lic
通讯作者：
Chan, Garnet Kin-Lic
熵估计的量子查询复杂度
影响因子：
2.5
作者：
Li, Tongyang;Wu, Xiaodi
通讯作者：
Wu, Xiaodi