References and related work
Many ideas are not necessarily invented as much as they are found and remixed.
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Optimal Qubit Purification and Unitary Schur Sampling via Random SWAP Tests
Random pairwise SWAP-test protocols for specified qubit purification and Schur-sampling tasks. Does not establish an arbitrary coherent Schur transform.
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A complexity phase transition at the EPR Hamiltonian
Proved Hamiltonian classification, EPR* tractability question, and named singlet conjecture.
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Complexity classification of local Hamiltonian problems
Background classification of two-local Hamiltonians. Match signs, weights, and graph restrictions to the precise result used.
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Testing product states, quantum Merlin-Arthur games and tensor optimisation
Product-state testing and applications to unentangled witnesses.
QuestionsQ16 - 082026
A quantum oracle separation between QMA(2) and QMA
A quantum-oracle separation using symmetric/antisymmetric projectors; also gives disentangler lower bounds. It is not an unrelativized separation.
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Symmetry-assisted adversaries for quantum state generation
Representation theory in adversary bounds and quantum state generation.
QuestionsQ17 - 102026
Quantum Lazy Sampling and Path Recording for Any Group
Purification, representation theory, and recording access to random group elements.
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The Compressed Oracle is a Worthy (Multiplicative) Adversary
Connects compressed-oracle methods with multiplicative adversaries; useful background for the requested purification/adversary bridge.
QuestionsQ17 - 122025
A General Quantum Duality for Representations of Groups with Applications to Quantum Money, Lightning, and Fire
Computational relationship between implementing representations and Fourier subspace extraction, with applications to quantum cryptography.
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Optimal Quantum de Finetti Theorems via Argmax Rounding
Quantum de Finetti and disentangling constructions. Input dimension, number of qubits, and approximation conventions matter when comparing bounds.
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Efficient Quantum Circuits for Schur and Clebsch–Gordan Transforms
Efficient coherent Schur and Clebsch–Gordan transforms; the representation-theoretic coordinate system.
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Tight Bounds for Inverting Permutations via Compressed Oracle Arguments
Purified random-permutation oracles, representation theory, and lower bounds.
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Spectral gap of Lee-Yang Hamiltonians
A uniform-field spectral-gap theorem yielding BQP ground-energy estimation for Lee–Yang Hamiltonians; applies to EPR*.
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Lee-Yang tensors and Hamiltonian complexity
The Lee–Yang tensor and Hamiltonian framework, including the EPR adiabatic approach and earlier gap conjectures.
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Guidable Local Hamiltonian Problems with Implications to Heuristic Ansätze State Preparation and the Quantum PCP Conjecture
QCMA formulations in which a suitable guiding state is promised to exist. A direct framework for the classical-starting-data question; it does not establish guides for every stoquastic YES instance.
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Monte Carlo simulation of stoquastic Hamiltonians
Projection Monte Carlo and MA verification with specified classical guiding-state promises. Those promises are additional assumptions, not consequences of stoquasticity alone.
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Quantum fingerprinting
Quantum-state comparison with the SWAP test and its application to communication complexity. The overlap formula assumes independent inputs.
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Lecture Notes on Quantum Algorithms
Chapters 11 and 15 develop representation theory, Fourier transforms, and Schur–Weyl duality. Background for the exposition of irreps, multiplicities, and coupling paths.
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Quantum Algorithms for Representation-Theoretic Multiplicities
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Polynomial time classical versus quantum algorithms for representation theoretic multiplicities
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Expository account of representation-theoretic multiplicity algorithms and the classical progress they prompted; mathematical claims here are linked to the primary papers.
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Forrelation: A Problem That Optimally Separates Quantum from Classical Computing
A Fourier-correlation problem with a nearly maximal quantum–classical query separation; a benchmark for spin-based oracle questions.
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The quantum Schur and Clebsch–Gordan transforms: I. Efficient qudit circuits
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The complexity of stoquastic local Hamiltonian problems
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Classical simulation of specified stoquastic frustration-free adiabatic paths and MA-completeness of stoquastic satisfiability.
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Exponential algorithmic speedup by quantum walk
An exponential oracle separation obtained by coherent graph traversal; a benchmark for walks on coupling and representation graphs.
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The Church of the Symmetric Subspace
A survey of symmetric-subspace methods in state estimation, cloning, de Finetti theorems, and concentration bounds.
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Universal qudit Hamiltonians
Universal Hamiltonian families for qudits, including SU(d) and spin-SU(2) Heisenberg interactions.
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A one-way quantum computer
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Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Order finding and Fourier-based quantum algorithms for factoring and discrete logarithms; a target for a direct spin-based formulation.
QuestionsQ02 - 381996
A fast quantum mechanical algorithm for database search
Quadratic quantum-query speedup for unstructured search. The benchmark for a direct subsystem-spin search protocol.
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Quantum Amplitude Amplification and Estimation
Generalizes Grover search using coherent preparation, its inverse, and reflections. Clarifies which operations a subsystem-spin implementation must realize.
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Strengths and Weaknesses of Quantum Computing
Black-box lower bounds, including the square-root barrier for quantum search. Supports the query benchmark without asserting a lower bound for every differently defined spin-search task.
QuestionsQ41
About this work
These ideas were refined through many conversations with researchers across quantum information.
We developed this framing and the motivating questions through notes and conversations, with AI assistance for editorial synthesis, mathematical illustrations, implementation, and source discovery.
Attribution feels strange in this new world. Knowledge can come from anywhere, and ideas are often rediscovered and remixed across fields. We hope this project sparks discussion and new ideas that contribute to a shared understanding of quantum computation.
Corrections are welcome.
Cite this work
Kunal Marwaha and James Sud (2026). Singlet: Subsystem spin as a primitive for quantum computation. https://marwahaha.github.io/singlet/
@misc{marwahaSud2026singlet,
author = {Marwaha, Kunal and Sud, James},
title = {{Singlet}: Subsystem spin as a primitive for quantum computation},
year = {2026},
url = {https://marwahaha.github.io/singlet/}
}Continuing the conversation
You can discuss the perspective, propose a research question, or write to Kunal. For a specific correction or a website problem, open an issue on GitHub. Please include a question number or a reference when relevant.
The earlier Quantum Max-Cut reference is another entry into this landscape. The present essay follows some of those connections through subsystem spin.