Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T05:03:48.279602Z
Paper Citation Record · LEDGER
As of 12 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 0 inbound Pith citation observations for arXiv:2412.18309.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T05:03:48.279602Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
51 of 51 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation c2058548-eb9f-4098-bb3e-ce7e6914e7aa · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access If im = 0, then we simply ignore it and only proceed with those operators with im > 0
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 5d6f2ccd-aa62-4c89-8fde-16ba1407afce · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Unresolved cited work
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation e8e063e9-8466-43fb-9012-31b0efb32d64 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Unresolved cited work
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation c890e2a8-9b50-4904-8153-5334c6851a39 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access where we remind that in the last line, M is the upper bound of the norm of gradient of f within the domain D
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 9d173b2b-83a2-4c30-890a-af7e4693a0c4 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access 0 0 0 · · ·xn,0 The time complexity, or quantum circuit depth of this step is O(log(n)) and spatial complexity is O(log(n))
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation b35d8707-256f-4898-bb4b-05534d2a54b5 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Unresolved cited work
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation a5425288-3d55-4294-a40b-1dbac0047b05 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access 0 0 0 · · ·xn,0 − 1 2M K ∂f (x1,0,x2,0,...,xn,0) ∂x1,0 0 0 0 0 ∂f (x1,0,x2,0,...,xn,0) ∂x2,0 0 0 0 0
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 699831cb-25c9-4bfc-94bd-2bfdcfbb220a · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Eventually, we obtain an ϵ-approximated block encoding of x1,T 0 · · ·0 0 x2,T · · ·0 0 0
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation c159bb06-1308-4e53-939d-f36e5d15b6e6 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access 0 0 0 · · ·xn,0 The time complexity, or quantum circuit depth of this step is O(log(n)) and spatial complexity is O(log(n))
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 4dfd7044-db5e-48fc-a2f2-768e7d162ef7 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access 0 0 0 · · ·xn,0 − →1 M P x1,0 0 · · · 0 0 P x2,0 · · · 0 0 0
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 1445751b-2d9b-4c39-adef-babf98717afd · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access 0 0 0 · · · P xn,0 − →η P x1,0 0 · · · 0 0 P x2,0 · · · 0 0 0
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 4579514c-a25e-4bdd-8651-9983bf6063d1 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access 0 0 0 · · ·xn,0 − η P x1,0 0 · · · 0 0 P x2,0 · · · 0 0 0
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 07eb969a-19db-4a1c-b3a5-9f5c6a98e640 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Then we obtain an ϵ-approximated block encoding of: x1,1 0 · · ·0 0 x2,1 · · ·0 0 0
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 2899d233-d767-4283-9ba6-707b5ffc2d31 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access 0 0 0 · · ·xn,T The total time complexity is O log(n) deg(P) log 1 ϵ T and spatial complexity is O log n IV
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation cd4638df-0f91-40cb-a200-8e756930a44e · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Thus, this method is a nice complement to the Ref
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 2d4832c7-889f-47c5-b265-f33e70757b6b · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Simulating physics with computers
Reference 16
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4f67c296-8d90-4009-a92a-65160ec0342e · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Quantum theory, the church–turing principle and the universal quantum computer
Reference 17
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2f052b71-8a77-44a5-a5fa-90b3d9ef5ce2 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Rapid solution of problems by quantum computation
Reference 18
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 18519f06-eb97-43fd-ac38-aea6a07874ac · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Universal quantum simulators
Reference 19
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 39096491-a272-451f-942e-ec27b9558d3a · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Reference 20
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 036114b3-fd1f-4083-842a-ea7445670325 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access A fast quantum mechanical algorithm for database search
Reference 21
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 08b9e9bd-49a3-4564-839b-e1812bf52ddf · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Efficient quantum algorithms for simulating sparse hamiltonians
Reference 22
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8361ae0a-60b3-4d55-bf77-bde2bd540fa9 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Black-box hamiltonian simulation and unitary implementation
Reference 23
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 52c8da48-d451-4987-a51f-4d4a3984b21b · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access High-order quantum algorithm for solving linear differential equations
Reference 24
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f82f5b19-a438-4f4b-b866-9c179ada33f3 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Hamiltonian simulation with nearly optimal dependence on all parameters
