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Classical Shadows versus Quantum Footage

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View a PDF of the paper titled The Efficiency Frontier: Classical Shadows versus Quantum Footage, by Shuowei Ma and 1 other authors

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Abstract:Interfacing quantum and classical processors is an important subroutine in full-stack quantum algorithms. The so-called “classical shadow” method efficiently extracts essential classical information from quantum states, enabling the prediction of many properties of a quantum system from only a few measurements. However, for a small number of highly non-local observables, or when classical post-processing power is limited, the classical shadow method is not always the most efficient choice. Here, we address this issue quantitatively by performing a full-stack resource analysis that compares classical shadows with “quantum footage,” which refers to direct quantum measurement. Under certain assumptions, our analysis illustrates a boundary of download efficiency between classical shadows and quantum footage. For observables expressed as linear combinations of Pauli matrices, the classical shadow method outperforms direct measurement when the number of observables is large and the Pauli weight is small. For observables in the form of large Hermitian sparse matrices, the classical shadow method shows an advantage when the number of observables, the sparsity of the matrix, and the number of qubits fall within a certain range. The key parameters influencing this behavior include the number of qubits $n$, observables $M$, sparsity $k$, Pauli weight $w$, accuracy requirement $\epsilon$, and failure tolerance $\delta$. We also compare the resource consumption of the two methods on different types of quantum computers and identify break-even points where the classical shadow method becomes more efficient, which vary depending on the hardware. This paper opens a new avenue for quantitatively designing optimal strategies for hybrid quantum-classical tomography and provides practical insights for selecting the most suitable quantum measurement approach in real-world applications.

Submission history

From: Junyu Liu [view email]
[v1]
Sun, 7 Sep 2025 21:46:56 UTC (742 KB)
[v2]
Tue, 9 Sep 2025 18:39:03 UTC (742 KB)



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AI Research

Historic US-UK deal to accelerate AI drug discovery, quantum and nuclear research

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image: ©Gorodenkoff | iStock

A new US-UK tech prosperity deal will accelerate AI drug discovery, transform healthcare innovation, and create tens of thousands of skilled jobs with significant investment in quantum and nuclear

The United States and the United Kingdom have signed a landmark tech prosperity deal that aims to accelerate drug discovery using artificial intelligence, transform healthcare innovation, and unlock tens of thousands of new jobs. Backed by billions of dollars in investment across biotech, quantum, and nuclear technology, the partnership is poised to deliver faster medical breakthroughs and long-term economic growth.

£75bn investment into AI, quantum, and nuclear

Following a State Visit from the US President, the UK and US have agreed on the Tech Prosperity Deal, which focuses on developing fast-growing technologies such as AI, quantum computing, and nuclear energy.

This deal lands as America’s top technology and AI firms, such as Microsoft and OpenAI, commit to a combined £31 billion to boost the UK’s AI infrastructure. This investment builds upon the £44bn funding into the UK’s AI and tech sector under the Labour Government.

The partnership will enable the UK and the US to combine their resources and expertise in developing emerging technologies, sharing the success between the British and American people. This includes:

  • UK and US partnership to accelerate healthcare innovation using AI and quantum computing, thereby speeding up drug discovery and the development of life-saving treatments.
  • Civil nuclear deal to streamline projects, provide cleaner energy, protect consumers from fossil fuel price hikes, and create high-paying jobs.
  • Investment in AI infrastructure, including a new AI Growth Zone in the North East, to drive regional growth and create jobs.
  • Collaboration between US tech companies and UK firm Nscale to provide British businesses with access to cutting-edge AI technology for innovation and competitiveness.

Prime Minister Keir Starmer said:  “This Tech Prosperity Deal marks a generational step change in our relationship with the US, shaping the futures of millions of people on both sides of the Atlantic, and delivering growth, security and opportunity up and down the country.

By teaming up with world-class companies from both the UK and US, we’re laying the foundations for a future where together we are world leaders in the technology of tomorrow, creating highly skilled jobs, putting more money in people’s pockets and ensuring this partnership benefits every corner of the United Kingdom.”

NVIDIA deploys 120,000 advanced GPUs

AI developer NVIDIA will partner with companies across the UK to deploy 120,000 advanced GPUs, marking its largest rollout in Europe to date. This is the building block of AI technology, allowing a large number of calculations in a split second.

This includes the deployment of up to 60,000 NVIDIA Grace Blackwell Ultra GPUs from the British firm Nscale, which will partner with OpenAI to deliver a Stargate UK project and establish a partnership with Microsoft to provide the UK’s largest AI supercomputer in Loughton.

World-leading companies invest in the UK

Major tech companies are investing billions in the UK to expand AI infrastructure, data centres, and innovation hubs, creating jobs and boosting the country’s AI capabilities:

  • Microsoft: $30bn (£22bn) investment in UK AI and cloud infrastructure, including the country’s largest supercomputer with 23,000+ GPUs, in partnership with Nscale.
  • Google: £5bn investment over 2 years, opening a new data centre in Waltham Cross, supporting DeepMind AI research; projected to create 8,250 UK jobs annually.
  • CoreWeave: £1.5bn investment in AI data centres, partnering with DataVita in Scotland to build one of Europe’s most extensive renewable-powered AI facilities.
  • Salesforce: $2bn (£1.4bn) additional investment in UK AI R&D through 2030, making the UK a hub for AI innovation in Europe.
  • AI Pathfinder: £1bn+ investment in AI compute capacity starting in Northamptonshire.
  • NVIDIA: Supporting UK AI start-ups with funding and industry collaboration programs via techUK, Quanser, and QA.
  • Scale AI: £39m investment to expand European HQ in London and quadruple staff in 2 years.
  • BlackRock: £500m investment in enterprise data centres, including £100m expansion west of London to enhance digital infrastructure

Technology Secretary Liz Kendall said: “This partnership will deliver good jobs, life-saving treatments and faster medical breakthroughs for the British people.

