论文标题
近期量子硬件的哈密顿模拟算法
Hamiltonian Simulation Algorithms for Near-Term Quantum Hardware
论文作者
论文摘要
量子电路模型是设计量子算法的事实上的方式。然而，任何水平的抽象都远离基础硬件的开销。在近期，嘈杂，中间尺度量子（NISQ）硬件具有严格限制资源的时代，此开销可能是不合理的。在这项工作中，我们开发了用于哈密顿模拟的量子算法“低于”电路模型的量子算法，从而利用了大多数量子硬件实现中对量子相互作用的基本控制。然后，我们在标准误差模型下分析了这些技术的影响，在标准误差模型中，每个门误差发生错误，以及一个单位时间恒定误差率的误差模型。 为了量化这种方法的好处，我们将其应用于一个规范的示例：2D自旋费米 - 哈伯德模型的时间动力学模拟。我们得出分析电路的身份，以有效地从两分相互作用中综合多量化的发展。结合针对非复杂性制度量身定制的Trotter产品公式的新误差界，以及对上述每门闸门和每次误差模型下误差传播的仔细分析，我们改进了先前通过多个尺度级的汉密尔顿模拟方法的最佳方法。根据我们的计算，对于5 $ \ MATHBF \ times $ 5费米 - - - - - - - - - 小时晶格，我们在每门误差模型中将电路深度从800,160降低到1460，或每次误差模型中电路深度等于440。这带来了汉密尔顿模拟，以前是当前硬件的非平凡示例，在NISQ时代更加可行。
The quantum circuit model is the de-facto way of designing quantum algorithms. Yet any level of abstraction away from the underlying hardware incurs overhead. In the era of near-term, noisy, intermediate-scale quantum (NISQ) hardware with severely restricted resources, this overhead may be unjustifiable. In this work, we develop quantum algorithms for Hamiltonian simulation "one level below" the circuit model, exploiting the underlying control over qubit interactions available in principle in most quantum hardware implementations. We then analyse the impact of these techniques under the standard error model where errors occur per gate, and an error model with a constant error rate per unit time. To quantify the benefits of this approach, we apply it to a canonical example: time-dynamics simulation of the 2D spin Fermi-Hubbard model. We derive analytic circuit identities for efficiently synthesising multi-qubit evolutions from two-qubit interactions. Combined with new error bounds for Trotter product formulas tailored to the non-asymptotic regime and a careful analysis of error propagation under the aforementioned per-gate and per-time error models, we improve upon the previous best methods for Hamiltonian simulation by multiple orders of magnitude. By our calculations, for a 5$\mathbf\times$5 Fermi-Hubbard lattice we reduce the circuit depth from 800,160 to 1460 in the per-gate error model, or the circuit-depth-equivalent to 440 in the per-time error model. This brings Hamiltonian simulation, previously beyond reach of current hardware for non-trivial examples, significantly closer to being feasible in the NISQ era.
