CAREER: Near-term quantum computing: achieving quantum advantage, and next steps

在过去的几年里，量子计算已经稳步地从理论科学过渡到现实。量子实验正在以令人眼花缭乱的速度发展，我们已经到达了一个令人兴奋的时代，在这个时代，量子计算实验正在突破在高效经典计算机上可能实现的极限。虽然这些实验令人印象深刻，但由于有限的量子资源(如少量的量子比特和浅的电路深度)以及迅速淹没量子信号的未经纠正的噪声，它们的功率仍然受到根本限制。这个项目的目标是表征这些现有的不完美量子实验的计算能力，并加快该领域的下一个主要步骤：从最初的“原则证明”实验转移到实现量子加速的最终目标，以解决有用的计算问题。这是一个跨越量子理论和实验的项目，将有助于缩小这两个领域的差距。该项目的成果将传播给学术界以外的各种科学界，包括政府和工业界。此外，该项目将通过开发新的量子计算课程和为下一代量子科学家创造新的夏季研究机会，帮助维持和加强最近全球对量子计算的兴趣激增。该项目的目标将通过两个相互关联的研究目标来实现。首先是在实验上真实的噪声模型存在的情况下理解随机量子电路的能力。重点将放在证明对噪声具有健壮性的新经典硬度结果上，以及开发针对噪声随机量子电路量身定做的新经典模拟算法。第二个目标将是开发新的量子算法，这些算法可以在近期的量子实验中运行，从而获得比类似资源受限的经典计算更快的速度。这项调查将建立在PI之前的工作基础上，PI建立了新的空间受限量子算法来解决有用的线性代数问题，如矩阵求逆、计算矩阵的幂和求解行列式。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

In the last few years quantum computation has steadily transitioned from theoretical science to reality. Quantum experiments are improving at a dizzying pace and we have arrived at an exciting era in which quantum computational experiments are pushing the boundaries of what is possible on an efficient classical computer. While these experiments are impressive, their power is still fundamentally restricted due to both limited quantum resources (such as small number of qubits and shallow circuit depth) and uncorrected noise that rapidly overwhelms the quantum signal. The goal of this project is both to characterize the computational power of these existing imperfect quantum experiments, and to expedite the next major step for the field: moving from initial “proof of principle” experiments to the ultimate goal of implementing a quantum speedup that solves a useful computational problem. This is a project that straddles quantum theory and experiment and will help narrow the gap between the two fields. Results from this project will be disseminated to a wide variety of scientific communities outside academia, including in government and industry. Moreover, the project will contribute to sustaining and enhancing the recent worldwide explosion of interest in quantum computation by developing new quantum computing courses and creating new summer research opportunities for the next generation of quantum scientists.The objectives of this project will be achieved through work on two interrelated research goals. The first is to understand the power of random quantum circuits in the presence of experimentally realistic noise models. The focus will be both on proving new classical hardness results that are robust to noise, as well as developing new classical simulation algorithms tailored to noisy random quantum circuits. The second goal will be to develop new quantum algorithms that can be run on near-term quantum experiments which obtain speedups over similarly resource bounded classical computations. This investigation will build upon prior work of the PI which established new space bounded quantum algorithms for solving useful linear algebraic problems such as inverting a matrix, computing a power of a matrix, and solving the determinant.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.