How do you actually make quantum algorithms work on real hardware?Build your own quantum circuits in Crumble: https://algassert.com/crumbleIn this episode, we speak with Craig Gidney of Google Quantum AI, whose work focuses on the practical realities of building fault-tolerant quantum computers. Gidney explains how seemingly small implementation choices, like how you perform arithmetic, can dominate the cost of entire quantum algorithms.We explore why factoring small numbers like 15 in Shor's algorithm can be misleadingly easy, and why scaling to larger numbers requires dramatically more resources due to operations like modular multiplication. He breaks down how quantum circuits are often dominated by classical reversible logic, and why optimizing these routines is critical for making quantum computing viable.The conversation covers quantum error correction, including why T gates are especially expensive, how magic state factories works, and how different hardware architectures change what “cost” even means. Gidney also explains how resource estimates for breaking cryptography have dropped by orders of magnitude and what drove those improvements.We also dive into the tools he built, including Stim, Quirk, and Crumble, which help researchers simulate noise, visualize circuits, and track how errors propagate through complex systems. Gidney shares his unconventional path into the field, the role of intuition and tooling in discovery, and how software engineering shapes modern quantum research.Whether you’re interested in quantum computing, error correction, cryptography, or the engineering challenges behind scalable quantum systems, this episode offers a clear and grounded look at what it really takes to turn quantum algorithms into reality.Follow us for more technical interviews with the world’s greatest scientists:Twitter: https://x.com/632nmPodcastInstagram: https://www.instagram.com/632nmpodcast?utm_source=ig_web_button_share_sheet&igsh=ZDNlZDc0MzIxNw==LinkedIn: https://www.linkedin.com/company/632nm/about/Substack: https://632nmpodcast.substack.com/Follow our hosts!Mikhail Shalaginov: https://www.linkedin.com/in/mikhail-shalaginov/Yudong Cao: https://www.linkedin.com/in/yudong-cao-25b6a929/Subscribe:Apple Podcasts: https://podcasts.apple.com/us/podcast/632nm/id1751170269Spotify: https://open.spotify.com/show/4aVH9vT5qp5UUUvQ6Uf6ORWebsite: https://www.632nm.comTimestamps:00:00 - Intro01:22 - Shor’s Algorithm04:02 - Why are Arithmetic Operations Important?08:35 - Why are T-Gates Important for QEC?13:47 - Motivations for Creating Crumble and STIM18:40 - Can AI Code Quantum Simulators?22:32 - Journey into Learning Quantum26:50 - How to Enter the Field of Quantum Computing31:16 - From Starcraft to Software Engineering36:05 - Crumble Demo53:18 - Quirk Demo1:00:48 - Estimating Resources for Quantum Computation1:08:58 - Optimizing Measurements for Computation1:16:40 - How Many Qubits Do We Actually Need?1:30:49 - Other Research Areas for Improving Fault Tolerance1:41:23 - Elliptic Curve Discrete Logarithm Problem1:46:55 - New Tools for Quantum Computing1:50:23 - What Would Craig Do with Unlimited Funding?1:52:28 - How Learning Has Changed for Craig with Experience1:57:31 - Riding the Wave of Innovation vs Sticking to One Idea1:59:53 - Advice for Young Scientists#quantumcomputing #quantumphysics #computerscience #googleai #googlequantum