# Key Papers in Quantum Computational Mechanics

*Annotated bibliography for the quantum emergence research area*

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## Foundational Papers

### 1. Occam's Quantum Razor (Gu et al., 2012)
**Full title**: "Quantum mechanics can reduce the complexity of classical models"

**Authors**: Mile Gu, Karoline Wiesner, Elisabeth Rieper, Vlatko Vedral

**Source**: Nature Communications 3, 763 (2012) | [arXiv:1102.1994](https://arxiv.org/abs/1102.1994)

**Key results**:
- Proves quantum models can be strictly more efficient than classical epsilon-machines
- Introduces the quantum statistical complexity $C_q = S(\rho)$
- Establishes the hierarchy: $E \leq C_q \leq C_\mu$
- Shows quantum models can approach the fundamental limit $E$

**Relevance to emic**:
- Central paper for the quantum extension
- Provides explicit construction of q-machines
- Perturbed coin example is a key validation target

**Notes**: Already summarized in `.project/references/gu2012quantum/`

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### 2. Towards Quantifying Complexity with Quantum Mechanics (Tan et al., 2014)
**Authors**: Ryan Tan, Daniel R. Terno, Jayne Thompson, Vlatko Vedral, Mile Gu

**Source**: EPJ Plus 129, 191 (2014) | [arXiv:1404.6255](https://arxiv.org/abs/1404.6255)

**Key results**:
- Proposes new complexity measure based on quantum epsilon-machines
- Applies to system undergoing constant thermalization
- Quantum measure aligns better with intuitive complexity

**Relevance to emic**:
- Provides concrete examples for validation
- Suggests alternative complexity measures to implement

**Status**: To read

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### 3. Unbounded Memory Advantage in Stochastic Simulation (Garner et al., 2017)
**Authors**: Andrew J. P. Garner, Qing Liu, Jayne Thompson, Vlatko Vedral, Mile Gu

**Source**: New J. Phys. 19, 103009 (2017) | [arXiv:1609.04408](https://arxiv.org/abs/1609.04408)

**Key results**:
- Quantum processors with fixed finite memory can simulate to arbitrarily high precision
- Proves **unbounded** memory advantage over best classical simulator
- Uses tools from computational mechanics

**Relevance to emic**:
- Strongest result on quantum advantage
- Important validation target
- Connects to continuous-variable processes

**Status**: To read

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### 4. Causal Asymmetry in a Quantum World (Thompson et al., 2018)
**Authors**: Jayne Thompson et al.

**Source**: [arXiv, likely 2018]

**Key results**:
- Studies temporal asymmetry in quantum causal models
- Connects to thermodynamic arrow of time

**Relevance to emic**:
- Already in references: `.project/references/thompson2018causal/`
- Connects to bidirectional machine analysis

**Status**: To read

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## Extended Reading List

### Computational Mechanics Foundations
- Crutchfield & Young (1989) - "Inferring statistical complexity" - Original epsilon-machine paper
- Shalizi & Crutchfield (2001) - "Computational mechanics" - Comprehensive theory
- Crutchfield (1994) - "Calculi of emergence" - Philosophical foundations

### Quantum Extensions
- **Aghamohammadi et al. (2018)** - "Extreme Quantum Memory Advantage for Rare-Event Sampling"
- **Mahoney et al. (2016)** - "Quantum Information in the Randomness of Quantum Processes"
- **Binder et al. (2018)** - "Practical Unitary Simulator for Non-Markovian Complex Processes"
- **Riechers & Crutchfield (2021)** - "Spectral Simplicity of Apparent Complexity" (metadynamics)

### Quantum Information Foundations
- Cerf & Adami (1997) - Quantum conditional probability
- Wilde (2017) - "Quantum Information Theory" (textbook)

### Recent Developments (2020-2026)
- **Inferring Kernel ε-Machines** (Jurgens & Brodu, 2024) - [arXiv:2410.01076](https://arxiv.org/abs/2410.01076)
- **Quantum Causal Unravelling** (Bai et al., 2022) - [arXiv:2109.13166](https://arxiv.org/abs/2109.13166)
- **Entanglement, Complexity, and Causal Asymmetry** (Williams, 2022) - [arXiv:2204.06742](https://arxiv.org/abs/2204.06742)

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## Papers to Acquire

| Paper | arXiv | Priority |
|-------|-------|----------|
| Aghamohammadi et al. (2018) | TBD | High |
| Mahoney et al. (2016) | TBD | High |
| Binder et al. (2018) | TBD | Medium |
| Riechers & Crutchfield (2021) | TBD | Medium |

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## Reading Plan

### Week 1
1. Re-read Gu et al. (2012) carefully, extract all equations
2. Read Tan et al. (2014) for concrete examples
3. Read Garner et al. (2017) for unbounded advantage

### Week 2
4. Read Thompson et al. (2018) on causal asymmetry
5. Survey recent papers (2020-2026)
6. Begin extracting mathematical framework

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*Last updated: 2026-01-27*
