Consultancy firm KPMG, together with a team of researchers from the Technical University of Denmark (DTU) and a yet-to-be-named European bank, has been piloting the use of quantum computing to determine which stocks to buy and sell for maximum return, an age-old banking operation known as portfolio optimization.

咨询公司KPMG与丹麦工业大学（DTU）的一个研究团队和一家未给出名字的欧洲银行合作，试图利用量子计算来决定股票的买入和沽出，目的是获得最大回报，这是一宗古老的银行业务，名为投资组合优化。

The researchers ran a model for portfolio optimization on Canadian company D-Wave's 2,000-qubit quantum annealing processor, comparing the results to those obtained with classical means. They found that the quantum annealer performed better and faster than other methods, while being capable of resolving larger problems – although the study also indicated that D-Wave's technology still comes with some issues to do with ease of programming and scalability.

这些研究人员在加拿大公司D-Wave的2000位量子退火处理器上运行了某个投资组合优化模型，并将结果与用经典手段获得的结果进行比较。他们发现，量子退火器的性能比其他方法更好及更快，同时还能够解决更大的问题，尽管该研究也表明，D-Wave的技术仍然存在一些问题，例如有关编程便利性和可扩展性方面的问题。

研究人员在加拿大公司D-Wave的2000位量子退火处理器上运行投资组合优化模型。（图：D-Wave）

The smart distribution of portfolio assets is a problem that stands at the very heart of banking. Theorized by economist Harry Markowitz as early as 1952, it consists of allocating a fixed budget to a collection of financial assets in a way that will produce as much return as possible over time. In other words, it is an optimization problem: an investor should look to maximize gain and minimize risk for a given financial portfolio.

证券资产的巧妙分配是占据银行业务核心的问题。经济学家Harry Markowitz早在1952年就将该问题进行理论化，证券资产分配包括将固定的预算在金融资产集合上配给，令其在一段时间内产生尽可能多的回报。换句话说，是个优化问题：投资者应该设法在给定的金融组合里实现收益最大化和风险最小化。

As the number of assets in the portfolio multiplies, the difficulty of the calculation exponentially increases, and the problem can quickly become intractable, even to the world's largest supercomputers. Quantum computing, on the other hand, offers the possibility of running multiple calculations at once thanks to a special quantum state that is adopted by quantum bits, or qubits.

投资组合的资产数量成倍增加时，计算的难度也会随着成倍增加，最后很快可能变成即使用上世界上最大的超级计算机也解决不了的优化问题。量子计算由于量子比特（或称Qubits）采用了特殊的量子状态可以同时进行多次的计算。

Quantum systems, for now, cannot support enough qubits to have a real-world impact. But in principle, large-scale quantum computers could one day solve complex portfolio optimization problems in a matter of minutes – which is why the world's largest banks are already putting their research team to work on developing quantum algorithms.

量子系统目前还未能支持足够的量子比特，还不足以对现实世界产生影响。但一般而言，大规模量子计算机有朝一日将可以在几分钟内解决各种复杂的投资组合优化问题，这也是为什么世界上最大的银行都已经在组建研究团队开发量子算法。

To translate Markowitz's classical model for the portfolio selection problem into a quantum algorithm, the DTU's researchers formulated the equation into a quantum model called a quadratic unconstrained binary optimization (QUBO) problem, which they based on the usual criteria used for the operation such as budget and expected return.

DTU的研究人员为了将Markowitz的投资组合选择问题的经典模型转化为量子算法，他们先将该方程表述为一个名为为二次无约束二元优化（QUBO）问题的量子模型，然后再在预算和预期收益等参数的基础上利用QUBO进行通常的操作。

When deciding which quantum hardware to pick to test their model, the team was faced with a number of options: IBM and Google are both working on a superconducting quantum computer, while Honeywell and IonQ are building trapped-ion devices; Xanadu is looking at photonic quantum technologies, and Microsoft is creating a topological quantum system.

DTU团队在决定选量子硬件测试他们的模型时也面临许多选择。IBM和谷歌都在研究超导量子计算机，Honeywell和IonQ则在打造陷离子（Trapped-ion）设备，而Xanadu则在研究光子量子技术，微软也在创建拓扑量子系统。

D-Wave's quantum annealing processor is yet another approach to quantum computing. Unlike other systems, which are gate-based quantum computers, it is not possible to control the qubits in a quantum annealer; instead, D-Wave's technology consists of manipulating the environment surrounding the system, and letting the device find a "ground state". In this case, the ground state corresponds to the most optimal portfolio selection.

D-Wave的量子退火处理器是量子计算的另一种方法。量子退火处理器与其他系统不同，其他系统是基于门的量子计算机，不能控制量子退火器里的量子比特，而D-Wave的技术则包括操纵系统周围的环境，使得设备可以找到一个 "基底状态"。在投资组合选择的情况下，基底状态对应的是最优化的组合选择。

This approach, while limiting the scope of the problems that can be resolved by a quantum annealer, also enable D-Wave to work with many more qubits than other devices. The company's latest device counts 5,000 qubits, while IBM's quantum computer, for example, supports less than 100 qubits.

D-Wave这种方法虽然限制了量子退火器所能解决的问题范围，但也令D-Wave能够比其他设备多出许多量子比特。D-Wave公司最新的设备可达5000量子比特，IBM的量子计算机支持的量子比特不到100。

The researchers explained that the maturity of D-Wave's technology prompted them to pick quantum annealing to trial the algorithm; and equipped with the processor, they were able to embed and run the problem for up to 65 assets.

研究人员解释称，D-Wave技术的成熟度促使他们选择了量子退火进行该算法的试用；他们利用配备的退火处理器能够嵌入并运行含多达65个资产的问题。

To benchmark the performance of the processor, they also ran the Markowitz equation with classical means, called brute force. With the computational resources at their disposal, brute force could only be used for up to 25 assets, after which the problem became intractable for the method.

