Quantum Algorithms · Circuit Optimization · Formal Verification · Computational Research
Exploring advanced computational methods through quantum algorithm research, circuit optimization, mathematical modeling and formally verified results. Our research emphasizes reproducibility, rigorous experimentation and evidence-backed conclusions.
This field is research. The following is not established, and we do not claim it.
Small, noisy machines today, and results that have to hold up anyway.
Before a computation is trusted, it should be reproducible, and where possible, proved.
Today's quantum computers are small and noisy. A circuit that is correct on paper can change its meaning when it is compiled for real hardware, and a result that looks good once may not survive a second run.
We work on circuits and algorithms, on compiling them without changing what they compute, and on checking results by machine: with simulators, independent verifiers and, where it fits, formal proofs in Lean 4. Negative results are recorded as carefully as positive ones.
Where this field stands: questions first, capabilities second.
How our experiments are set up, so that a result can be checked again, including when it fails.
Hypothesis and pass criteria are written down first.
Checked against a written description of what it must compute.
Exact values are computed in simulation.
Measured counts are stored unchanged.
A separate verifier compares counts with the expected values.
Positive, negative or inconclusive, it stays on record.
In research This is how we set up experiments. Most ran on simulators; some ran on IBM quantum hardware.
Research work and its evidence. No capability in this field is shown as demonstrated.
Circuits, how they are compiled, and what survives contact with hardware.
Our work for the Classiq Quantum Circuit Optimization Challenge: reducing the depth of a reference circuit, with every search approach recorded. Several approaches closed negative: they did not improve on our own earlier design.
In researchInternal, not publishedCompiling a quantum feature map for kernel methods under a written semantic contract, and checking the compiled circuit against exact kernel values in simulation. Not independently verified.
In researchInternal, reproducibleExploratory runs on IBM quantum hardware. In the documented kernel experiment (ibm_marrakesh, five circuits, 4,096 shots each, August 2026), hardware noise collapsed the measured kernel values towards zero: a negative result, kept on record. Further hardware runs are not yet published here.
In researchExploratory hardware resultsBuilt in public, with the code published.
Two entries built during the hackathon (9–11 October 2026): a Mermin–Peres magic-square game and a four-player non-local game. Each ships with a frozen verifier. Runs were made on simulators, not on IonQ hardware.
Implemented / documentedPublic codeEvidenceResults stated as theorems and checked by a proof assistant, kept apart from experimental results.
Using the Lean 4 proof assistant to check constructions by machine instead of trusting a run or a hand argument.
In researchResearch CenterA lower-bound study for Langton's Ant on a strip five rows high. One construction is reported as checked locally in Lean 4. The files are not published and nobody outside FeedOracle has reviewed them, so we do not classify it further and claim no novelty.
Status to confirm—Preparing signed records for a time when today's signature schemes can be broken.
feedoracle.io publishes an ML-DSA-65 public key next to its classical ES256K keys. Production-wide post-quantum signing is not demonstrated.
In researchFeedOracleEvidenceNone yet.
There is no product in this field. Results stay in the Research Center until they can be reproduced and, where possible, checked by someone outside FeedOracle.
Where this field meets the other three.
Quantum feature maps for kernel methods: a compiled study whose documented IBM hardware run gave a negative result.
In researchPost-quantum signatures for records that must stay verifiable for years.
In researchExperiment records with raw counts and an independent verifier, as in our public hackathon code.
Implemented / documentedThis field is research today. It feeds two research directions, and its results stay in the Research Center until they are reproducible and, where possible, independently checked.
FeedOracle Research CenterReal starting points only. Pages that do not exist yet are not linked.
Bring a question about circuits, compilation, or formal verification of computational results.
Our hackathon entries publish their code and verifiers. If your result differs from ours, we want to know.