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arXiv 2403.01760quant-ph
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通过冷却进行量子计算

Quantum Computation by Cooling

Jaeyoon Cho

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8 pages, 3 figures
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AI总结：

本文提出受腔冷却启发、通过模拟零温储层并反复丢弃辅助量子比特来制备基态的哈密顿量模型，证明其与量子线路计算能力等价，并用于组合优化和多体基态制备。

摘要：

绝热量子计算是一种范式模型，旨在通过寻找封装了解的多体基态来解决计算问题。然而，它使用依赖于复杂多体哈密顿量谱隙的绝热演化，这使得对其进行分析令人生畏。虽然直接冷却绝热演化的最终有隙系统似乎是可行的替代方案，但在一般基础上对此类方案的分析仍然缺失。在这里，我们为此目的提出了一个特定的哈密顿量模型。该方案受腔冷却启发，涉及对零温储层的模拟。反复丢弃辅助储层量子比特会提取系统的熵，驱动系统趋向其基态。同时，对被丢弃量子比特的测量反过来提示系统的能级结构。我们表明，基于这种冷却过程的量子计算在计算能力上与基于量子电路的量子计算等价。随后，我们用组合优化问题的几个说明性用例来示例该方案。在第一个例子中，冷却不受任何局部能量极小值影响，使该方案退化为带有若干改进的 Grover 搜索算法。在第二个例子中，冷却受到大量局部能量极小值困扰。为规避这一点，我们在哈密顿量中植入一种机制，使被困在局部极小值中的布居能够通过高阶跃迁隧穿出来。我们通过针对一个特定组合优化问题的数值模拟来支持这一想法。我们还讨论了其在制备量子多体基态方面的应用，并论证谱隙是决定冷却时间尺度的关键因素。

英文摘要：

Adiabatic quantum computation is a paradigmatic model aiming to solve a computational problem by finding the many-body ground state encapsulating the solution. However, its use of an adiabatic evolution depending on the spectral gap of an intricate many-body Hamiltonian makes its analysis daunting. While it is plausible to directly cool the final gapped system of the adiabatic evolution instead, the analysis of such a scheme on a general ground is missing. Here, we propose a specific Hamiltonian model for this purpose. The scheme is inspired by cavity cooling, involving the emulation of a zero-temperature reservoir. Repeated discarding of ancilla reservoir qubits extracts the entropy of the system, driving the system toward its ground state. At the same time, the measurement of the discarded qubits hints at the energy level structure of the system as a return. We show that quantum computation based on this cooling procedure is equivalent in its computational power to the one based on quantum circuits. We then exemplify the scheme with a few illustrative use cases for combinatorial optimization problems. In the first example, the cooling is free from any local energy minima, reducing the scheme to Grover's search algorithm with a few improvements. In the second example, the cooling suffers from abundant local energy minima. To circumvent this, we implant a mechanism in the Hamiltonian so that the population trapped in the local minima can tunnel out by high-order transitions. We support this idea with a numerical simulation for a particular combinatorial optimization problem. We also discuss its application to preparing quantum many-body ground states, arguing that the spectral gap is a crucial factor in determining the time scale of the cooling.

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