Structure before circuit tricks

StatePreparationWiki

Research targets with explicit access models, acceptance tests and model-matched lower-bound obligations. A candidate route is not a proved open-problem classification.

An arbitrary N=2^n dimensional vector is not a succinct structured input. Parameter-counting and access-model lower bounds must be compared in their own precision, gate and ancilla models. Do not promise universal poly(n) loading of an arbitrary explicitly supplied vector. Do not confuse exponential gate count with ancilla count.

The resource contract

input representation and bit length
data qubits and workspace qubits
classical preprocessing and memory
oracle construction, inverse and controlled access
primitive gates, T/Toffoli count and depth
connectivity and parallelism
success probability and amplification
state/operator/trace error and confidence
readout and end-to-end application cost

Search application, obstacle or technique

Priority 0 · research target

Uncompute: digesting discovered reversible circuits

First research priority: digest the whole pinned paper and its existing proofs into readable, audited mechanisms, then use them in controlled SP/BE construction-evolution experiments. Start with Appendix A branch recovery and the DQI theorem boundary, then connect real circuit semantics, error and resources; do not stop at a toy arithmetic identity or claim a resource improvement before a matched-contract comparison.

No new ASPBE Lean closure yet. Upstream recurrence/DQI proofs do not certify all eight circuit tasks. A 590-step worst-case result does not accept the 533-step failure-budget circuit. TQ is a paper objective, not a replacement for ASPBE correctness-first resource contracts.

Priority 1 · research target

Coherent parameter-dependent families

Produce one coherent template for jointly structured parameters and data with a uniform error bound.

A family of individually easy states need not have an easy coherent supplier. Per-parameter correctness up to phase is insufficient.

Priority 1 · research target

Preconditioned function preparation with an explicit envelope

Construct g for one useful localized function class so that reference preparation, ratio implementation and amplification are all controlled.

Coherent rejection and reweighting are prior art. Uniform g recovers kappa_env=1/F2 where F2=||f||2/(sqrt(M)||f||infinity). A small ratio on average does not imply a valid pointwise envelope.

Priority 1 · research target

High-dimensional structured function states

Prove a constructive cost and state-error theorem for a precisely specified low-rank, sparse-frequency, mixed-smoothness or compositional class; do not equate these assumptions.

Generic tensor-product degree-q expansions have (q+1)^D coefficients; smoothness alone does not remove dimensionality. Hermite's one-dimensional exact-real compiler is a substrate, not this multivariate theorem.

Priority 2 · research target

CV–DV function preparation and non-Gaussian resources

Relate a declared finite-energy oscillator encoding to qubit-grid preparation with a rigorous embedding and separate resource budgets.

The finite Hermite state is a useful first example. No CV–DV equivalence or GKP preparation theorem is currently supplied by this route.

Priority 2 · research target

Diagonal operators: space, depth, accuracy and success

Formalize unitary phase synthesis and non-unitary diagonal dilation as separate suppliers, then derive a state-preparation consumer with full resource accounting.

Reduced depth may require much more workspace without reducing total size. A non-unitary diagonal is an accepted block, not a deterministic system-only gate; approximation may require stronger smoothness for transformed angle functions. Local staging checks the literal Figure3 accepted1<-0 action, success mass and normalized branch. Printed rejected-phase and clean0<-0 discrepancies are retained as source gaps; no scalable resource theorem or full-paper admission follows.

Priority 2 · research target

Fault-tolerant resource trade-offs for structured preparation

Compile the exact-real structured route into a finite gate set with a proved error budget and declared connectivity.

The Hermite exact-real primitive theorem is already a useful substrate. Full bit complexity and stable angle generation are additional obligations.

Priority 2 · research target

Data loading without a free QRAM assumption

Identify succinct data classes for which explicit access construction preserves the intended algorithmic advantage.

General sparse-access and block-encoding constructions can require near-linear cost in matrix dimension. Sparsity does not make all entries free.

Priority 2 · research target

Joint design of preparation and experimental verification

Automatically derive a low-sample fidelity witness for a precisely defined structured state class.

A Lean ideal-circuit proof does not certify noisy hardware. The user-supplied 2609.08414 reference remains primary-source-unavailable in this ledger.

Priority 2 · research target

Walsh-series state preparation: phase is not amplitude

Formalize the source Walsh Series Loader, including its constant mode, normalized approximation and success-dependent complexity.

