Quantum assembly semantics: The fallacious lingo of occupation numbers

Pakgohar, Amirpouya

This paper presents the S-QPU v1.0 (Semantic Quantum Processing Unit), the first deterministic semantic processor designed to execute the Quranic Assembly Language (QAL) and implement its formal semantic state-transition model directly in hardware. The S-QPU extends conventional vector-processing architectures by introducing a novel semantic state register R_\Psi, immutable semantic memory banks (VMEM and WMEM), and microcoded semantic operators—including ALIGN, MAPVW, and ENTANGLE—that enable reproducible semantic evolution with fixed, mathematically grounded execution paths. Unlike statistical machine-learning accelerators, the S-QPU provides deterministic, timing-invariant execution with strict hazard rules, static microcode schedules, and complete invariance of semantic transformations across hardware generations. The architecture defines a full ISA, semantic ALU cluster, entanglement engine (KRED), pipeline organization, error-handling model, numerical stability constraints, and an analytical performance framework. A rigorous verification strategy—including ISA-level correctness via QVM, RTL simulation, formal proofs, and microarchitectural validation—ensures exact correspondence between software and hardware semantics. We further present deployment models across FPGA, ASIC, cloud clusters, and embedded systems, along with a scalable roadmap for future versions featuring multi-engine parallelism, multi-state processing, and distributed semantic meshes. The S-QPU v1.0 establishes the foundational hardware substrate for deterministic semantic computation derived from the structural properties of Quranic semantic embeddings, enabling reproducible, mathematically exact semantic processing at scale.

Robert I. Booth, Cole Comfort

The stabiliser fragment of quantum theory is a foundational building block for quantum error correction and the fault-tolerant compilation of quantum programs. In this article, we develop a sound, universal and complete denotational semantics for stabiliser operations which include measurement, classically-controlled Pauli operators, and affine classical operations, in which quantum error-correcting codes are first-class objects. The operations are interpreted as certain affine relations over finite fields. This offers a conceptually motivated and computationally-tractable alternative to the standard operator-algebraic semantics of quantum programs (whose time complexity grows exponentially as the state space increases in size). We demonstrate the power of the resulting semantics by describing a small, proof-of-concept assembly language for stabiliser programs with fully-abstract denotational semantics.

Alеxander Raikov

Jerome R. Busemeyer, Peter Bruza

Robert I. Booth, Cole Comfort

The stabiliser fragment of quantum theory is a foundational building block for quantum error correction, and hence for the fault-tolerant compilation of quantum programs. In this article, we develop a sound, universal, and complete denotational semantics for stabiliser operations, including measurement, classically controlled Pauli operators, and affine classical computation, thereby supporting an explicit treatment of quantum error-correcting codes. We interpret stabiliser operations as affine relations over finite fields, yielding a semantics that reflects the algebraic structure underlying stabiliser quantum error correction. Because stabiliser quantum mechanics has a well-behaved algebraic structure, our relational semantics is conceptually transparent and computationally tractable when compared to standard denotational models for general quantum programs. We demonstrate the resulting semantics by describing a small, low-level assembly language for stabiliser programs with fully abstract denotational semantics.

Hutan Ashrafian

A quantum Boltzmann brain would arise if a fluctuation assembled an observer whose information processing used quantum switches, in which the order of physical operations is coherently controlled. A comparison with conventional substrates must account for both the assigned computation and the probability that the assembled apparatus can sustain it. I develop this comparison for a network distinguishing unknown commuting from anticommuting operations. With one invocation of each operation, an exact certificate bounds single-task fixed-order success by 11/12 for a specified finite ensemble. With an answer committed before each fresh task, the bound extends to networks retaining arbitrary quantum memory and identifies reliability requirements that the switch can satisfy but the matched fixed-order architecture cannot. For a shared fluctuating phase, a finite execution schedule also gives a lower bound on completed-batch success, including the probability that the reliable episode persists; an explicit example exceeds the causal upper bound. The network’s reliability region links residual order information, tolerated errors and phase correlations to both occupation and duration. With a fixed error budget, a fixed number r of phase coordinates and inverse-size visibility loss below the feasibility threshold, occupation scales as N^{-r/2}, while Brownian noise imposes an exponential penalty for sustaining a fixed duration as the number of outputs N grows. For one common phase with finite frequency-correlation time, fixed survival quantiles instead scale as N^{-1/2}. Incorporating these operational probabilities into a common thermal formation model yields a crossover criterion for the assembly saving required to offset the loss of reliable operation. The resulting theory makes a coherent-order contribution to fluctuation-observer comparisons calculable, conditional on the complete apparatus, its noise law and the functional requirements assigned to an observer.