The research behind Qelly
We build financial decision systems whose answers can be recomputed: exact search over every plan, bounded judgments about evidence, and an open benchmark for classical, quantum-inspired and quantum solvers.
Read the research thesisOur thesis
A financial decision system should show every plan it considered, prove the one it recommends, and say which fact would change its mind.
We separate three jobs. Bounded models read evidence into typed judgments. Exact search explores the actions. Deterministic code does the arithmetic and replays every recommendation. Language models explain; they never supply figures.
Specialized Qwen components, trained only on eligible data, are compared with unmodified and general models on frozen cases. Each proposal must decode into an action we can check, calculate, and explain. A fluent answer alone does not establish feasibility.
See the product exampleEach part of the system has a specific job.
Documents, accounts, and timestamps become structured financial facts with provenance and material gaps.
Every combination of typed actions is covered by the same exact model: how many plans are feasible, which is cheapest, and what working plans share, under each stress scenario.
Independent tools calculate cash outcomes and check evidence, permissions, obligations, and hard constraints.
A decision brief preserves alternatives and uncertainty for human review. Accepted cases can improve training.
Exact decision search
A liquidity decision is a chain in time. Between two weeks, all that matters is the closing cash and which decisions are still open. That makes the whole plan space a one-dimensional tensor network: one tensor per week, joined by a bond that carries this state.
Contracting the chain with ordinary arithmetic counts every plan that never breaches a reserve. Contracting the same network in min-plus arithmetic returns the cheapest plan. Other element types give the number of optimal plans, the full cost spectrum, and the share of working plans that use each option.
This is dynamic programming in tensor-network language, and we say so plainly. The language earns its place three ways: one model answers many questions, each with its own contraction; its bond dimension measures how much state this exact method has to carry, which is what makes an instance expensive for it; and the same instance exports to the QUBO and Ising formats that annealers and gate-model samplers accept.
| Question | Arithmetic used in the contraction |
|---|---|
| How many plans work? | ordinary: add, multiply |
| Which plan is cheapest? | tropical: minimum, add |
| How many plans are optimal? | tropical with multiplicities |
| How is cost distributed? | polynomials in the cost |
| What do working plans share? | recounts with one option fixed |
Method lineage: Liu, Wang & Zhang, PRL 2021 · Liu et al., SIAM J. Sci. Comput. 2023 · Crosswhite & Bacon, PRA 2008 · Markov & Shi, SIAM J. Comput. 2008
Measured on one laptop · 22 September 2026 · synthetic instances
On 20 instances, the largest with 544 million possible plans, the contraction's optimum equals an independent MILP solver (HiGHS), and a separate replay confirms feasibility and cost. HiGHS was faster on 16 of them: a median of 3.8 milliseconds against 88 for the contraction.
The median number of states the contraction carries between weeks rose from 10 for one company to 330, 30,186 and 338,803 as two, three and four entities were coupled through transfers and a shared credit line. Its median time to the optimum rose from 0.09 milliseconds to 14.6 seconds; the HiGHS median stayed under 10 milliseconds. Fees paid in cash create many distinct cash states. These are properties of this method and these instances, not a limit for every exact solver.
Simulated annealing in software, on the standard slack-variable QUBO, found the optimum on 1 of 10 instances and a feasible plan on 4; a simple greedy repair rule found the optimum on 8. With a median of 126 binary variables and coefficients spanning almost twelve orders of magnitude, the encoding is the first obstacle, before any hardware question. Penalty weights were left at their defaults.
HiGHS reached every optimum in at most 20 milliseconds. What this contraction adds is exact counts, shares and the cost spectrum, at a price that rises steeply with coupling. Counting and sampling are where hard instances and new hardware become interesting.
Single run on an Apple-silicon laptop in Python, on synthetic instances generated from fixed seeds, with every fee paid in cash. No quantum hardware was used. No advantage over classical methods is claimed.
Qelly Bench v0 · research preview
Each instance ships as JSON with its exact optimum, the number of feasible and optimal plans, its bond dimensions, and ready-made exports: QUBO in the unbalanced-penalty encoding and, up to 400 variables, the slack-variable encoding; Ising; and an LP file that MILP and CQM solvers read directly. A single-file checker replays any plan, whether it came from an annealer, a gate-model sampler, a quantum-inspired method or a classical solver, and emits a hash-linked certificate.
The quantum-optimization literature itself names finance as a domain that lacks benchmarks with ground truth. Our instances are synthetic today. With design partners they will be derived from real decisions, with permission and without identifying data.
