Has quantum advantage actually been achieved — or is the field still arguing over its own milestones? Dominik Hangleiter, one of the leading theorists working on quantum computational advantage, joins the podcast to make the case that it has, explain why so many physicists remain unconvinced, and map the path toward fault-tolerant, verifiable quantum advantage.

Why This Episode Matters

If you follow quantum computing and want to cut through the noise around quantum advantage claims, this episode is for you. Dominik Hangleiter — an Ambizione Fellow at ETH Zürich and postdoctoral fellow at UC Berkeley's Simons Institute — has spent over a decade studying the boundary between what quantum and classical computers can do. His March 2026 paper "Has quantum advantage been achieved?" synthesizes years of experiments, classical simulation attacks, and complexity theory into a clear-eyed assessment. Whether you're an experimentalist, a theorist, or simply quantum-curious, you'll come away with a sharper understanding of what's been demonstrated, what hasn't, and what comes next.

What You'll Learn

• Why random circuit sampling became the primary arena for proving quantum advantage — and why the task's "uselessness" is a feature, not a bug
• How the linear cross-entropy benchmark (XEB) works as a statistical proxy for verifying classically intractable quantum computation
• Why audiences of physicists are still split on whether quantum advantage has been demonstrated, despite multiple experiments since 2019
• What "peaked circuits" are and how they interpolate between random sampling and structured computation
• How post-quantum cryptography (learning with errors) exploits problems that quantum computers can't solve — and what that reveals about quantum computation's limits
• Why basic arithmetic is surprisingly hard for fault-tolerant quantum computers, and how that bottlenecks algorithms like Shor's
• How fault-tolerant compilation co-designs quantum circuits with error-correcting codes to make advantage experiments scalable
• The difference between "native" quantum operations and the overhead required for universal fault-tolerant computation
• Why the interplay between quantum and classical computing strengths — not quantum dominance — may define the field's future

Resources & Links

Papers & Articles

• Has quantum advantage been achieved? — Hangleiter's March 2026 paper synthesizing the quantum advantage debate
• Computational Advantage of Quantum Random Sampling — Hangleiter & Eisert's comprehensive review in Reviews of Modern Physics (2023)
• Fault-Tolerant Compiling of Classically Hard IQP Circuits on Hypercubes — The Harvard/ETH collaboration on fault-tolerant IQP circuits (PRX Quantum 2025)
• Secret-Extraction Attacks against Obfuscated IQP Circuits — Hangleiter & Gross's attack paper breaking proposed verification protocols (PRX Quantum 2025)
• Verifiable Measurement-Based Quantum Random Sampling with Trapped Ions — Experimental realization with the Innsbruck trapped-ion group (Nature Communications 2025)

Blog Series & Commentary

• Has quantum advantage been achieved? (Quantum Frontiers blog series) — The three-part mini-series on the Caltech IQIM blog that grew into the paper
• Scott Aaronson's reaction — Endorsement on Shtetl-Optimized: "quantum supremacy on contrived benchmark problems has almost certainly been achieved by now"

Guest Links

• Dominik Hangleiter — personal website & publications
• Google Scholar profile (4,372 citations)
• QuICS profile (University of Maryland)

Key Quotes & Insights

• "Really what sets random circuit sampling apart is that it's really programmable. I give an input to the device, I design a circuit — I draw it randomly, yes — but then I give the circuit to the device, and whoever controls the device runs the circuit and gives me back the samples." — On why RCS qualifies as genuine computation
• "We typically do in physics experiments a lot of extrapolation, a lot of circumstantial experiments that validate that the experiment you really care about is actually what you want to probe. And that's the sense in which I think these random circuit sampling experiments have been verified." — On the physics-style epistemology of quantum advantage
• "Classical computers are really good at doing basic arithmetic, but quantum computers — it's really hard to do basic arithmetic. And that's for the reason that fault tolerance is very restrictive in terms of the operations that you can do on encoded information." — On the surprising asymmetry between quantum and classical capabilities
• "I can't just tell the quantum computer to give me the outcome I want. There's rules to it. And how those rules apply to computational problems that we face in the real world beyond quantum simulation is, I think, a really intriguing challenge." — On the structured nature of quantum interference
• "Maybe there's a world where we can stitch together different hardware systems and won't have a single platform that wins the race." — On heterogeneous quantum architectures

Related Episodes

• Ep 35: Quantum Benchmarking with Jens Eisert — Hangleiter's PhD advisor discusses benchmarking quantum devices — essential context for understanding how we measure quantum performance.
• Ep 12: Quantum Supremacy to Generative AI and Back with Scott Aaronson — Aaronson's perspective on quantum supremacy and computational complexity — directly relevant to the advantage debate.
• Ep 73: Peaked quantum circuits with Hrant Gharibyan — The peaked circuits approach discussed in this episode, explained in depth.
• Ep 47: Megaquop with John Preskill and Rob Schoelkopf — The road to a million quantum operations — the scale needed for the fault-tolerant advantage Hangleiter envisions.
• Ep 74: Majorana qubits with Chetan Nayak — Another approach to fault tolerance with different native capabilities — relevant to Hangleiter's point about modality-specific strengths.

Calls to Action

Dominik's Quantum Frontiers blog series is one of the most accessible deep dives on quantum advantage available anywhere — start there if you want to explore beyond this conversation. Links in the show notes.

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