Purpose of This Document

This document records the conceptual discussion between Dr. Michael Rhoades and Claude (Anthropic) regarding Phase IV of the Quantum Computational Creativity research project. It is intended as a reference for when active development begins, preserving the creative and technical intentions formulated during this early planning stage. It also serves as supporting context for the IBM Quantum Credits Program grant application.

Previous Phases Summary — Where We Are Now

Completed Work

“Reflections from Hilbert Space” comprises seven completed quantum computer music compositions totaling 76 minutes, including “The Infinite and the Infinitesimal” created using Quantum Inspire’s Tuna-9 hardware processor. A research paper has been submitted to Computer Music Journal’s special issue on Quantum Computer Music.

Core Methodology Validated

The fundamental approach of Phases II and III — using quantum circuit evolution directly as waveform generation, with entanglement topology determining compositional relationships — has been validated on real quantum hardware. Key findings include:

• Entanglement correlation structures survive real hardware execution
• Quantum interference patterns in Hilbert space translate meaningfully to acoustic interference patterns in Ambisonics listening space
• Hardware noise and decoherence are not errors but authentic creative signatures
• Moderate asymmetric entanglement produces the richest compositional output
• Eight distinct circuit schemas (Star, Chain, Ring, Pairs, Tree, GHZ, Gradient, Islands) each produce unique sonic character

Tomographic Data Collection — Complete

Full quantum state tomography (X, Y, Z measurement bases, 2048 shots, 600 parameter steps) has been executed on Tuna-9 for all eight schemas. Each schema produces a 600-row Bloch coordinate CSV used for both audio synthesis and Blender VR visualization. All eight schemas are complete.

Blender VR Visualization — Work in Progress

A parallel visual art project renders the quantum tomographic data as animated 3D filaments in a chrome reflective VR environment. Each of the eight qubits is represented as a luminous filament whose spatial position, motion, and dynamic behavior are governed entirely by the Bloch sphere trajectory data extracted during tomographic execution.

Schema 01 — Star topology — was rendered on a high-performance cluster equipped with multiple NVIDIA RTX 4090 GPUs, producing 2400 frames at 30fps for an 80-second stereoscopic VR animation. Early review of the initial frames has already yielded a significant finding: an unexpected organic coherence between the visual animation and the Phase II composition “The Infinite and the Infinitesimal” — both derived independently from the same quantum hardware execution. This cross-modal coherence, emerging naturally from shared quantum physical origin rather than deliberate synchronization, validates a core premise of the research.

Blender scenes for the remaining seven schemas are planned, with potentially multiple scenes per schema exploring different visual interpretations of the same quantum data. Given the extensive rendering times involved, this work represents a long-term visual art project extending well into 2026 and beyond. Phase IV development will proceed in parallel with the ongoing Phase III rendering work.

Phase IV Vision — Conceptual Framework

Core Departure from Previous Phases

Phase IV is not an extension of the previous phases — it is a fundamental reimagining of the methodology. The goal is to produce material that is sonically and compositionally distinct from anything previously produced. This requires changes at multiple levels: circuit architecture, gate vocabulary, parameter sampling strategy, and compositional interpretation.

Scale — Toward Maximal Qubit Utilization

Phase IV targets 16 circuit schemas, each using 9 qubits, for a total of 144 qubits — approaching the maximum of IBM’s 156-qubit Heron-series processors. This represents a nearly 18× increase in total qubit utilization compared to the 8-qubit architecture of previous phases. This scale is directly aligned with IBM’s stated interest in projects that maximize qubit utilization and push hardware limits.

The Unified Composition Concept

Unlike previous phases where each schema produced an independent composition, Phase IV envisions the 16 waveforms as raw material for a single, larger compositional ecosystem. The waveforms are not movements — they are layers. Their value lies in combinatorial flexibility:

• Layered simultaneously in varying combinations and densities
• Cut into sections and recombined in non-linear arrangements
• Interpreted differently across multiple distinct compositions from the same source material
• The same quantum data yielding many different musical outcomes depending on editorial choices

This approach positions the quantum hardware execution as the generative foundation and the composer as the interpreter — a true creative symbiosis between quantum physics and human artistic judgment.

Non-Uniform Parameter Spacing — A Key Innovation

Previous phases used evenly spaced theta values across the parameter range (0 to 2π). Phase IV will use deliberately structured non-uniform spacing to give each waveform internal rhythmic and textural life — phrases, breaths, accelerations, decelerations, and clumping. This is not random (which would be as uninteresting as even spacing) but compositionally intentional.