他们为了测试处理器的性能还用经典方法运行了Markowitz方程，即所谓的蛮力法。在他们所掌握的计算资源下，蛮力法最多只能用于解决25个资产的问题，再多蛮力法就难以解决了。

Comparing between the two methods, the scientists found that the quality of the results provided by D-Wave's processor was equal to that delivered by brute force – proving that quantum annealing can reliably be used to solve the problem. In addition, as the number of assets grew, the quantum processor overtook brute force as the fastest method.

科学家们在两种方法之间进行比较后发现，D-Wave的处理器提供的结果质量与蛮力法提供的结果质量不差上下，这证明了量子退火可以可靠地用于解决这个问题。此外，随着资产数量的增加，量子处理器超过蛮力法成了最快的方法。

From 15 assets onwards, D-Wave's processor effectively started showing significant speed-up over brute force, as the problem got closer to becoming intractable for the classical computer.

在资产达到15个或更多时，D-Wave的处理器的有效速度明显开始快过蛮力法，15个资产优化问题接近经典计算机的不可解局限。

To benchmark the performance of the quantum annealer for more than 25 assets – which is beyond the capability of brute force – the researchers compared the results obtained with D-Wave's processor to those obtained with a method called simulated annealing. There again, shows the study, the quantum processor provided high-quality results.

为了对量子退火器的性能在资产超过25时（蛮力法已力不能及）进行基准测试，研究人员还比较了使用D-Wave处理器获得的结果与另外一种使用名为模拟退火的方法获得的结果。这里的研究也表明，D-Wave量子处理器提供了高质量结果。

Although the experiment suggests that quantum annealing might show a computational advantage over classical devices, therefore, Ulrich Busk Hoff, researcher at DTU, who participated in the research, warns against hasty conclusions.

虽然实验表明量子退火可能显示了比经典器件更强的计算优势，但参与了该项研究的DTU研究员Ulrich Busk Hoff表示要谨慎，不能草率地就此下结论。

"For small-sized problems, the D-Wave quantum annealer is indeed competitive, as it offers a speed-up and solutions of high quality," he tells ZDNet. "That said, I believe that the study is premature for making any claims about an actual quantum advantage, and I would refrain from doing that. That would require a more rigorous comparison between D-Wave and classical methods – and using the best possible classical computational resources, which was far beyond the scope of the project."

他告诉记者，" D-Wave量子退火器对于小一点的问题确实具有竞争力，因为量子退火器提供了更快速度和高质量的解决方案。但话又说回来，我认为这项研究要对于实际的量子优势做出任何结论还为时过早，我会避免做出结论。要最后做结论的话需要在D-Wave和经典方法之间进行更严格的比较，得用上最好的经典计算资源，这已经远远超出了这个项目的范围。"

DTU's team also flagged some scalability issues, highlighting that as the portfolio size increased, there was a need to fine-tune the quantum model's parameters in order to prevent a drop in results quality. "As the portfolio size was increased, a degradation in the quality of the solutions found by quantum annealing was indeed observed," says Hoff. "But after optimization, the solutions were still competitive and were more often than not able to beat simulated annealing."

DTU团队还提出了一些可扩展性问题，特别是随着组合规模的增加，量子模型的参数需要进行微调后才能防止结果质量的下降。Hoff表示，"随着组合规模的增加，量子退火法找到的解确实出现质量上的下降。但经优化后解决方案仍然具有竞争力，更多的时候仍然能够击败模拟退火。"

In addition, with the quantum industry still largely in its infancy, the researchers pointed to the technical difficulties that still come with using quantum technologies. Implementing quantum models, they explained, requires a new way of thinking; translating classical problems into quantum algorithms is not straightforward, and even D-Wave's fairly accessible software development kit cannot be described yet as "plug-and-play".

此外，由于量子产业在很大程度上仍处于起步阶段，研究人员指出，使用量子技术在操作上还存在一些困难。他们解释表示，实现量子模型需要一种新的思维方式；要将经典问题转化为量子算法并不容易，即便是D-Wave已经相当方便的软件开发工具包都也还不能说可以 "即插即用"。

The Canadian company's quantum processor nevertheless shows a lot of promise for solving problems such as portfolio optimization. Although the researchers shared doubts that quantum annealing would have as much of an impact as large-scale gate-based quantum computers, they pledged to continue to explore the capabilities of the technology in other fields.

不过，这家加拿大公司的量子处理器在解决投资组合优化等问题上表现出了很好的前景。尽管研究人员对于量子退火是否会像大规模基于门的量子计算机那样产生巨大影响表示怀疑，但他们表示一定会继续探索该技术在其他领域的应用。

"I think it's fair to say that D-Wave is a competitive candidate for solving this type of problem and it is certainly worthwhile further investigation," says Hoff.

Hoff表示，"我认为可以公平地说，D-Wave是解决这一类问题的有力竞争者，当然也值得进一步研究。"

KPMG, DTU's researchers and large banks are far from alone in experimenting with D-Wave's technology for near-term applications of quantum computing. For example, researchers from pharmaceutical company GlaxoSmithKline (GSK) recently trialed the use of different quantum methods to sequence gene expression, and found that quantum annealing could already compete against classical computers to start addressing life-sized problems.

利用D-Wave技术试验量子计算近期应用的远不止KPMG、DTU的研究人员和大型银行。例如，制药公司GlaxoSmithKline (GSK)的研究人员最近在用不同的量子方法对基因表达进行测序的试验，也发现量子退火在一些现实世界问题上已经可以与经典计算机一较高低了。