作者：Alessandro Summer Cecilia Chiaracane Mark T. Mitchison John Goold
量子统计力学使我们能够从多体系统的微观描述中提取热力学信息。一个关键步骤是计算态密度，由此可以计算配分函数和所有有限的温度平衡热力学量。在他的工作中，我们设计并实现了一种量子算法，以在数字量子计算机上对态密度进行估计，该算法受到核多项式方法的启发。经典的核多项式方法允许通过切比雪夫多项式展开对谱函数进行采样。我们的算法使用用于随机轨迹评估的随机状态准备和控制器数量算子的组合来计算量子硬件上的展开矩。我们使用我们的算法来估计18个量子位的受控寄存器的量子H1-1俘获离子芯片上的非可积哈密顿量的态密度。这不仅代表了一种艺术计算的状态
Quantum statistical mechanics allows us to extract thermodynamic informationfrom a microscopic description of a many-body system. A key step is thecalculation of the density of states, from which the partition function and allfinite-temperature equilibrium thermodynamic quantities can be calculated. Inthis work, we devise and implement a quantum algorithm to perform an estimationof the density of states on a digital quantum computer which is inspired by thekernel polynomial method. Classically, the kernel polynomial method allows tosample spectral functions via a Chebyshev polynomial expansion. Our algorithmcomputes moments of the expansion on quantum hardware using a combination ofrandom state preparation for stochastic trace evaluation and a controlledunitary operator. We use our algorithm to estimate the density of states of anon-integrable Hamiltonian on the Quantinuum H1-1 trapped ion chip for acontrolled register of 18 qubits. This not only represents a state-of-the-artcalculation of thermal properties of a many-body system on quantum hardware,but also exploits the controlled unitary evolution of a many-qubit register onan unprecedented scale.
论文链接：http://arxiv.org/pdf/2303.13476v1
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