Possible spacing strategies under consideration:

• Logarithmic spacing — gradual acceleration through the parameter space
• Fibonacci-derived intervals — naturally proportioned irregular spacing
• Harmonically related proportions — spacing derived from musical interval ratios
• Acceleration and deceleration curves — the feeling of quantum states rushing toward or receding from configurations
• Clumped phrasing — dense clusters separated by longer gaps, creating phrase-like structures

Different schemas may use different spacing strategies, so that when layers are combined their phrasings drift in and out of alignment — creating emergent polyrhythmic structures that were never explicitly composed.

Circuit Architecture — Beyond Previous Phases

Previous phases relied primarily on RZZ, Ry, Rz, and CNOT gates. Phase IV will expand the gate vocabulary to include native IBM gate families not available or practical on Tuna-9, creating fundamentally different interference geometries in Hilbert space. Different gate types create different quantum interference structures which translate directly to different sonic character.

The 16 schemas will likely include:

• Variations on Phases II and III topologies (Star, Chain, Ring, etc.) with expanded gate sets
• Entirely new topologies exploiting 9-qubit connectivity
• Schemas specifically designed to produce complementary or contrasting sonic material

The specific 16 schemas will be developed collaboratively once IBM hardware access is confirmed and the native gate set is known precisely.

IBM Quantum Credits Program — Grant Application

Application Strategy

The application is being submitted proactively due to IBM’s stated multi-week review backlog. The one-year credit validity means there is no urgency to begin immediately — applying now ensures access is available when Phase IV development is ready to begin, estimated several months from submission.

Grant strategy follows standard academic practice: request more than the minimum needed to ensure sufficient compute budget, with willingness to reduce scope if IBM awards a smaller allocation.

Compute Requirements — Based on Direct Benchmark Testing

A direct benchmark comparison between Quantum Inspire’s Tuna-9 processor and IBM’s ibm_fez backend was conducted using identical 60-step Chain schema tomographic circuits (180 circuits, 2048 shots). ibm_fez completed execution in 1.94 minutes versus 9.31 minutes on Tuna-9 — a 4.8× speed advantage. Scaling to Phase IV — 16 schemas × 600 steps × 3 bases = 28,800 circuits — yields a linear extrapolation of approximately 5 hours for full execution on ibm_fez. Adding overhead for iterative circuit development, testing, and the expanded 9-qubit circuit complexity, the estimated Phase IV execution requirements will fall comfortably within the 10–15 hours afforded by the grant if awarded. The application will request compute time at the upper end of this estimate.

Key Application Arguments

• Established methodology: Phases I, II, and III validated on real quantum hardware with published research outcomes
• Novel application domain: quantum computing as direct creative instrument — no classical equivalent
• State-of-the-art utilization: 144 of 156 available qubits — maximal hardware engagement
• Methodological innovation: non-uniform parameter sampling as compositional tool
• Concrete deliverables: compositions, VR visualizations, and peer-reviewed publications
• Documented prior work: quantumcomputationalcreativity.com and Computer Music Journal submission

Supporting Documentation

The following resources are available as supporting links in the application:

• IDIA Lab profile: https://idialab.org/michael-rhoades/
• Overall research phases documentation: https://quantumcomputationalcreativity.com
• Computer Music Journal submission (pending publication)

Open Questions for Phase IV Development

The following questions remain to be resolved when active development begins:

• Final selection of 16 circuit topologies and their specific gate architectures
• Specific non-uniform spacing algorithms for each schema
• Target qubit count confirmation based on IBM hardware availability
• Whether 16 schemas can be executed as parallel jobs on a single large circuit or must be sequential
• Transduction methodology — how Bloch coordinates map to audio parameters in ways that produce fundamentally different material than previous phases
• VR visualization approach for Phase IV — same chrome environment with different objects, or entirely new environment per schema
• Whether Phase IV visual and audio work will be synchronized to create unified audiovisual compositions

Notes on AI Collaboration

This project has been developed through an ongoing collaborative process between Dr. Rhoades and Claude (Anthropic). Claude has served as technical intermediary, code generator, and conceptual discussion partner throughout all phases of the research. All creative decisions, circuit designs, compositional choices, and research directions have remained under Dr. Rhoades’ sole authorship and control.

For grant application purposes, Dr. Rhoades is listed as sole PI. The AI collaboration is acknowledged as a methodological tool in the research documentation at quantumcomputationalcreativity.com.

Quantum Computational Creativity — Phase IV Initial Conceptualization — Updated March 2026