The good, the bad, and quantum computers
If you read this blog post, it’s safe to assume that it’s not your first take on quantum computing. You probably read blogposts, articles, and even research papers featuring an introduction paragraph stating some variation of the following (warning: AI-generated, watch out for tedium):
Quantum computers offer a paradigm shift in computational capability by leveraging the unique properties of quantum mechanics, such as superposition and entanglement. These machines have the potential to solve certain problems exponentially faster than classical computers, making them especially promising for fields like cryptography, optimization, and simulation of complex quantum systems. Applications range from enhancing drug discovery and materials science to revolutionizing logistics and financial modeling. As research advances, quantum computers could enable breakthroughs that are currently beyond the reach of traditional computing technologies, opening avenues for innovation across science and industry.
John Singer Sargent: Gasset. Oil on canvas.
It is hardly a secret that quantum computing research received a tremendous funding boost from defense agencies after Peter Shor discovered a quantum-accelerated factorization algorithm. Factorization, the mathematical operation of finding the prime numbers that comprise the multiplication of a given number (e.g, 3×7=21), is assumed to be a problem that is exponentially hard to compute on any classical computer. Oversimplifying a bit, it means that no one has found a significantly cleverer way of solving this problem other than checking all the possible combinations. For large numbers represented by a strong 2048-bit encryption (these are numbers with more than 600 digits…), this exercise simply explodes and requires about a similar fantastic number of logical operations, making it an age-of-the-universe kind of assignment even for the strongest supercomputers. Why is this so important? Because the magic of the RSA asymmetric encryption protocol (want to know more on asymmetric encryption? read below the blogpost), which is responsible for secure authentication and encryption key exchange over the internet, relies solely on the impracticality of the factorization problem. Now imagine why defense agencies are so desperately interested in a technology that promises to eliminate this exponential complexity. The problem of peeking into one’s encrypted information can become manageable by performing just a couple of billions logical operations, which for an ideal full-scale quantum computer will take something between seconds and hours.
Hold your horses, you must think now, are we spending all these dollars to develop a technology whose primary benefit is compromising everyone’s online privacy? The answer to that is two-fold: yes, and as humanity demonstrated once and again, it is eventually inevitable to stop technological development, even if it contributes to negative causes, and no, because as these tedious introductions teach us, quantum computing can contribute to solving many problems with potential for immense positive impact on humanity.
An important class of problems that quantum computers are expected to accelerate the solution of is simulating the behavior of physical systems subjected to the interaction between a large number of degrees of freedom. Those problems are inherently hard to solve, since each degree of freedom can interact with many others, and simple combinatorics can show that it requires running a number of calculations that scale as the exponent of the number of degrees of freedom, taking us back to the fantastic calculation overhead we encountered above. This might be the case in large logistics optimizations and complex financial modeling problems, for example. If these are microscopic degrees of freedom in a real physical system we’re considering (e.g, particles in a large molecule), then the interaction is by itself quantum mechanical, and one cannot hope to solve it without quantum computers. Feynman stated this fundamental truth in his memorable words: “Nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical, and by golly it’s a wonderful problem, because it doesn’t look so easy”. New drug discovery and material science emerge as promising applications that fall under this category.
Take, for example, the Haber-Bosch process, which is one of the most important industrial breakthroughs in human history, enabling the production of ammonia required for nitrogen-based fertilizers. Historically, industrial production of fertilizers allowed a massive increase in crop yield. Before it, crop yields were limited by the availability of naturally occurring nitrates. After it, food production skyrocketed, making it instrumental for feeding the billions of lives inhabiting our planet. Research suggests that quantum computers can dramatically enhance our ability to model complex reactions and understand precisely how the metal catalysts in ammonia factories work. This opens the door to designing new catalysts that work under milder pressure and temperature conditions than those used today. In practical terms, this means making ammonia with less energy, lowering costs, and cutting carbon emissions (estimated to be 1-2% of total global emissions), all by using quantum simulations to guide smarter catalyst development.
