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 the planning stages. It also serves as supporting context for the IBM Quantum Credits Program grant application.

Overview

Phase IV represents the most ambitious execution of the Quantum Computational Creativity methodology to date. Sixteen circuit schemas, each utilizing nine qubits, will engage 144 of IBM Kingston’s 156 available qubits in a single large-scale hardware execution. This is not simply a scaling of previous phases. Phase IV introduces fundamental changes at the circuit architecture level, changes driven directly by discoveries made during Phase III development that exposed both the limitations of the previous approach and the path beyond them.

A pilot execution on April 1, 2026 confirmed that 144-qubit parallel circuit execution on Kingston is fully viable: 6,816 circuits executed in 7 minutes 47 seconds of quantum time, at a calibrated rate of 0.069 seconds per circuit. 180 minutes of compute time on Kingston were subsequently made available following usage that exceeded the 20-minute threshold, valid for one year from April 2026. This resource provides the foundation for the initial steps of Phase IV execution. A separate application to IBM’s Quantum Credits Program, requesting extended compute time to support full-scale execution, has been submitted and is currently pending review.

All Phase IV circuit designs will be validated in Qiskit Aer simulation before any IBM compute time is committed. This simulation-first discipline, established during Phase III development, ensures that hardware execution is reserved for designs that have demonstrated their value and viability computationally.

The IBM/Quantum Inspire hardware comparison benchmark, documented fully on the quantumcomputationalcreativity.com research pages and reproduced in the hardware section below, provides the empirical foundation for the compute time estimates submitted in the grant application.

Discoveries from Phase III that Inform Phase IV

Three specific challenges emerged during Phase III audio and visual development. Each is inherent to the Phase III circuit architecture and cannot be resolved in post-production. Each must be addressed at the circuit design level in Phase IV.

The Chord Challenge

Within each Phase III schema, all eight qubits evolve together through the same parameter sweep, arriving at significant quantum states simultaneously. When complex samples derived from Bloch sphere trajectories are played back across all eight voices at once, the result collapses into an undifferentiated mass. Individual voices cannot be tracked perceptually. The solution requires circuits in which different qubits arrive at significant states at different times — temporal separation built into the quantum architecture itself.

The Waveform Similarity Challenge

Phase III tomographic waveforms are too similar across qubits and across schemas. Entanglement keeps qubits correlated, which is physically accurate but compositionally limiting. The eight voices within a schema move together rather than independently. Phase IV circuits must be designed to produce genuinely distinct waveform shapes between qubits, with timbral variety arising from asymmetric gate structures rather than from post-production manipulation.

Unified Temporal Phrasing

A third insight functions less as a challenge and more as a design opportunity: if non-uniform temporal distribution is built into the circuit execution through non-uniform parameter sampling, then audio and visual material emerge from the same underlying temporal structure from the beginning. The phrasing is not imposed on the data after the fact. It is inherent in the quantum execution itself. This is the deepest realization of the QCC unified methodology to date: compositional phrasing as an emergent quantum phenomenon, arising from the circuit execution rather than from artistic interpretation applied afterward.

Phase IV Design Principles

Principle 1 — Temporal Separation by Design

Phase IV circuits are designed so that different qubits arrive at significant quantum states at different times. Approaches under development include staggered parameter sweeps, sequential entanglement activation, and topology-driven temporal structure. The entanglement topology becomes the compositional structure. The physics and the music are unified at the circuit level rather than reconciled afterward.

Principle 2 — Timbral Variety by Design

Phase IV circuits move away from uniformly scaled rotation gates toward asymmetric gate structures that produce distinctly different waveform shapes between qubits. Different rotation gate types per qubit, deliberately varied entanglement strengths, non-uniform parameter ranges, and non-uniform parameter sampling all contribute to a palette of genuinely distinct quantum voices within each schema.

Principle 3 — Compositional Requirements as Circuit Constraints

The most significant methodological shift in Phase IV is treating desired sonic and perceptual outcomes as design constraints on the quantum circuits themselves. In Phases II and III, circuits were designed for quantum hardware execution and compositional interpretation came afterward. In Phase IV, the composition informs the circuit architecture from the beginning. The quantum physics and the artistic vision are no longer sequential — they are simultaneous.

Dynamic Entanglement Architecture

The most significant conceptual advancement in Phase IV circuit design is making entanglement topology itself a dynamic variable. In Phases II and III, each schema had a fixed entanglement topology determined at design time and held constant throughout execution. Phase IV proposes circuits in which different qubit pairs become entangled and disentangled at different points during the parameter sweep.

A qubit’s Bloch trajectory is shaped by what it is entangled with and when. A qubit entangled with one partner in early parameter steps, decoupled in the middle range, and re-entangled with a different partner in the final steps will exhibit three distinctly different characters across those regions. This is genuine timbral variation arising from the circuit architecture, not from post-production processing.

