Quickly Quantum

This Weekend Bonus connects a mathematical limit on random-input speedups with a map of 24 possible quantum-advantage targets. It also covers Chicago’s operating IBM system, hybrid battery chemistry work, topological-material evidence and the gap between investment, booked business and recognized revenue.

Chapters

00:00 Today's headlines

00:59 Aaronson-Ambainis conjecture is now a theorem

03:40 IBM Quantum System Two operational in Chicago

06:30 Horizon Quantum letter of intent for Entropica

08:48 IQM Volkswagen QC-AFQMC runtime reduction

11:21 Cologne team observes predicted Andreev states

13:48 2026 Quantum Index Report: $10.9 billion invested

16:34 Pasqal QPU services revenue increased 53%

18:58 Study maps 24 problems with quantum advantage

Quickly Quantum is an AI-voiced podcast, built and run by a real person. Nothing in this episode is financial advice.

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What is Quickly Quantum?

The daily quantum computing briefing you don't need a physics degree to follow. Every day, Quickly Quantum cuts through the hype to bring you the breakthroughs, funding rounds, policy moves, and research that actually matter, with plain-English analysis a smart non-physicist can follow. Hosted by Brian Lampert. AI-voiced, human-built, always skeptical of press releases. Nothing on this show is financial advice.

Also from Brian Lampert: Concrete Compute and Space Stakes.

A company says it has proved a conjecture that bounds how much faster quantum computers can be on random inputs, while a new compendium maps 24 problems with credible prospects for quantum advantage. Put those beside a quantum computer now operating in Chicago and $10.9 billion in reported quantum investment for 2025, and the week’s tension comes into focus: the field is learning both where quantum might help and what must be true before it does. This is your Weekend Bonus, with the week’s other big stories and the connections between them. We’ll move from the mathematics of limits to machines, chemistry, error resistance and the money behind the effort. Welcome back to Quickly Quantum, your daily brief on the quantum frontier. It's Saturday, November 7, 2026. Let's get into it.

A result about quantum computing’s limits starts with a familiar distinction: some problems have a hidden pattern that a quantum algorithm can exploit, while random inputs generally don’t offer that structure. PSI says the Aaronson-Ambainis conjecture is now a theorem; the conjecture, open since 2008, concerns when quantum computers can be exponentially faster than ordinary computers. This is a single-source claim from PSI.

The point isn’t that quantum computers lose their advantage everywhere. PSI’s article contrasts structured problems with random inputs, using Shor’s factoring algorithm as an example of a speedup that relies on a repeating pattern. The conjecture asks whether an exponential speedup is possible for yes-or-no questions about random strings, which almost never have such structure. Its stated consequence is that an ordinary computer can predict a quantum computer’s yes-or-no probability for all but a small fraction of strings, up to a small error, with the number of input reads growing at most like a fixed power rather than exponentially.

Here, a “look” means reading an input bit; a quantum computer’s look can be spread in superposition across many positions. Superposition is a way for a quantum system to represent combinations of states, and it helps explain why structured inputs can produce a different computational route. PSI says its internally developed research system found a proof using a non-public Anthropic model, and that Lean—a proof assistant that checks each step—accepted it. The system had a complete proof during the third day of the run, then improved the result twice, with Lean accepting the final version.

There’s important context in the same account: in August 2026, researchers at Stanford settled the prediction in a special case, for quantum algorithms that look at their input in a fixed number of parallel rounds. PSI says those researchers have read its proof, sent comments and are preparing a shorter exposition for experts. Their words, quoted by PSI, are: “This is a huge result. It resolves a decades-old conjecture with important implications for the nature of problems that admit quantum speedups. The proof draws on and extends several lines of work in the analysis of boolean functions and probabilistic combinatorics. Everything is brought together in a rather magical way.”

I think the distinction is useful precisely because it trims a broad claim without diminishing the cases where structure matters. A checked formal proof is meaningful evidence about the mathematics, while independent scrutiny still matters for a company-announced result. The practical consequence is a sharper boundary around one kind of speedup—not a verdict on every quantum application. For you, the useful takeaway is that “quantum is faster” always needs the problem attached.

A different kind of progress has a physical address: IBM Quantum System Two is now operational at Hyde Park Labs in Chicago, hosted by the University of Chicago, according to Interesting Engineering. It’s IBM’s first quantum computer deployment in Illinois, and it’s powered by IBM Quantum Nighthawk, which IBM describes as its most powerful quantum processor to date.

The machine is intended to give researchers and businesses in Illinois access to quantum hardware. Its future home is also specified: the system will eventually move to the Illinois Quantum and Microelectronics Park, a technology campus under construction in Chicago. System Two will serve as the anchor system of the National Quantum Algorithm Center, established in 2024 by Illinois Governor JB Pritzker, with IBM as a leading member. The center brings together companies, universities and research institutions to develop algorithms and applications that can scale with advances in quantum hardware.

