Each entry was checked by a script against arXiv, Crossref, or the publisher’s page before it was cited. Hover a citation key to preview it; the full formatted list is at the bottom of this page.
Research papers¶
| Source | Levels | Scope |
|---|---|---|
| Aspect et al., 1982 | 3, 4, 5 | Early photonic Bell-inequality experiment |
| Hensen et al., 2015 | 3, 4, 5, 6 | Loophole-free Bell test |
| Preskill, 2018 | 3, 4, 5 | Overview of noisy intermediate-scale quantum computing |
| Bell, 1964 | 4, 5, 6 | Bell local causality and incompatible quantum correlations |
| Clauser et al., 1969 | 4, 5, 6 | The CHSH inequality and experimental assumptions |
| Pearl, 1995 | 4, 5, 6 | Backdoor and frontdoor criteria, intervention calculus, and identification |
| Pearl, 2009 | 4, 5, 6 | SCMs, adjustment, identification, and counterfactuals |
| Schuld et al., 2021 | 5, 6 | Data encoding and expressivity of variational quantum models |
| Peters et al., 2015 | 5, 6, 7 | Invariance assumptions across environments |
| Havlicek et al., 2019 | 5, 6 | Feature maps and quantum kernel estimation |
| Mitarai et al., 2018 | 5, 6 | Hybrid variational circuit learning |
| Wang et al., 2021 | 5, 6, 7 | Noise-dependent trainability under explicit assumptions |
| Zheng et al., 2018 | 5, 6 | Smooth acyclicity constraints and structure learning |
| McClean et al., 2018 | 5, 6, 7 | Gradient concentration for specified random circuit ensembles |
| Procopio et al., 2015 | 5, 6, 7 | Photonic experiment on superposed gate orders |
| Biamonte et al., 2017 | 5, 6 | Quantum learning task classes and resource assumptions |
| Rubino et al., 2017 | 5, 6, 7 | Experimental causal witness for indefinite causal order |
| Schölkopf et al., 2021 | 5, 6, 7 | Causal representations and open machine learning questions |
| Schuld et al., 2019 | 5, 6 | Conditions for exact parameter-shift gradient rules |
| Cerezo et al., 2021 | 5, 6 | Review of variational quantum algorithms |
| Huang et al., 2021 | 6, 7 | Data-dependent comparisons with classical learning |
| Allen et al., 2017 | 6, 7 | Quantum common causes and quantum Markov structure |
| Barrett et al., 2019 | 6, 7 | Quantum processes, conditional independence, and causal structure |
| Chaves et al., 2015 | 6, 7 | Entropy constraints on quantum causal networks |
| Chiribella et al., 2009 | 6, 7 | Quantum combs and higher-order transformations |
| Costa & Shrapnel, 2016 | 6, 7 | Process-based causal modelling, Markov condition, and faithfulness |
| Fritz, 2012 | 6, 7 | Correlation scenarios beyond the Bell setting |
| Giarmatzi & Costa, 2018 | 6, 7 | Algorithm for discovering quantum causal structure from process matrices |
| Henson et al., 2014 | 6, 7 | Generalized Bayesian networks and theory-independent correlation limits |
| Liu et al., 2025 | 6, 7 | Inference within a specified two-time measurement setting |
| Wolfe et al., 2019 | 6, 7 | Inflation technique for testing causal structures with latent variables |
| Leifer & Spekkens, 2013 | 6, 7 | Quantum conditional states and causal neutrality |
| MacLean et al., 2017 | 6, 7 | Experiment on coherent mixtures of common-cause and cause-effect relations |
| Oreshkov et al., 2012 | 6, 7 | Process matrices and a causal inequality |
| Pienaar & Brukner, 2015 | 6, 7 | Graph separation (d-separation analogue) for quantum causal models |
| Araújo et al., 2015 | 6, 7 | Causal witnesses and causal nonseparability |
| Ried et al., 2015 | 6, 7 | Quantum interventions and observations for inferring causal structure |
| Huang et al., 2020 | 6, 7 | Classical shadows and observable-dependent sample complexity |
| Chiribella et al., 2013 | 6, 7 | Quantum control of channel order |
| Wood & Spekkens, 2015 | 6, 7 | Classical causal discovery applied to Bell correlations and fine-tuning |
| Junge et al., 2018 | 7 | Recovery and approximate sufficiency; advanced background |
| Bai et al., 2022 | 7 | Learning causal structure of quantum processes from interventions |
Books¶
| Source | Levels | Scope |
|---|---|---|
| Illowsky & Dean, 2023 | 1, 2, 3 | Probability, sampling, and estimation |
| Bareinboim, 2025 | 2, 4, 7 | Core textbook for causal AI: SCMs, Pearl’s causal hierarchy, identification, counterfactuals, fairness, transportability, causal decision-making and learning |