Offset Phase RZZ Entanglement Layers

The primary implementation approach uses multiple RZZ entanglement layers with offset phase angles. Rather than a single entanglement layer at uniform strength, the circuit employs several layers whose gate angles are functions of θ with different phase offsets:

Layer 1: RZZ(sin(θ)) between qubits 0-1, 2-3, 4-5, 6-7 — peaks at θ=π/2

Layer 2: RZZ(sin(θ+π/4)) between qubits 1-2, 3-4, 5-6 — peaks offset by π/4

Layer 3: RZZ(sin(θ+π/2)) between qubits 0-4, 1-5, 2-6, 3-7 — peaks offset by π/2

Each layer’s entanglement peaks and troughs at different points in the sweep. Qubits experience constantly shifting entanglement relationships, with some strengthening while others weaken. This directly addresses the chord challenge, the waveform similarity challenge, and unified temporal phrasing simultaneously.

Mid-Circuit Measurements as Topology Change Triggers

A more radical approach uses mid-circuit measurements to trigger topology changes during execution. When a qubit is measured mid-circuit, its wavefunction collapses to a definite classical state, breaking all entanglement relationships at that point. The circuit then continues with the collapsed qubit entering new entanglement relationships with different partners.

The resulting Bloch trajectory shows complex entangled evolution in the first section, a sharp discontinuity at the measurement point, and a new evolution under different entanglement conditions afterward. Those discontinuities are themselves compositionally significant. In audio they translate to timbral shifts. In visual output they produce sudden changes in filament movement character.

Mid-circuit measurements with classical feedforward are supported on IBM’s Heron processors including Kingston, one of the advanced capabilities that makes Kingston the appropriate platform for this architecture. This approach places Phase IV at the leading edge of current quantum circuit research. It emerged organically from the compositional challenges identified in Phase III, and the novel perspectives on dynamic topology change that it opens represent a genuinely original contribution to the field — one that extends well beyond the artistic domain into quantum circuit design and research.

Post-Measurement Hadamard Reinitialization

After a mid-circuit measurement collapses a qubit to a classical state, a Hadamard gate throws it back into superposition, equal probability of |0⟩ and |1⟩. New entangling gates then establish fresh entanglement relationships with different partners. The qubit begins a new quantum evolution within the same circuit execution.

The full sequence — entangle, evolve, measure, reinitialize, re-entangle differently — applied to different qubits at different points in the sweep, produces a quantum counterpoint in which voices drop out and re-enter the texture at staggered intervals with fresh quantum characteristics. The compositional analogy is a fugal entry structure, but one governed by quantum physical laws rather than contrapuntal convention.

Hardware

IBM Kingston — Primary Platform

IBM Kingston is IBM’s most advanced currently available quantum processor, featuring 156 qubits and 340K CLOPS. 180 minutes of compute time became available following usage that exceeded the 20-minute threshold in April 2026, valid for one year from the award date. Phase IV will engage 144 qubits across 16 schemas of 9 qubits each. Kingston supports mid-circuit measurements and classical feedforward, both essential for the dynamic entanglement architecture described above.

A separate IBM Quantum Credits Program grant application requesting extended compute time to support full-scale Phase IV execution has been submitted and is pending review. The 180 minutes currently available provide the foundation for the initial simulation-validated circuit designs that will form the basis of that larger execution if the grant is awarded.

IBM ibm_fez — Secondary Platform

ibm_fez benchmarked at 4.8× faster than Quantum Inspire’s Tuna-9 in direct comparison testing conducted in February 2026, and at virtually identical execution time per circuit to Kingston in subsequent comparison. ibm_fez remains available as a secondary platform for circuit validation and comparison runs. The full hardware comparison benchmark is documented on the quantumcomputationalcreativity.com research pages and reproduced below.

Quantum Inspire Tuna-9 — Legacy Platform

Tuna-9 executed all Phase II transduction work and all Phase III tomography. It remains available as a validation and testing platform, and its characteristic hardware noise signature gives the Phase II and III material its distinctive quantum character — a reminder that hardware identity is embedded in the creative output.

Composition Concept

Phase IV envisions a single unified compositional ecosystem rather than the independent schema compositions of previous phases. Sixteen waveform sets serve as a palette of quantum-derived sonic objects from which a multi-movement or continuous composition is constructed. The dynamic entanglement architecture will produce waveforms with internal variation that no previous phase has achieved — voices that change timbral character mid-evolution as entanglement topology shifts during execution.

The visual methodology established in Phase III extends to Phase IV at dramatically larger scale. 144 individual quantum voices, each spatializable in an Ambisonics field and visualizable as animated filaments, will produce a visual environment of unprecedented complexity and internal variety. The dynamic entanglement architecture introduces a new visual dimension: filament trajectories that shift character mid-animation in direct correspondence with the mid-circuit measurement events that produce the same shifts in the audio domain. The coherence between audio and visual that was discovered organically in Phase III becomes, in Phase IV, an architectural certainty.

Preparation and Next Steps

Phase IV active development begins after the following are complete:

• Phase III visual renders for all eight schemas
• Phase III audio composition, Dance of the Qubits, finalized
• CMJ paper review outcome received and any revisions completed
• Phase IV circuit simulations validated using Qiskit Aer on clasical computer hadware.
• Dynamic entanglement architecture experiments: offset phase RZZ, mid-circuit measurements, Hadamard reinitialization
• IBM Quantum Credits Program grant decision received