The projects give that institutional setup some substance. Deloitte and AbbVie are working with IBM and Northwestern University on molecular simulation methods through the center’s Grand Challenges program. The Electric Power Research Institute and the University of Illinois Urbana-Champaign are exploring whether quantum optimization algorithms could help make electricity grids more efficient. Fermilab is working with IBM on high-energy physics research and technologies for distributed quantum computing. Those are research efforts, not evidence that the machine has already delivered practical advantage on those problems.

IBM’s own post on X called the unveiling a milestone for Illinois’s quantum future and said the system expands access to advanced quantum technology. That’s a company’s description of its deployment; the concrete change is that the system is operating at Hyde Park Labs, with a later move to the park planned. Qiskit posted on X, “.@IBM, @UChicago and IQMP unveil IBM Quantum System Two in Chicago Hyde Park Labs:” The Illinois EDC posted on X that Hyde Park Labs is the system’s home until it moves to the park.

The article also describes an IBM and University of Chicago demonstration of quantum advantage over leading classical methods using an approach with guaranteed correctness. That is a separate research result; the deployment itself doesn’t establish that the current machine will outperform classical computers on useful work. IBM CEO Arvind Krishna said the deployment would help organizations produce scientifically useful results, and the company expects it to support development of algorithms and applications with potential real-world uses.

I’m glad to see a real system available to local researchers, because access is a necessary step between a hardware announcement and experiments people can actually run. The harder question is what those projects produce. Illinois now has a working machine and a set of research partners; the commercial and scientific value will depend on results from that work.

The software side of the field is also consolidating around the challenge of making quantum programs work despite errors. Quantum Computing Report says Horizon Quantum has signed a non-binding letter of intent to acquire Singapore-based Entropica Labs in an all-equity transaction with anticipated consideration of $27 million in Horizon Quantum Class A ordinary shares. The proposed acquisition remains subject to due diligence, financial audits, definitive agreements and regulatory approvals.

The companies work at different layers of the software stack. Horizon focuses on quantum program synthesis through its Triple Alpha integrated development environment, a tool intended to let classical software developers compile hardware-agnostic algorithms without manually mapping each operation to hardware gates. Entropica specializes in systems software for quantum error correction, the methods that use information spread across a system to detect and manage errors in fragile quantum computations. Its Loom compiler is architected to let hardware manufacturers integrate error-corrected logical operations into their quantum processors without independently creating full error-correction toolchains.

The intended combination is to connect high-level program creation with fault-tolerant execution. In plain language, the aim is to help translate a developer’s program into circuits that can run with error correction, rather than treating the application and error-correction layers as separate pieces. Quantum Computing Report says the proposed integration targets the transition from physical gate compilation to logical fault-tolerant computing, as commercial logical processors mature.

That is an ambitious product direction, and the deal’s status matters: this is a non-binding letter of intent, not a completed acquisition. The $27 million is anticipated consideration in shares, not cash already paid. The account says customary due diligence, audits, definitive agreements and regulatory approvals remain part of the process.

I think the strategic logic is coherent: developers need tools that connect the program they want to run with the error-managed operations future hardware may support. But software integration can’t make the underlying hardware fault-tolerant by itself. The value of this proposed combination will be clearer in the products it actually delivers and the systems those products can support.

From software layers to a chemistry workload, Quantum Computing Report describes advances by IQM Quantum Computers and Volkswagen Group Innovation in a hybrid algorithm for studying electronic structure. Their Quantum-Classical Auxiliary-Field Quantum Monte Carlo method—QC-AFQMC—combines quantum-generated information with classical computation. The collaboration reports up to a 124× reduction in classical execution time for a 50-orbital benchmark and validated the workflow on IQM’s commercial Emerald superconducting processor.

The reduction is in classical post-processing runtime, not a claim that the entire battery simulation ran 124 times faster. The team changed how it reconstructs overlaps between a quantum-prepared trial state and classical Monte Carlo walkers. Their method, matchgate shadow tomography, uses classical post-processing to estimate those overlaps. Aitken’s block transformation handles singular Pfaffians that arise in the calculation, and algorithmic differentiation helps calculate force-bias terms. The reported per-step classical post-processing scaling shifts from Õ(N5.5) to Õ(N4.5).

Why does that matter for batteries? Modeling complex chemical reactions can overwhelm classical electronic-structure methods because the number of Slater determinants needed to capture strong electron correlation grows exponentially. The group says QC-AFQMC uses a quantum computer to prepare high-fidelity, multi-determinant trial states, while classical Monte Carlo does other parts of the calculation. Their approach aims to ease a computational bottleneck in that hybrid workflow.

