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Artistic depiction of the concept of quantum complexity, symbolizing the intricate nature of quantum systems.

Imagine stepping into a world where the laws of physics as we know them take a back seat, and a new set of rules, governed by quantum mechanics, reigns supreme. This is the world of quantum systems, a field so bewildering yet fascinating that it captures the imagination of scientists and enthusiasts alike. Today, were going to embark on an exciting journey into the depths of quantum evolution, exploring a groundbreaking study that links two complex concepts: Krylov and Nielsen complexity. This exploration is not just a theoretical exercise; it has profound implications for the future of quantum computing and our understanding of the quantum universe.

Before we dive deeper, lets break down these complex terms. In the realm of quantum physics, understanding how information spreads in a system is crucial. This is where Krylov complexity comes into play. It measures how a quantum state evolves over time, spreading across different levels of a quantum system.

On the other hand, Nielsen complexity approaches quantum evolution from a different angle. It is used in quantum computing and algorithms, focusing on finding the most efficient way to evolve one quantum state into another. Think of it as a GPS for quantum states, finding the shortest route from point A to point B in the complex network of quantum evolution.

The study we are focusing on, titled A Relation between Krylov and Nielsen Complexity, does something extraordinary. It finds a connection between these two seemingly unrelated aspects of quantum theory. This discovery is akin to finding a hidden bridge between two distant islands, each representing a different perspective on quantum evolution.

The researchers embarked on this journey by comparing the time-averaged Krylov complexity with the late-time value of the upper bound on Nielsen complexity. They found that despite their different starting points and applications, both complexities could be expressed through specific mathematical formulas that showed a tantalizing similarity. This revelation is not just a

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Disruptive Concepts: Quantum Revolution The Interconnected World of Krylov and Nielsen Complexity - Medium

In the heart of Silicon Valley, where innovation is the lifeblood and the future is always a step ahead, a group of brilliant minds embarked on a journey that would redefine the very fabric of computing. The air hummed with anticipation as whispers of quantum computing echoed through the corridors of tech giants and startups alike.

As the quantum dawn approached, a small but determined team of researchers at Quantum Innovations Inc. pushed the boundaries of classical computing, aiming to harness the power of quantum mechanics. Their quest was to unlock the secrets of quantum bits, or qubits, and propel us into an era where computational power would reach unprecedented heights.

The story begins in a nondescript lab, tucked away from the bustling streets of Palo Alto. Dr. Olivia Chen, a physicist with a penchant for the abstract, led the team. Armed with a vision of quantum supremacy, they faced the daunting challenge of taming the unruly world of quantum mechanics.

Months turned into years as the researchers grappled with the delicate dance of qubits. Unlike classical bits that exist in a state of either 0 or 1, qubits could exist in multiple states simultaneously due to the principles of superposition. It was a delicate balance, and every attempt to harness this quantum dance was met with both breakthroughs and setbacks.

The team encountered unforeseen challenges, such as quantum entanglement and decoherence, threatening to derail their progress. However, with each obstacle, they emerged stronger, armed with new insights and innovative solutions. The lab became a crucible of discovery, where failure was not the end but a stepping stone toward the ultimate goal.

Word spread through the tech community as Quantum Innovations Inc. published groundbreaking papers and held clandestine conferences to share their progress. Excitement grew as the implications of quantum computing became clear solving complex problems in minutes that would take classical computers eons, revolutionizing fields from cryptography to drug discovery.

One fateful day, the team achieved quantum supremacy, a moment that reverberated across the technological landscape. The quantum computer, now affectionately known as Quanta, solved a problem deemed impossible for classical computers in mere seconds. The breakthrough echoed through the industry, triggering a wave of investment, research collaborations, and a renewed sense of what was possible.

As Quanta continued to evolve, the boundaries of what we thought achievable in computing were shattered. The story of Quantum Innovations Inc. became a beacon of inspiration, symbolizing the relentless pursuit of knowledge and the triumph of human ingenuity over the complexities of the quantum realm.

The world watched in awe as the quantum revolution unfolded, ushering in an era where the impossible was merely a challenge waiting to be conquered. In the hallowed halls of Silicon Valley, the quantum pioneers continued to push the boundaries of technology, unveiling a future where quantum leaps were not just a metaphor, but a reality shaping the digital landscape for generations to come.

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Quantum Leaps: Unraveling the Mysteries of Quantum Computing | by ATHARV AMBADE | Dec, 2023 - Medium

This week, Shenzhen, China-based company SpinQ claimed the shipment of the first China-made Quantum Processing Unit (QPU), Shaowei, based on superconducting qubit technology. The claim that SpinQ is now the first Chinese quantum-focused company to sell its technologies beyond mainland China - whilst leveraging a superconducting qubit design setup at that - seems to point to a newfound source of quantum processing chips for any global players that wouldn't be easily provided for by the western market. According to SpinQ, the recipient of its Shaowei chips (and the first international customer of the company's product) is located somewhere in the Middle East.

Qubits are the quantum computing equivalent of a classical bit; while bits are deterministic and can only ever represent either a 0 or a 1, qubits are probabilistic, and consider the entire solution space between both. Recent advantages have brought quantum computing up to a point where the best products actually have enough quantum volume (a measure of a quantum computer's overall performance) to provide useful calculations that are beyond what could be possible with classical computers or even supercomputers.

Established in 2018, SpinQ recently drew our attention to its quantum processing offerings by providing "quantop" solutions: these are relatively simple, one-to-three-qubits, desktop-based quantum processing systems meant for the research and education markets. Far and away from providing any significant quantum computing capability, the "quantops" delivered by SpinQ used nuclear magnetic resonance qubits. But the new Shaowei QPU, being based on superconducting qubit technology that's theoretically similar to IBM's approach, means that the company is branching out its understanding and capability to deliver useful quantum computers. SpinQ says Shaowei utilizes a stable, all-solid-state system that's especially geared towards taking advantage of and reusing more classical chip manufacturing technology.

