Approximate Quantum Arithmetic Units

量子技术商业化的最新进展对量子计算领域产生了重大影响。量子计算是一个很有前途的范例，对于需要底层硬件提供强大计算能力的应用来说，它具有巨大的未来潜力。量子计算使得经典计算机无法解决的具有挑战性的问题成为可能。虽然量子技术还处于早期阶段，但社区正在探索量子计算机在实际应用中的计算优势。最近，谷歌声称拥有一台53量子比特（qubits）的量子计算机，可以在200秒内完成一个计算任务，而在最先进的经典超级计算机上，同样的任务可能需要1万年的时间。目前最先进的量子计算机是基于嘈杂的中等规模量子（NISQ）计算模型，其中硬件量子位是嘈杂的。NISQ器件由于量子退相干、栅极误差、串扰等因素导致器件不稳定，存在误差。因此，在当代量子计算机上实现大规模量子电路是不可行的。在这项合作研究中，我们提出使用近似计算来实现NISQ设备上的算术运算。诸如乘法、除法、平方根等算术运算是许多应用程序（如图像处理应用程序）的基础。我们利用近似计算来简化算术量子电路，并在NISQ器件上实现。有一大类新兴的应用程序可以抵御不精确。这些应用并不总是需要精确和精密的电路。因此，这种特性提供了一个机会，以减少量子算术电路的大小，并在真正的量子计算机上实现它们。这项合作研究为高素质人才在量子计算领域获得宝贵经验提供了一个独特的机会，这反过来将帮助加拿大高科技公司，并将使他们在量子计算行业中占据优势。

Recent progress in commercialization of quantum technologies has had significant impact on the landscape of quantum computing. Quantum computing is a promising paradigm with tremendous future potentials for applications that require significant computing power from the underlying hardware. Quantum computing makes it feasible to run challenging problems that are beyond the capability of classical computers. Although, quantum technology is in early stages, the community is exploring computing advantages from quantum computers for practical applications. Recently, Google claimed a 53 quantum bits (qubits) quantum computer that can offer quantum supremacy by completing a computational task in 200 seconds whereas the same task may take 10K years on a state-of-the-art classical supercomputer. Current state-of-the-art quantum computers are based on Noisy Intermediate-Scale Quantum (NISQ) computing model where hardware qubits are noisy. Due to quantum decoherence, gate errors, crosstalks, etc., NISQ devices are not stable and suffer from errors. As a result, it is not feasible to implement large scale quantum circuits on contemporary quantum computers. In this collaborative research, we propose using approximate computing to implement arithmetic operations on NISQ devices. Arithmetic operations such as multiplication, division, square root, etc. are the backbone of many applications such as image processing applications. We exploit approximate computing to simplify arithmetic quantum circuits and implement them on NISQ devices. There are a large class of emerging applications that are resilient against imprecision. Accurate and precise circuits are not always needed for these applications. Thus, this characterization provides an opportunity to reduce the size of quantum arithmetic circuits and implement them on real quantum computers. This collaborative research provides a unique opportunity for highly-qualified personnel to gain valuable experience in the area of quantum computing which in turn will help Canadian high-tech companies and will give them an edge in quantum computing industry.