The state after postselection is proportional to -i(I-exp(-i tau F_S))|+^n>, not exactly to f_S at finite tau. Increasing fidelity can reduce success probability. The zero-order-term implementation issue must be tested explicitly. Local staging now checks the actual H-controlled-diagonal-H-phase composition, constant relative phase and exact sine-squared accepted mass; independent source/semantic admission and approximation/resources remain open.

Priority 3 · research target

Low-temperature Gibbs preparation with quantitative mixing

For a restricted noncommuting local Hamiltonian family, prove a mixing certificate and implemented-channel error bound.

KMS detailed balance and stationarity are not polynomial mixing. Classical sampling inequalities cannot be transferred to quantum operators without a hypothesis map.

Priority 3 · research target

Useful trial states for strong-correlation ground-state preparation

For a specified physical family, construct a cheap trial-state supplier with a proved useful overlap or target-subspace guarantee.

Lin–Tong provides algorithms and lower bounds under overlap/gap assumptions. Strong correlation does not itself certify an MPS rank or overlap.

Audited baselines and candidate references

Discovering state-of-the-art quantum circuits with large language models

primary-text-checked v1: design principles; Methods Eqs. (10)-(22); Appendix A, A.1-A.8 (PDF pp. 44-46). Other case studies remain a queued source audit.

Priority intake for reversible computation and proof digestion. First batch audits existing branch-recovery and DQI proof interfaces; full paper and circuit/resource closure remain open.

uncompute: pinned author circuit, evaluator and Lean artifacts

primary-text-checked Commit 64b5a13aa249f1360846657392e6c66817b26d0f; lean/divsteps/README.md, lean/dqi/README.md; selected Recovery.lean and Complete.lean theorem interfaces; not yet a whole-module audit or local build.

Observed pins: divsteps Lean/Mathlib4.32.2; DQI Lean/Mathlib4.33.1. Apache-2.0 repository; divsteps also retains MIT safegcd-bounds attribution. Upstream source and claimed builds are not ASPBE acceptance.

Efficient Quantum State Preparation with Walsh Series

primary-text-checked arXiv v3, 9 November 2023; checked 29 September 2026: Theorem 1, Corollary 1, Table I and Appendix B (B14–B19, B28).

Walsh Series Loader: epsilon is state infidelity. Smooth fixed-function single-attempt depth O(epsilon^-1/2), size O(n+epsilon^-1/2), success Theta(epsilon); expected depth O(epsilon^-3/2), expected size O((n+epsilon^-1/2)/epsilon). Constants retain function/derivative/nonzero-mass assumptions. Sparse variants require supplied coefficients and Hamming-weight bounds. Amplification also charges reflections and inverses.

Efficient Quantum Circuits for Non-Unitary and Unitary Diagonal Operators with Space-Time-Accuracy trade-offs

primary-text-checked arXiv v4, 21 January 2025; checked 29 September 2026: II.1, III.1–III.2, IV.1 Eqs. (15)–(16), V.1 Eqs. (19)–(21), VI A, VIII.1 and Tables I–II. Figure 4 signal-sector and III.2/VIII.1 accounting ambiguities remain explicit source obligations.

Parallel scheduling trades ancillas for depth, not automatically total size. Table I uses spectral-norm error; Eq. (18) bounds normalized-block error delta, corresponding to total-scale times delta in the unscaled-operator convention. Exact-block success in source notation is ||D psi||^2/(alpha^2 dmax^2); alpha>1 controls the transformed-angle derivative in smooth approximation. No local source theorem or resolution of source ambiguities is claimed.

Comment on arXiv:2307.08384: Efficient Quantum State Preparation with Walsh Series

primary-text-checked arXiv v1 full HTML, Sections II.2–II.3, Eq. (11), Fig. 2: controlled zero-order term; checked 29 September 2026.

Companion adversarial implementation review, not a refutation of the WSL theory. Retain the constant Walsh coefficient in a controlled phase circuit; use constant and constant-plus-parity regression cases.

Efficient Quantum Circuits for Accurate State Preparation of Smooth, Differentiable Functions

primary-metadata-checked Abstract: explicit function to MPS to circuit; requested v1 HTML was unavailable in this audit

Prior art for function-to-MPS preparation. The ASPBE Hermite specialization must not be credited with inventing polynomial-to-MPS or sequential MPS preparation.

Optimal (controlled) quantum state preparation and improved unitary synthesis by quantum circuits with any number of ancillary qubits

primary-metadata-checked Abstract and publication version notice: published arXiv v2; later v3 exists

Baseline for arbitrary and controlled state preparation and ancilla/depth trade-offs. Pin a version and gate model before comparing bounds.