Considering how China keeps skirting the impact of the US technological sanctions and has achieved an internal 5 nm chip manufacturing milestone without the aid of US tech, this looks like a winning bet.

According to SpinQ, its new superconducting-qubit Shaowei chips were built completely in-house through the company's factories in the Shenzhen-Hong Kong Innovation and Technology Cooperation Zone. Its approach is much like IBM's (and like that of most quantum tech suppliers) in that the company aims to provide a "full-stack" approach to quantum computing by delivering every required element of the ecosystem: quantum processing units, low-temperature electronics, temperature and qubit measurement and control systems, as well as software and algorithm development applications.

Unfortunately, there's little information available on what exactly makes a Shaowei chip, well, tick. Qubit number and connection density are useful metrics, but SpinQ provides none. However, the company claims the coherence time for the qubits inside Shaowei is in the order of 10-100 microseconds (where a higher window of qubit coherence means the qubits are processing information without any catastrophic data loss). But in quantum computing (and every computational effort), results have to be trusted: SpinQ mentioned that Shaowei can perform both single and double-bit gate operations (in the nanosecond scale) and can achieve more than 99.9% single-bit gate fidelity and more than 98% double-bit gate fidelity. While that may sound like a lot, it really isn't: when your CPU can process millions of calculations per second, that 0.01% error rate can add up quickly, and impact the validity (and truthfulness) of the computed results.

It remains to be seen where SpinQ will take its superconducting qubits next, but it's perhaps surprising that China is already selling Quantum Processing Units overseas before 2023 comes to a close.

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Chinese SpinQ ships "undisclosed" superconducting Quantum Processing Units (QPUs) to the Middle East market ... - Tom's Hardware

As of 15 December 2023, famous quantum researcher Harry Buhrman of Centrum Wiskunde & Informatica (CWI) in the Netherlands, QuSoft and the University of Amsterdam will start a new position. He will then begin as Chief Scientist Quantum Algorithms & Innovation at the worlds largest integrated quantum computing company Quantinuum , based in their London research centre. I still have ten years until I retire. It is time to hand over my work to a new generation and for me a chance to start a new adventure and work on new things, close to the development of physical quantum computers, Buhrman says.

Harry Buhrman started in 1994 as a post-doc researcher at CWI the national research institute for mathematics and computer science in the Netherlands - in Paul Vitnyi's group. In the second half of the 1990s he set up his own quantum group at CWI, the current Algorithms & Complexity group. Buhrman: While most research at that time was about physical quantum computers, I focused on quantum software and quantum information, from the perspective of computer science. You could say that the quantum software research in the Netherlands was set up at CWI. In Europe and worldwide Buhrman is also considered as one of the founding fathers of the field. Starting in 2000, Buhrman also became a professor at the University of Amsterdam, in addition to his work at CWI.

One of the things Buhrman is proud of is that the quantum field has grown from a small group of interested scientists, mainly physicists, to a large group of people, including in computer science, mathematics and now even business. In 2015, he founded the QuSoft Research Center for Quantum Software, a collaboration of CWI together with the UvA, with which approximately 80 people are now affiliated. Buhrman became director of QuSoft, along with Kareljan Schoutens.

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World-renowned quantum researcher Harry Buhrman takes on new position in London's business community - Centrum Wiskunde & Informatica (CWI)

I know, I know, the above title has much eyebrow-raising potential. After all, what do Airbus and BMW have in common, and what business do they have getting involved in quantum computer research? Read on, and all shall be revealed.

These are efforts aimed at pulling into their respective businesses ideas from interested parties around the world, ideas that may one day change the way vehicles, regardless of their type, are designed, built, and operated. After all, quantum computers have the potential to come up with solutions "that have remained insurmountable for classical computers," as per Airbus.

The new joint effort is officially called The Quantum Mobility Quest, and it is aimed at all those with an interest in quantum computing or the automotive and aviation industries. More to the point, submissions of ideas are accepted from students, PhDs, academics, researchers, start-ups, and companies.

But what are BMW and Airbus looking for? In a nutshell, the new challenge targets four main areas: improving aerodynamics design with quantum solvers, automated mobility with quantum machine learning, sustainable supply chain with quantum optimization, and enhanced corrosion inhibition with quantum simulation. Additionally, participants can submit their own ideas if they feel they have the potential to change in some way any of the two industries.

The two companies have set up a special page for entries of ideas to be submitted in what is described as a first-of-its-kind challenge, hosted by The Quantum Insider. The project is also supported by Amazon Web Services (AWS), which will those who need to run their algorithms access to the Braket quantum computing service.

Entries won't be accepted before mid-January 2024, and the challenge will close on April 30. During these four months, the involved parties will have to develop a theoretical framework for one of the challenges mentioned above.

A jury comprising people from Airbus, BMW, and Amazon will then look at the ideas and select the best ones. They'll have to put to the test through some sort of implementation, including by running these solutions through Braket.

A single winner will be declared for each of the challenges, and they will receive each a 30,000 euros ($32,300) prize. The winners are expected to be announced by the end of next year.

Airbus and BMW hope to be left at the end of this entire project with solutions for real-world industrial applications. The most optimistic of the two is the airplane maker, which hopes the effort will "create a massive paradigm shift in the way aircraft are built and flown."

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Airbus and BMW Join Hands in First-of-Its-Kind Quest for Quantum Computer Breakthroughs - autoevolution