Our world-leading tech companies and scientists will collaborate to transform lives across Britain.

This is a vote of confidence in Britain’s booming AI sector – building on British success stories such as Arm, Wayve and Google Deepmind – that will boost growth and deliver tens of thousands of skilled jobs.”



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Google invests £5bn to help power the UK’s AI economy

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Demis Hassabis, co-founder and chief executive of Google DeepMind (Credit: Ange.original)

Google has opened a data centre in Hertfordshire to meet growing demand for AI services, as part of a two-year £5bn investment in the UK.

The centre in Waltham Cross, opened by chancellor Rachel Reeves, encompasses Google DeepMind with its AI research in science and healthcare, and will help the UK develop its AI economy by advancing AI breakthroughs and supporting around 8,250 jobs.

It is part of a £5bn investment including capital expenditure, research and development, and related engineering.

Reeves said: “Google’s £5bn investment is a powerful vote of confidence in the UK economy and the strength of our partnership with the US, creating jobs and economic growth for years to come.”

Google is investing to support people across the UK to gain the skills for AI adoption and is part of an industry group, announced by the government in July 2025, to train 7.5 million people by 2030.

Demis Hassabis, co-founder and chief executive of Google DeepMind, said: “We founded DeepMind in London because we knew the UK had the potential and talent to be a global hub for pioneering AI.

“The UK has a rich history of being at the forefront of technology – from Lovelace to Babbage to Turing – so it’s fitting that we’re continuing that legacy by investing in the next wave of innovation and scientific discovery in the UK.”

Google will establish a community fund, managed by Broxbourne Council, to support local economic development.

Ruth Porat, president and chief investment officer at Alphabet and Google, said: “With today’s announcement, Google is deepening our roots in the UK and helping support Great Britain’s potential with AI to add £40bn to the economy by 2030 while also enhancing critical social services.

“Google’s investment in technical infrastructure, expanded energy capacity and job-ready AI skills will help ensure everyone in Broxbourne and across the whole of the UK stays at the cutting-edge of global tech opportunities.” 

The news follows announcements from pharmaceutical giants Merck and AstraZeneca that they are pulling out of the UK.

Merck, known as MSD in Europe, halted plans to build a £1bn research centre under construction in London and is cutting more than 100 scientific staff, citing concerns about the UK’s commercial environment.

Meanwhile, AstraZeneca has paused a planned £200 million investment in its Cambridge research site, which was expected to create thousands of jobs. 

This is a blow for the government, which is seeking to boost economic growth and attract investment to life sciences, with Wes Streeting, health secretary, pledging to make Britain a “powerhouse” for the sector.

The government’s Life Sciences Sector Plan, published in July 2025, sets an ambition to harness scientific innovation for economic growth, which includes making the UK “an outstanding place to start, scale and invest”.

Commenting on Google’s investment, Nick Lansman, chief executive and founder of the Health Tech Alliance, said: “This kind of scalable computing and world‑class R&D will help health tech innovators accelerate discovery, deployment and safe adoption across the NHS, supporting the UK’s ambition to be a global hub for life sciences growth.”



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5 steps for deploying agentic AI red teaming

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AI-based agentic sources of security exploits aren’t new. The Open Worldwide Application Security Project (OWASP) published a paper that examines all kinds of agentic AI security issues with specific focus on model and application architecture and how multiple agents can collaborate and interact. It reviewed how users of various general-purpose agent frameworks such as LangChain, CrewAI and AutoGPT should better protect their infrastructure and data. Like many other OWASP projects, its focus is on how application development can incorporate better security earlier in the software lifecycle.

Andy Swan at Gray Swan AI led a team to publish an academic paper on AI agent security challenges. In March, they pitted 22 frontier AI agents in 44 realistic deployment scenarios that resulted in observing the effects of almost two million prompt injection attacks. Over 60,000 attacks were successful, “suggesting that additional defenses are needed against adversaries. This effort was used to create an agent red teaming benchmark and framework to evaluate high-impact attacks.” The results revealed deep and recurring failures: agents frequently violated explicit policies, failed to resist adversarial inputs, and performed high-risk actions across domains such as finance, healthcare, and customer support. “These attacks proved highly transferable and generalizable, affecting models regardless of size, capability, or defense strategies.”

Part of the challenge for assembling effective red team forays into your infrastructure is that the entire way incidents are discovered and mitigated is different when it comes to dealing with agentic AI. “From an incident management perspective, there are some common elements between agents and historical attacks in terms of examining what data needs to be protected,” Myles Suer of Dresner Advisory, an agentic AI researcher, tells CSO. “But gen AI stores data not in rows and columns but in chunks and may be harder to uncover.” Plus, time is of the essence: “The time between vulnerability and exploit is exponentially shortened thanks to agentic AI,” Bar-El Tayouri, the head of AI security at Mend.io, tells CSO.



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