Circuit complexity of quantum access models for encoding classical data

primary-text-checked Results: circuit complexity lower bound; construction of LCU-based block-encoding; Methods: state preparation

Explicit access construction is not a free oracle. PREPARE together with SELECT and uncomputation can supply a block encoding; a single prepared state alone does not determine an arbitrary operator.

Quantum State Preparation without Coherent Arithmetic

primary-metadata-checked Abstract; Physical Review Letters 136, 240603, published 18 June 2026

QET-based function preparation with few ancillas. Approximation, normalization and success probability remain separate costs.

Quantum state preparation via piecewise QSVT

primary-metadata-checked Abstract and article record

Piecewise function preparation baseline; partition access, degree, success amplification and primitive compilation must be specified before a resource comparison.

Quantum state preparation for multivariate functions

primary-metadata-checked Abstract and article record

Multivariate preparation baseline; a tensor-product coefficient count is not automatically polynomial in dimension.

QKAN: quantum Kolmogorov-Arnold networks with applications in machine learning and multivariate state preparation

primary-text-checked Abstract, Introduction and Discussion: shallow compositional state preparation

Composition-dependent bounds, not an efficient preparation theorem for every continuous multivariate function.

Quantum Rejection Sampling

primary-metadata-checked Authors' publication page: quantum state generation, query characterization and matching lower bound

Prior art for coherent amplitude reweighting. Novelty must be in an explicit structured envelope, guarantees, implementation or model-matched bound, not in rejection sampling itself.

Near-optimal ground state preparation

primary-metadata-checked Abstract: initial overlap, spectral-gap promise, energy information and lower bounds

Use the promised overlap/gap model; do not erase these costs in a generic strong-correlation claim.

Initial State Preparation for Quantum Chemistry on Quantum Computers

primary-metadata-checked Article record and abstract

Application motivation for trial-state construction, assessment and refinement; not a proved overlap guarantee for arbitrary molecules.

Efficient Quantum Gibbs Samplers with Kubo–Martin–Schwinger Detailed Balance Condition

primary-text-checked Article abstract and Gibbs-sampler construction; Communications in Mathematical Physics 406, 67

Invariant Gibbs state and efficient mixing are different obligations. A low-temperature polynomial mixing claim needs additional model-specific evidence.

Efficient quantum state preparation on Quantinuum hardware (candidate reference)

primary-source-unavailable User-supplied arXiv identifier; primary fetch failed; do not use reported hardware numbers as evidence

Retained in the candidate queue rather than silently promoted from secondary indexing.

Samplinglib theorem-publication and conceptual-mirror protocols

primary-text-checked Author once; graph contribution; independent encoder–denoiser; unchanged historical audit debt

Design attribution. QuantumComputinglib has its own register, oracle, clean-ancilla and resource contracts; Samplinglib is not an imported Lean dependency.

Asymptotically Optimal Quantum Circuits for Comparators and Incrementers

primary-text-checked Sections 2–6; Figures 3–5; Eq. (16) controlled-adder rewrite; Eq. (17) quantum–quantum comparator contract

Primary source for the partial PromiseGateOptimization route and the planned source-faithful adder/comparator/incrementer formalization. Existing generic controlled-conjugation and dirty-flag lemmas do not certify the complete paper circuits or optimality claims.

Representation-theoretic methods in quantum information theory

primary-text-checked 10 April 2026 edition (79 pages), SHA256 90784b02b568b8c7bb6a1ec20588d801541d047779333bd2b2b8e63749dc0fe3; bounded first slice checked 8 October 2026 on printed pages3–4, Definition2.1, Eq.(2.4) and pure-state forward assertion. Stable registry ID retains the course-directory year FT25, not the PDF edition year.

Peer Part III curriculum anchor: states, measurements, tensor systems, representation theory, Schur–Weyl duality and information applications. No new local theorem or whole-textbook completion is claimed by this reader release.

Quantum Algorithms for Scientific Computation

primary-text-checked 29 April 2026 public 447-page edition; PDF SHA256 56825000d53025dea4c2998dd6a061592b8fb2b9a446c3194c5f408183327599. First bounded source slice: Chapter 9 Section 9.1, printed pages 141–143, equations (9.2), (9.9), (9.10), (9.12); standing partial-application convention Definition 2.25, page 37. Parts I–IV remain curriculum anchors, not completed formalisation.

Peer Part IV curriculum anchor, reusing existing ASPBE state-preparation/block-encoding APIs. New Chapter 9 adapters, operator-norm approximation, scientific constructions and resource certificates still require separate production admission. No whole-section/book completion is claimed.