Reference 25
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 762f21d2-a069-4145-8ef8-f49d099cf0b9 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Optimal hamiltonian simulation by quantum signal processing
Reference 26
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fec2f1c8-fc91-459a-adb1-3844502d82c5 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Hamiltonian simulation by qubitization
Reference 27
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2094e17f-2f91-4a08-9431-eeeccc602d1b · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Quantum simulation of real-space dynamics
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 987ca3dc-e804-4b9c-b005-990d6d192f29 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Quantum algorithm for linear systems of equations
Reference 29
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0ad7700e-7e64-42c5-805d-b3ffcecd1fa5 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
Reference 30
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8ee0ef5a-34a6-45ec-9f99-f582b95a54a1 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Quantum algorithms for supervised and unsupervised machine learning
Reference 31
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b2f2c436-4902-4642-908b-8869d8b75d51 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Quantum principal component analysis
Reference 32
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cceb9d6a-8cd4-46a0-99cc-58598529fbce · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Quantum algorithms for topological and geometric analysis of data
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation d829f3de-3564-44df-9faa-b5b2a26f325c · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Quantum embeddings for machine learning
Reference 34
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2cc09efb-a386-41fc-88c7-1756f3ed6cc4 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Quantum algorithm for data fitting
Reference 35
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f606b390-1241-4da3-8eb8-25f35319a513 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Quantum Algorithms for Nearest-Neighbor Methods for Supervised and Unsupervised Learning
Reference 36
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cad7f01c-5563-42f9-90e9-47ebfe79aed7 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
Reference 37
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cb63d315-0d23-4507-8f12-f0ae54406c32 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access On the relationship between continuous-and discrete-time quantum walk
Reference 38
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 06e47c6c-99af-482d-8767-7ad066aefaa0 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Quantum walk algorithm for element distinctness
Reference 39
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation aa8e6d26-c652-43ef-886c-2dedcb716c25 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Lecture notes on quantum algorithms
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation c5c66a20-fa9d-4c1b-a67e-722cd1e3d6ce · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Quantum support vector machine for big data classification.Physical review letters, 113(13):130503, 2014
Reference 41
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 177bbd70-3d14-46d8-aae1-638c45547a01 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Quantum Algorithm For Estimating Eigenvalue
Reference 42
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 73e0c472-7060-487e-bc27-6b1bdff47825 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Improved Quantum Algorithms for Eigenvalues Finding and Gradient Descent
Reference 43
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation af3ec7d4-2c9a-4997-a840-ab9208c86b15 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Improved Quantum Power Method and Numerical Integration Using Quantum Singular Value Transformation
Reference 44
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2c2e1c3d-2233-4ee1-9307-86ae90006a76 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Quantum algorithm for petz recovery channels and pretty good measurements
Reference 45
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1d5fd85a-60cc-40ab-8cc3-a0dae37eee12 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Quantum gradient descent and newton’s method for constrained polynomial optimization
Reference 46
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5bcfb924-255d-4eb7-8333-8c19feb1f5aa · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Non-Linear Transformations of Quantum Amplitudes: Exponential Improvement, Generalization, and Applications
Reference 47
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ad834936-c9b4-4062-8936-f273c19ec47f · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access A method for solving the convex programming problem with convergence rate o (1/k2)
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 337f6f98-aa1a-4ed6-a401-c027bf717dee · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Introductory lectures on convex optimization: A basic course, volume 87
Reference 49
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4260c9a8-f116-4767-840e-04b4cceec9e0 · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Convex optimization
Reference 50
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8e95c726-9428-4d25-86dd-127af036209e · outbound
Simple Quantum Gradient Descent Without Coherent Oracle Access Approximate quantum circuit synthesis using block encodings
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
No inbound Pith citation observations are available.