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In a new paper, 夜色直播 scientists have perfected a way of doing maths with diagrams instead of symbols

June 14, 2024

Doing mathematical physics with diagrams instead of traditional formalism allows researchers to tackle difficult problems in an intuitive and mathematically strict way that opens the door to new insights and solutions. The new calculus we are developing that we refer to as ZX calculus, also known as Penrose Spin Calculus, .

夜色直播 researchers Harny Wang, Razin A. Shaikh, and Boldizs谩r Po贸r have proven the 鈥渃ompleteness鈥 of this ZX calculus in finite dimensions, meaning that one can now use diagrams instead of linear algebra to perform calculations in finite dimensional quantum mechanics. This is a remarkable achievement.

鈥淣ow very complicated formulas in quantum chemistry and loop quantum gravity can be derived by diagrams,鈥 said co-author Harny Wang.

Physicists have used graphical calculus for a long time. They are used widely in quantum field theory, in the form of Feynman diagrams, or in gravitational theory, in the form of Penrose diagrams. Graphical calculation strategies are generally very well appreciated as they replace a lot of difficult and tedious 鈥榝ormal鈥 mathematics with a simpler, more intuitive, but no less accurate diagrammatic approach.

Our researcher鈥檚 work on ZX and ZXW calculus (a near cousin to ZX) is the latest but most innovative shift from 鈥渟hut up and calculate鈥 to 鈥渄epict and rewrite鈥, a shift that many researchers are sure to welcome.

ZX calculus was initially developed by scientists as a tool for working on problems in quantum mechanics that require intricate calculations. ZX calculus, created by Professor Bob Coecke and Dr. Ross Duncan, both of whom are senior scientists at 夜色直播, has developed over the course of 15 years, leading to a growing global community of researchers. This most recent paper marks the transition of important parts of ZX from 鈥榓 work in progress鈥 to something that is fully formed.

Both ZX and ZXW calculus are known for efficiently expressing quantum relations such as entanglement. It is hoped these new formalisms may uncover connections between some of the most challenging problems in science and quantum computing.

Distinguished physicist Carlo Rovelli has already expressed interest in using ZX and ZXW graphical calculus for his work, stating 鈥淚ndeed, there are concrete steps in place to translate quantum gravity problems into quantum computing problems, and I have hope that the powerful conceptual and technical tools developed by Bob [Coecke], Harny [Wang] and their collaborators could play a major role in this.鈥

In addition to interest from the gravity community, ZX is being adopted in the wider quantum computing community. Dr. Peter Shor recently worked with colleagues to .

About 夜色直播

夜色直播,聽the world鈥檚 largest integrated quantum company, pioneers powerful quantum computers and advanced software solutions. 夜色直播鈥檚 technology drives breakthroughs in materials discovery, cybersecurity, and next-gen quantum AI. With over 500 employees, including 370+ scientists and engineers, 夜色直播 leads the quantum computing revolution across continents.聽

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May 1, 2025
GenQAI: A New Era at the Quantum-AI Frontier

At the heart of quantum computing鈥檚 promise lies the ability to solve problems that are fundamentally out of reach for classical computers. One of the most powerful ways to unlock that promise is through a novel approach we call Generative Quantum AI, or GenQAI. A key element of this approach is the (GQE).

GenQAI is based on a simple but powerful idea: combine the unique capabilities of quantum hardware with the flexibility and intelligence of AI. By using quantum systems to generate data, and then using AI to learn from and guide the generation of more data, we can create a powerful feedback loop that enables breakthroughs in diverse fields.

Unlike classical systems, our quantum processing unit (QPU) produces data that is extremely difficult, if not impossible, to generate classically. That gives us a unique edge: we鈥檙e not just feeding an AI more text from the internet; we鈥檙e giving it new and valuable data that can鈥檛 be obtained anywhere else.

The Search for Ground State Energy

One of the most compelling challenges in quantum chemistry and materials science is computing the properties of a molecule鈥檚 ground state. For any given molecule or material, the ground state is its lowest energy configuration. Understanding this state is essential for understanding molecular behavior and designing new drugs or materials.

The problem is that accurately computing this state for anything but the simplest systems is incredibly complicated. You cannot even do it by brute force鈥攖esting every possible state and measuring its energy鈥攂ecause 聽the number of quantum states grows as a double-exponential, making this an ineffective solution. This illustrates the need for an intelligent way to search for the ground state energy and other molecular properties.

That鈥檚 where GQE comes in. GQE is a methodology that uses data from our quantum computers to train a transformer. The transformer then proposes promising trial quantum circuits; ones likely to prepare states with low energy. You can think of it as an AI-guided search engine for ground states. The novelty is in how our transformer is trained from scratch using data generated on our hardware.

Here's how it works:

  • We start with a batch of trial quantum circuits, which are run on our QPU.
  • Each circuit prepares a quantum state, and we measure the energy of that state with respect to the Hamiltonian for each one.
  • Those measurements are then fed back into a transformer model (the same architecture behind models like GPT-2) to improve its outputs.
  • The transformer generates a new distribution of circuits, biased toward ones that are more likely to find lower energy states.
  • We sample a new batch from the distribution, run them on the QPU, and repeat.
  • The system learns over time, narrowing in on the true ground state.

To test our system, we tackled a benchmark problem: finding the ground state energy of the hydrogen molecule (H鈧). This is a problem with a known solution, which allows us to verify that our setup works as intended. As a result, our GQE system successfully found the ground state to within chemical accuracy.

To our knowledge, we鈥檙e the first to solve this problem using a combination of a QPU and a transformer, marking the beginning of a new era in computational chemistry.