The hardware demonstrations and larger simulation need to be kept distinct. On IQM’s 54-qubit Emerald processor, the researchers calculated the ground-state energy of a stretched H8 hydrogen chain and used matrix product state filtering to discard noisy measurements. Separately, in classical simulation, they modeled the rearrangement pathway of a lithium superoxide dimer, Li2O4, across a 40-qubit active space, capturing the activation barrier and transition-state geometry described in the article. That is not a full commercial battery simulation.

The report also says the team estimates deep modified Hadamard test circuits would require millennia of execution time for even modest systems. That’s why reducing the classical work around the quantum calculation matters: the bottleneck can sit outside the quantum processor itself. I find this a more useful kind of hybrid-computing result than a headline about qubit count alone, because it names a specific task and where the improvement occurs. The open question is how the accuracy and runtime hold up as the simulated systems grow.

A different route toward more reliable qubits begins with materials physics. Quantum Physics News reports that researchers at the University of Cologne observed quantum states behaving as predicted in a material system being studied for topological quantum computing. Topological systems rely on special quantum states expected to be more resistant to local disturbances, which is why researchers investigate them as a possible route to more robust quantum bits, or qubits.

The team studied a Josephson junction, a structure made of two superconductors connected by a region that is not superconducting. Using tunneling spectroscopy—a way to probe quantum states in the junction—they varied the phase difference between the superconductors. They observed highly transmissive Andreev states, which form when electrons and holes interact at a superconducting junction. Those states appeared across a range of charge-carrier densities, consistent with predicted behavior at the surface of a topological insulator, a material that conducts electricity along its surface but not through its interior.

The results support a theoretical description of how superconductivity interacts with that surface. They agree with predictions based on a model proposed by Liang Fu and Charles Kane in 2008, as well as numerical simulations by a group at RWTH Aachen University. Professor Yoichi Ando said, “Understanding how superconductivity interacts with the distinctive electronic properties of topological insulators is essential for assessing their potential for topological quantum computing.” Ella Nikodem said, “It is super exciting to see our experimental results align so well with theoretical predictions. This is very encouraging in terms of future applications in quantum computing.”

Here’s the important limit: the experiment has not confirmed the predicted topological phase transition. Researchers need more precise measurements to determine whether the states show the predicted closing and reopening of an energy gap. Such a change could signal the transition, in which certain quantum states may be protected against local disturbances. Dr. Jakob Schluck said the lab needs to improve the experiment’s energy and time resolution.

I think the result deserves attention as evidence that the model describes observed behavior, while the stronger claim—a demonstrated transition and a working topological qubit—remains ahead. That distinction is central for computing: a material that behaves as predicted may help researchers assess a path to more error-resistant qubits, but it doesn’t yet provide one. The measured gap behavior is the concrete scientific question the Cologne team says comes next.

Money supplies another measure of the field’s momentum, though investment and useful computing are different things. Quantum Zeitgeist reports that the 2026 Quantum Index Report, compiled by researchers at MIT and Accenture, puts quantum computing investment at $10.9 billion in 2025. Public-market financing and late-stage venture capital drove much of that total: $5.7 billion came from financing for companies already listed on Nasdaq, and $2.3 billion arrived through late-stage venture rounds.

That mix points to capital flowing toward more mature quantum companies, according to the report described by Quantum Zeitgeist. It also captures a field that is drawing industrial and geopolitical attention. Jonathan Ruane, principal investigator at the MIT Initiative on the Digital Economy, said, “The second quantum revolution is no longer only a scientific project,” adding that it is also becoming “an industrial, economic and geopolitical one.”

The report’s account pairs that investment with a sobering qualification: practical quantum advantage remains elusive, and current quantum computers still lag classical systems for most applications. It quotes the report saying, “Most experts agree that quantum computers remain below the capabilities of classical computers for all useful tasks today.” That is a substantial gap between financing momentum and demonstrated broad utility.

The report also describes differences in research influence and patent activity. It says the United States maintains a lead in research influence and impact, while China filed more quantum computing patents in 2025 than the United States, the World Intellectual Property Organization, the European Patent Office and Japan combined. In the specific figures given, China registered 9,790 patents compared with 2,423 for the United States. Patent volume and research influence measure different things; the report cautions that the filings disparity doesn’t necessarily reflect a difference in innovation quality.

For quantum communications, the report says China produced 35.8% of related research between 2021 and 2025, compared with 12.2% for the United States. It also says U.S. Department of Defense awards mentioning quantum reached a record $285.3 million in 2025, a 49% increase over the previous year. Those measures show that money and research activity are coming from several directions, but they don’t establish that useful quantum computing has arrived.