| Cunningham, 2021 | 2, 3, 4 | Causal comparisons and research design |
| Feynman, 1966 | 3, 4, 5 | Quantum amplitudes and interference |
| Hernan & Robins, 2020 | 4, 5, 6 | Potential outcomes, exchangeability, consistency, positivity |
| Nielsen & Chuang, 2012 | 4, 5, 6 | Standard textbook on quantum computation and information |
| Pearl, 2009 | 5, 6, 7 | Monograph on causal models, reasoning and inference |
| Peters et al., 2017 | 5, 6 | Causal discovery and structural models |
| Spirtes et al., n.d. | 5, 6, 7 | Conditional independence, Markov equivalence, and discovery |
| Watrous, 2018 | 6, 7 | Operators, channels, entropy, and discrimination |
Lecture notes and courses¶
| Source | Levels | Scope |
|---|---|---|
| Neal, n.d. | 3, 4, 5 | Free online course on causal inference |
| Basics of quantum information, n.d. | 3, 4, 5 | States, gates, measurement, and entanglement |
| Preskill, n.d. | 5, 6, 7 | Quantum information and quantum channels |
Software¶
| Source | Levels | Scope |
|---|---|---|
| Zheng et al., 2023 | 4, 5, 6 | Python library for causal discovery |
| Sharma & Kiciman, 2020 | 4, 5 | Python library for causal effect estimation |
| Bergholm et al., 2018 | 4, 5 | Python library for differentiable quantum programming |
Web resources¶
| Source | Levels | Scope |
|---|---|---|
| Nobel Prize in Physics 2022, 2022 | 0, 1, 2, 3 | Press release for the 2022 physics prize on entangled-photon experiments |
- Aspect, A., Grangier, P., & Roger, G. (1982). Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell’s Inequalities. Physical Review Letters, 49(2), 91–94. 10.1103/physrevlett.49.91
- Hensen, B., Bernien, H., Dréau, A. E., Reiserer, A., Kalb, N., Blok, M. S., Ruitenberg, J., Vermeulen, R. F. L., Schouten, R. N., Abellán, C., Amaya, W., Pruneri, V., Mitchell, M. W., Markham, M., Twitchen, D. J., Elkouss, D., Wehner, S., Taminiau, T. H., & Hanson, R. (2015). Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature, 526(7575), 682–686. 10.1038/nature15759
- Preskill, J. (2018). Quantum Computing in the NISQ era and beyond. Quantum, 2, 79. 10.22331/q-2018-08-06-79
- Bell, J. S. (1964). On the Einstein Podolsky Rosen paradox. Physics Physique Fizika, 1(3), 195–200. 10.1103/physicsphysiquefizika.1.195
- Clauser, J. F., Horne, M. A., Shimony, A., & Holt, R. A. (1969). Proposed Experiment to Test Local Hidden-Variable Theories. Physical Review Letters, 23(15), 880–884. 10.1103/physrevlett.23.880
- Pearl, J. (1995). Causal diagrams for empirical research. https://ftp.cs.ucla.edu/pub/stat_ser/R218-B.pdf
- Pearl, J. (2009). Causal inference in statistics: An overview. Statistics Surveys, 3(none), 96–146. 10.1214/09-ss057
- Schuld, M., Sweke, R., & Meyer, J. J. (2021). The effect of data encoding on the expressive power of variational quantum machine learning models. Physical Review A, 103(3). 10.1103/PhysRevA.103.032430
- Peters, J., Bühlmann, P., & Meinshausen, N. (2015). Causal inference using invariant prediction: identification and confidence intervals. https://arxiv.org/abs/1501.01332
- Havlicek, V., Córcoles, A. D., Temme, K., Harrow, A. W., Kandala, A., Chow, J. M., & Gambetta, J. M. (2019). Supervised learning with quantum enhanced feature spaces. Nature, 567(7747), 209–212. 10.1038/s41586-019-0980-2
- Mitarai, K., Negoro, M., Kitagawa, M., & Fujii, K. (2018). Quantum Circuit Learning. Physical Review A, 98(3). 10.1103/PhysRevA.98.032309
- Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., & Coles, P. J. (2021). Noise-Induced Barren Plateaus in Variational Quantum Algorithms. Nature Communications, 12(1). 10.1038/s41467-021-27045-6
- Zheng, X., Aragam, B., Ravikumar, P., & Xing, E. P. (2018). DAGs with NO TEARS: Continuous Optimization for Structure Learning. https://arxiv.org/abs/1803.01422
- McClean, J. R., Boixo, S., Smelyanskiy, V. N., Babbush, R., & Neven, H. (2018). Barren plateaus in quantum neural network training landscapes. Nature Communications, 9(1). 10.1038/s41467-018-07090-4
- Procopio, L. M., Moqanaki, A., Araújo, M., Costa, F., Calafell, I. A., Dowd, E. G., Hamel, D. R., Rozema, L. A., Brukner, Č., & Walther, P. (2015). Experimental Superposition of Orders of Quantum Gates. Nature Communications, 6(1). 10.1038/ncomms8913