In all seven generated cases, every feasible plan defers the investment; the homepage case has feasible order-placing plans. These are test cases for solver development, not a representative sample of business decisions.
Provided for research and benchmarking. License terms are being finalized; contact us before redistributing the bundle or building a product on it. Bundle use terms
Send us a certificateHardware teams and algorithm groups: run the suite on an annealer, a gate-model device or your own solver, and send the certificates. We will publish verified results with your permission.
Bounded judgments about evidence
We are evaluating a class of fast models that return typed judgments: a yes-or-no probability, one choice among stated options, or a position on a rubric. They never return free text. One call asks many small questions about a customer message: does it concern this invoice, is a payment date stated, is payment conditional, does it contain instructions aimed at the system?
In our prototype, code extracts candidate dates and performs all date arithmetic. A judgment can only draft a proposed change to one fact. A payment that depends on an event, or a date stated ambiguously, stays unconfirmed, and a person reviews every draft before the exact search reruns.
Development tests so far use 36 original synthetic messages in English, Spanish and Japanese. Independent annotation comes before any accuracy claim.
Pilot · no accuracy claimOne product, an independent research program
Qelly launches through familiar assistant interfaces. Specialized models can later improve selected Qelly tools without asking customers to change how they work.
Our training pipeline excludes host-platform requests and generated answers by default. Research material follows a separate provenance and rights process: original verified cases, eligible public data, independently collected permissioned records, and expert annotations.
A reviewer's approval is feedback, not proof of correctness. Real outcomes inform the record, but do not reveal the outcomes of alternatives that were never taken.
Deployment requires better quality on defined workflows, or comparable quality at materially lower cost, with reliable constraints and uncertainty handling. Quantum and quantum-inspired solvers are measured on the same verified instances; they are not a prerequisite for launch.
Training program
Begin with the unmodified model using the same tools and evidence. Then change the training objective only when the data and evaluation support it.
LoRA adapters on a quantized Qwen base learn verified demonstrations: request information, call a tool, compare feasible actions, and produce a supported conclusion. User content and tool observations are context, not fabricated output targets.
GRPO will compare fresh trajectories through a controlled financial environment. Independent checks score numerical correctness, material gaps, constraint satisfaction, and decision usefulness.
DPO is reserved for trustworthy preferred/rejected examples, such as explaining a covenant condition clearly. An unverified model score is insufficient to establish the preferred answer.
What would count as progress
We evaluate whole workflows, with the same available evidence, tools, and inference budget. General models and unmodified Qwen remain active comparisons.
| Question | Evidence we require |
|---|---|
| Are the numbers right? | Executable calculations with checked amounts, units, and dates. |
| Is the recommendation feasible? | Hard constraints hold. Unconfirmed financing or consent stays conditional. |
| Did it ask what matters? | Material missing facts are identified; irrelevant questions do not earn credit. |
| Does it generalize? | Business, source-document, period, and scenario-family holdouts; related examples stay together. |
| Is the search exact? | Agreement with exhaustive enumeration on small instances and with an independent MILP solver on larger ones. |
| Can anyone check it? | Inputs, plan and replayed cash path are published with a fingerprint. |
| Did training help? | Base, prompted, and trained models compared on frozen cases, with cost and latency recorded. |
Research record
Exact search and its benchmark are measured and reproducible from seeds. Model training is a bounded local pilot. Customer performance and quantum advantage have not been established. Results belong here only after the run, split, and evaluation can be traced.
Bounded judgments with independent annotation. Baseline → supervised adapter → frozen holdout, with independent numerical checks alongside qualitative review.
Permissioned inputs and adviser-reviewed conclusions with real operating feedback; certificates from annealing, gate-model and quantum-inspired solvers on the shared suite.
Preprints
Sole-author work by Qelly's founder, Luis Lozano, posted on arXiv and not yet peer-reviewed. The first is one reason this site claims no quantum advantage; the benchmark above is how we intend to find out when that changes.
An audit of D-Wave's hybrid solver on portfolio problems. It matches the proven optimum, yet quantum-processor access is under 1% of its time budget, and a classical tabu search with the same budget reaches the same objectives. It proposes what hybrid results should report so that service time is not mistaken for quantum contribution.
A validation protocol for using a quantum annealer as a sampler, tested on two D-Wave processor generations: it checks whether readouts have forgotten their starting state and whether they match a calibrated reference, and shows how a readout can pass the first test while landing in the wrong state.
Our research builds on published tensor-network and optimization methods, established training methods, and independently checkable financial tasks.
For researchers, partners, and investors
We can't find the internet
Attempting to reconnect
Something went wrong!
Attempting to reconnect