I read the investment total as evidence of commitment, especially from public markets and late-stage investors, rather than proof of commercial performance. When experts quoted in the same account say useful tasks remain out of reach today, that deserves at least as much attention as the headline total. Capital can fund the work; results still have to earn the confidence.

The difference between commercial interest and recognized revenue is especially visible in Pasqal’s quarterly update. The Quantum Insider reported that the neutral-atom quantum computing company recorded €3.3 million in third-quarter 2026 revenue, down from €5.7 million a year earlier, while QPU-related services revenue increased 53% to €3.1 million. The company said there were no QPU sales realized in the current period, while the prior-year period included €3.2 million in revenue recognized from QPU sales.

QPU services include consulting, remote access, upgrades and maintenance for quantum processing units. That category grew even as total revenue declined, giving a more concrete signal of customer activity around the hardware. The Quantum Insider reported that the company cited €69.8 million in booked and awarded business and €312.8 million in cash and cash equivalents as of September 30, 2026. Booked and awarded business includes grants, tax credits and multi-year customer contracts, so it should not be read as current-quarter revenue.

Pasqal CEO Dr. Wasiq Bokhari said, “Although the order book and revenue do not show it yet, we have made important progress in our technology roadmap, scaling on-chip photonic control and bringing AI-assisted workflows to Pasqal Cloud.” He also described increased traction with reference customers and a broader reach across the company’s priority verticals. Those are the company’s statements about its progress and pipeline; the quarter’s reported revenue gives a separate, current financial measure.

The company listed other developments, including an AI-assisted workflow on Pasqal Cloud, available as a plugin for agentic coding environments such as Claude Code, Cursor and Codex. It says the workflow takes a well-defined scientific idea through to a running experiment on its cloud-accessible QPUs. It also cited progress in photonic integrated circuit technology for trapped atoms and a partnership with USA Rare Earth and Riven Systems on quantum machine learning for rare-earth separation molecules.

I’ve previously read Pasqal’s services revenue as a more concrete commercial signal than a hardware roadmap, while the wider financial picture needs care. This quarter strengthens the services part of that view: the reported increase is specific, while booked business remains a different category from recognized revenue. I’d want to see how orders convert before treating the order book as evidence that the revenue decline has turned around.

After the funding and revenue numbers, a new study offers a map of where quantum advantage might be worth pursuing—and what can make it disappear. The Quantum Insider reports that researchers from institutions including the Open Quantum Institute at CERN, Google Quantum AI, Microsoft, Oratomic, NVIDIA, JPMorganChase, MIT and Harvard University identified 24 computational problems with credible prospects for quantum advantage. The study is a synthesis of existing research, posted as a preprint on arXiv.

Quantum advantage means a quantum machine outperforming classical computing methods on a task. For each problem, the researchers describe the mathematical structure, data requirements and other conditions needed to preserve the potential edge. The collection includes number theory, optimization, statistical inference, quantum simulation, linear algebra and analysis of shapes and connections in data, with possible applications in chemistry, materials research, signal processing and code breaking. The evidence and maturity vary across the entries.

The authors focus on speedups greater than quadratic, arguing that this threshold will likely be needed to overcome the substantial operating costs of early quantum computers equipped with error correction. A quadratic speedup is an improvement in how the required work grows: the article gives the example of a classical computer needing roughly 1 million steps while a quantum algorithm might need about 1,000. But that does not mean the quantum computer necessarily finishes 1,000 times faster, because each quantum step can take more time and resources.

The researchers emphasize the full calculation. Preparing data, correcting errors and reading results can erase expected time savings, even if the quantum algorithm itself requires fewer steps. Their comparisons are generally against the best classical methods currently known, and those methods can improve. The study also separates rigorous mathematical results from evidence limited to particular classes of classical methods, and from numerical or heuristic studies. A maximum-speedup label describes the strongest result identified under specified conditions; it isn’t a promise for every instance.

I think the compendium’s most useful contribution is its demand for a complete accounting: a theoretical gain has to survive data preparation, error correction, readout and comparison with improving classical methods. It’s a guide to plausible targets, not evidence that any of these 24 problems has already been solved faster on a production machine. The researchers’ suggested direction is to start with tasks whose quantum advantages are supported, then look for real problems that fit their requirements. That keeps the search tied to the mathematics instead of assuming every urgent problem has a quantum solution.

If this map helps researchers identify a problem whose full calculation beats leading classical methods under the stated conditions, that would give the field a more concrete destination than a list of possible applications.

Follow Quickly Quantum wherever you listen, and take this week’s mix of proof, hardware and hard commercial numbers into your next quantum conversation. This has been Quickly Quantum, an AI-voiced podcast, created and built by a real human using today's cutting-edge technology. Nothing you heard on this show is financial advice. I'm Brian Lampert, and I'll catch you all tomorrow — take care!

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