Purpose: Ultrametric quantum computation MVP program—a comprehensive case for passive geometric fault tolerance as the highest-leverage bet in quantum computing hardware. Audience: Program officers (DARPA, IARPA, DOE, NSF, ERC), laboratory directors, VC/corporate due diligence teams, experimental collaboration PIs. Principle: Every factual claim is accompanied by its source. Every number is traceable to its origin. Every calculation exposes its assumptions and arithmetic. Nothing is asserted without provenance. Compilation: This document synthesizes all prior research notes, technical monographs, engineering proposals, auditable editions, experimental execution plans, and numerical prediction analyses into a single comprehensive reference.
Purpose: Ultrametric quantum computation MVP program—a comprehensive case for passive geometric fault tolerance as the highest-leverage bet in quantum computing hardware. Audience: Program officers (DARPA, IARPA, DOE, NSF, ERC), laboratory directors, VC/corporate due diligence teams, experimental collaboration PIs. Principle: Every factual claim is accompanied by its source. Every number is traceable to its origin. Every calculation exposes its assumptions and arithmetic. Nothing is asserted without provenance. Compilation: This document synthesizes all prior research notes, technical monographs, engineering proposals, auditable editions, experimental execution plans, and numerical prediction analyses into a single comprehensive reference.
Quantum computing is stalled. Despite decades of investment, no quantum computer has solved a problem that a classical computer cannot. The standard explanation — that we need better error correction — assumes the mathematical framework itself is correct. This document argues that the framework is not correct. The assumption that quantum state space is a continuous manifold — inherited from classical physics without scrutiny — may be the root cause of the field's stagnation. Replacing the continuous manifold with an ultrametric (tree-based) geometry provides passive fault tolerance: errors are geometrically confined rather than actively corrected. This document presents the mathematical foundations, computational validation results, and a set of pre-registered falsifiable predictions. If ultrametric encoding produces the predicted error suppression, it offers a path to fault-tolerant quantum computing at 4 K with dramatically reduced qubit overhead. If it does not, the hypothesis is falsified. Either outcome advances the field.
Realizing fault-tolerant quantum computing requires mapping logical programs to heterogeneous quantum error correction (QEC) codes and diverse fault-tolerant execution models, scheduling physical resources, and coupling to real-time classical control and feedback. Specialized tools exist for each step but rely on manual composition and translation that discard assumptions and provenance, separating resource estimates from the compiler artifacts they describe, and making it difficult to validate correctness, compare architectures, or attribute costs to specific design choices. We present CUDA-Q Logical, an extensible compiler infrastructure for retargetable fault-tolerant compilation, analysis, and execution. Interoperable with CUDA-Q and other mainstream front-ends, CUDA-Q Logical progressively lowers target-independent logical programs through a constrained logical virtual machine, QEC microcode, physical gate schedules, and real-time control plans, with each layer preserving semantics and provenance, while verifying composition and resource constraints. By deriving every resource estimate directly from compiler artifacts, the framework unifies compilation and resource analysis, enabling successively refined estimates and principled cross-architecture comparison while permitting QEC codes, execution models, decoders, and hardware architectures to be introduced as modular extensions. Across workloads ranging from application-architecture studies to qLDPC surgery and detector-error-model composition, we show that schedule-derived estimates reconcile with established independent models. Crucially, this compiler-visible structure exposes cost drivers hidden by aggregate analytical formulas, carries QEC artifacts intact into simulation, and demonstrates a complete compilation pipeline for fault-tolerant quantum computing.
A 20-chapter beginner's guide to quantum computing that starts with an honest question — why don't we have quantum computers yet? The guide teaches the standard curriculum accurately, explains why the standard approach faces a thermodynamic wall (a 20,000-fold cooling gap that is Carnot-limited), and introduces the ultrametric alternative: passive geometric fault tolerance on Bruhat-Tits trees, with DOI-registered evidence, computationally validated error thresholds 75 times higher than surface codes, and three falsifiable predictions. This is the v1.2 edition (August 2026). Five quantitative statements from the May 2026 edition are corrected, each verified by an independent computation deposited with this record (artifacts/verification/verify_guide_claims.py, 35 checks, all passing; see Appendix B). Appendix A records the research program's progress since May 2026, including a trapped-ion falsifiability register, an audit of a 2026 no-go theorem on quantum error correction and quantum Darwinism, and the program's own correction on prime-valuation readings of quantum codes. This deposit includes the complete source set: manuscript, HTML, PDF, references (BibTeX), citation audit, project plan, license, and verification artifacts. v1.2.1 (August 2026): post-publication audit corrections. Chapter 20's summary now lists seven open problems (including the QEC–Darwinism tradeoff); the LHC temperature comparison is marked approximate (95×, rounded); Appendix A correction #5 completed; the citation audit's internal-reference count corrected; open problem 7 carries its numeric bound (F_L > 0.874). No quantitative claims changed. v1.2.2 (August 2026): deposit-file corrections. LICENSE now contains the full CC BY 4.0 International legal code, and README.md is the deposit manifest (a project-blueprint README was attached in v1.2.1 by an automation error). No content changes.
The HHL algorithm is a prominent quantum algorithm that offers exponential speedup over its classical counterparts for solving a system of linear equations. However, synthesizing and executing HHL circuits demand significant computational resources from both classical and quantum systems. In this paper, we benchmark the HHL algorithm using the optimized Quantum Phase Estimation (QPE) generation algorithm, LuGo [1], to enhance its scalability and efficiency. We leverage various highperformance computing (HPC) systems–the National Energy Research Scientific Computing Center's (NERSC's) Perlmutter supercomputer and Oak Ridge Leadership Computing Facility's (OLCF's) Andes system and Frontier supercomputer–to evaluate the scalability of generating HHL circuits and to measure the time to simulate the generated circuits. Additionally, enabled by the Quantum Computing User Program (QCUP) of OLCF, we provide a comprehensive analysis of the algorithm's performance on various state-of-the-art superconducting and trappedion quantum devices, including studies on qubit connectivity, fidelity comparisons, and hardware compatibility and robustness. Our results offer preliminary insights into potential practical applications of the HHL algorithm enabled by LuGo and the performance of various types of quantum hardware.11Notice: This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Contract No. DE-AC02-05CH11231.
This is an introduction to software methods of quantum fault tolerance. Broadly speaking, these methods describe strategies for using the noisy hardware components of a quantum computer to perform computations while continually monitoring and actively correcting the hardware faults. We discuss parallels and differences with similar methods for ordinary digital computation, we discuss some of the noise models used in designing and analyzing noisy quantum circuits, and we sketch the logic of some of the central results in this area of research.