The Future of Quantum Chemistry

The idea of using a generative model guided by quantum measurements can be extended to a whole class of problems鈥攆rom to materials discovery, and potentially, even drug design.

By combining the power of quantum computing and AI we can unlock their unified full power. Our quantum processors can generate rich data that was previously unobtainable. Then, an AI can learn from that data. Together, they can tackle problems neither could solve alone.

This is just the beginning. We鈥檙e already looking at applying GQE to more complex molecules鈥攐nes that can鈥檛 currently be solved with existing methods, and we鈥檙e exploring how this methodology could be extended to real-world use cases. This opens many new doors in chemistry, and we are excited to see what comes next.

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April 11, 2025
夜色直播鈥檚 partnership with RIKEN bears fruit

Last year, we joined forces with RIKEN, Japan's largest comprehensive research institution, to install our hardware at RIKEN鈥檚 campus in Wako, Saitama. This deployment is part of RIKEN鈥檚 project to build a quantum-HPC hybrid platform consisting of high-performance computing systems, such as the supercomputer Fugaku and 夜色直播 Systems. 聽

Today, marks the first of many breakthroughs coming from this international supercomputing partnership. The team from RIKEN and 夜色直播 joined up with researchers from Keio University to show that quantum information can be delocalized (scrambled) using a quantum circuit modeled after periodically driven systems. 聽

"Scrambling" of quantum information happens in many quantum systems, from those found in complex materials to black holes. 聽Understanding information scrambling will help researchers better understand things like thermalization and chaos, both of which have wide reaching implications.

To visualize scrambling, imagine a set of particles (say bits in a memory), where one particle holds specific information that you want to know. As time marches on, the quantum information will spread out across the other bits, making it harder and harder to recover the original information from local (few-bit) measurements.

While many classical techniques exist for studying complex scrambling dynamics, quantum computing has been known as a promising tool for these types of studies, due to its inherently quantum nature and ease with implementing quantum elements like entanglement. The joint team proved that to be true with their latest result, which shows that not only can scrambling states be generated on a quantum computer, but that they behave as expected and are ripe for further study.

Thanks to this new understanding, we now know that the preparation, verification, and application of a scrambling state, a key quantum information state, can be consistently realized using currently available quantum computers. Read the paper , and read more about our partnership with RIKEN here. 聽

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Blog
April 4, 2025
Why is everyone suddenly talking about random numbers? We explain.

In our increasingly connected, data-driven world, cybersecurity threats are more frequent and sophisticated than ever. To safeguard modern life, government and business leaders are turning to quantum randomness.

What is quantum randomness, and why should you care?

The term to know: quantum random number generators (QRNGs).

QRNGs exploit quantum mechanics to generate truly random numbers, providing the highest level of cryptographic security. This supports, among many things:

  • Protection of personal data
  • Secure financial transactions
  • Safeguarding of sensitive communications
  • Prevention of unauthorized access to medical records

Quantum technologies, including QRNGs, could protect up to $1 trillion in digital assets annually, according to a recent by the World Economic Forum and Accenture.

Which industries will see the most value from quantum randomness?

The World Economic Forum report identifies five industry groups where QRNGs offer high business value and clear commercialization potential within the next few years. Those include:

  1. Financial services
  2. Information and communication technology
  3. Chemicals and advanced materials
  4. Energy and utilities
  5. Pharmaceuticals and healthcare

In line with these trends, recent by The Quantum Insider projects the quantum security market will grow from approximately $0.7 billion today to $10 billion by 2030.

When will quantum randomness reach commercialization?

Quantum randomness is already being deployed commercially:

  • Early adopters use our Quantum Origin in data centers and smart devices.
  • Amid rising cybersecurity threats, demand is growing in regulated industries and critical infrastructure.

Recognizing the value of QRNGs, the financial services sector is accelerating its path to commercialization.

  • Last year, HSBC conducted a combining Quantum Origin and post-quantum cryptography to future-proof gold tokens against 鈥渟tore now, decrypt-later鈥 (SNDL) threats.
  • And, just last week, JPMorganChase made headlines by using our quantum computer for the first successful demonstration of certified randomness.

On the basis of the latter achievement, we aim to broaden our cybersecurity portfolio with the addition of a certified randomness product in 2025.

How is quantum randomness being regulated?

The National Institute of Standards and Technology (NIST) defines the cryptographic regulations used in the U.S. and other countries.

  • NIST鈥檚 SP 800-90B framework assesses the quality of random number generators.
  • The framework is part of the FIPS 140 standard, which governs cryptographic systems operations.
  • Organizations must comply with FIPS 140 for their cryptographic products to be used in regulated environments.

This week, we announced Quantum Origin received , marking the first software QRNG approved for use in regulated industries.

What does NIST validation mean for our customers?

This means Quantum Origin is now available for high-security cryptographic systems and integrates seamlessly with NIST-approved solutions without requiring recertification.

  • Unlike hardware QRNGs, Quantum Origin requires no network connectivity, making it ideal for air-gapped systems.
  • For federal agencies, it complements our "U.S. Made" designation, easing deployment in critical infrastructure.
  • It adds further value for customers building hardware security modules, firewalls, PKIs, and IoT devices.

The NIST validation, combined with our peer-reviewed papers, further establishes Quantum Origin as the leading QRNG on the market. 聽

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It is paramount for governments, commercial enterprises, and critical infrastructure to stay ahead of evolving cybersecurity threats to maintain societal and economic security.

夜色直播 delivers the highest quality quantum randomness, enabling our customers to confront the most advanced cybersecurity challenges present today.

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