I’ve cunningly chosen this example as it gives a fascinating historical case-study demonstrating that technology is nothing but a double-edged sword, which can be wielded by humanity to heal or to harm. The Haber-Bosch process is named after Fritz Haber, the chemist who discovered it in 1909, and Carl Bosch, the engineer who developed the industrial-scale process. Fritz was born in 1868 to a Jewish family in Breslau (then part of the German Empire). He was a brilliant chemist who believed in the power of science to uplift nations. He was also deeply patriotic, and both qualities are strongly manifested in his words: “The scientist belongs in wartime, like everyone, to their fatherland. In peacetime, he belongs to humanity.”
Fritz Haber in his laboratory. Picture from the Max Planck Society.
During World War I, driven by his fervent nationalism, Haber turned his talents toward warfare. He became the architect of Germany’s chemical weapons program. In 1915, he personally oversaw the first large-scale chlorine gas attack on French troops at Ypres, Belgium. Thousands died. Haber reportedly saw this not as cruelty, but as science in service of his country. He believed gas warfare would shorten the war, though, in reality, there is no evidence for that. The cost of that decision reached into his own home. Just days after the Ypres attack, his wife Clara Immerwahr, herself a chemist and a pacifist, shot herself with Haber’s service revolver. She was said to be horrified by his work on poison gas. Haber left the very next day to supervise gas attacks on the Eastern Front.
After the war, Haber’s legacy only grew more complex. He won the Nobel Prize in Chemistry in 1918 for his discovery of the ammonia synthesis. Many protested, and some boycotted the ceremony, but his scientific contribution to agriculture was undeniable. Then came the ultimate irony. In 1933, Fritz Haber, once hailed as a German national hero for revolutionizing agriculture and developing wartime chemical weapons, was forced to flee the country he had devoted his life to. Despite converting to Christianity and serving Germany with unwavering loyalty, the Nazis classified him as Jewish under their racial laws and ordered him to dismiss all Jewish employees from the research institute he was heading. Unable to comply with such injustice, he resigned in protest and left Germany, first for Cambridge, and later, hoping to continue his scientific work and embracing his Jewish origin in what was then British Mandate Palestine. There, Chaim Weizmann invited him to help establish a new scientific research institute that would later become the Weizmann Institute of Science (which the author of this blogpost is proud to be alumnus of). Haber saw it as a chance to rebuild something meaningful, but his health was failing, and the trauma of exile weighed heavily on him. He died in a Basel hotel in 1934, just a year after leaving Germany, betrayed by the very nation he helped feed and defend. To add a final bitter twist, the pesticides developed in part from his earlier research would later evolve into Zyklon B – the gas used in Nazi extermination camps to extinguish his people.
One thing is certain: his life raises thorny, unresolved questions about science and morality and while the complicated legacy of Fritz Haber stretches between a hero and a villain – that of quantum computers has not been written yet.
Additional text: Asymmetric encryption in a nutshell
The idea and power of asymmetric encryption can be explained quite faithfully also in non-mathematical terms. Imagine that you have a common language, say English, and another secret language, say Chinese. In the days before Google Translate and AI, printed bilingual dictionaries were divided into two sections: English-Chinese and Chinese-English, each organized in alphabetical order to allow an efficient search. Imagine taking the English-Chinese part, and distributing it publicly – this is called the public key. Anyone can now take an English message and encrypt it to Chinese in a relatively efficient manner by searching the words alphabetically and translating them. The message can then be broadcast freely through a public channel, without worrying about interception, because Chinese is a secret language. The Chinese-English part of the dictionary, or the private key, is kept secret by the distributing party (e.g., your credit card company), allowing it to decrypt Chinese messages to English with the same efficiency exclusively.
and decrypting any intercepted message? It is a hard, yet manageable, problem for a human, but it can be done in the blink of an eye by a simple computer. The ingenious idea behind the RSA protocol is to use mathematics to make the inversion problem exponentially hard. It is very easy to multiply two large prime numbers, the result being the public key, but it is very hard, even for a supercomputer, to factor it back to these prime factors. These prime factors are essential for deriving the private key. The product, however, is made public and can be used by anyone to encrypt messages intended for the private key holder
