Project summary

The Causal Recovery Gap, or CRA, project started with a simple question.

Instead of understanding information loss and recoverability in quantum systems mainly through assumptions, could we analyse the mathematical information already available and obtain a clearer scientific result?

The aim is not to claim that every piece of lost information can always be recovered. The aim is to understand what the available data can really tell us, what still depends on assumptions, and how much uncertainty remains.

At first, I looked at two different situations separately.

The first was recovery using an unrestricted global operation. The second was recovery under local restrictions, where separate subsystems cannot be controlled as one complete system.

I wanted to understand how close each situation could bring us to the desired result. After that, I began looking at whether the information obtained from these two situations could be connected in a meaningful way.

The difference between them is represented in CRA as a Recovery Gap.

The basic idea is that a quantum state may appear recoverable when a global operation is allowed, but the same recovery may become weaker or impossible when the available operations are limited to separate local subsystems.

This difference may provide useful information about the physical and mathematical limits of recovery.

Another important part of CRA is the subsystems.

This difference may provide useful information about the physical and mathematical limits of recovery distinction between different kinds of results.

In quantum software, a number may come from an exact mathematical identity, a rigorous bound, a theorem, a numerical optimisation process, or a particular simulation model.

These results do not have the same scientific meaning.

For this reason, CRA is being developed so that mathematical certificates, upper bounds, numerical estimates, and simulation-dependent results are clearly separated.

A numerical estimate should not be presented as proof. A simulation result should also not automatically be presented as hardware validation.

The project currently consists of two Python packages.

CRA Core contains the main mathematical and analytical functions.

CRA-Qiskit connects the CRA analysis to Qiskit workflows.

The current v0.3.0 releases pass 81 tests in total.

CRA Core passes 48 tests.

CRA-Qiskit passes 33 tests.

Both packages have also been built as wheel and source distributions. Clean-install checks have been completed. Release manifests and SHA-256 integrity records have also been prepared.

During development, I tested the mathematical and numerical behaviour using different sets of states and different system structures.

The purpose was to see whether the results remained consistent when the rank, subsystem order, environment structure, and state conditions changed.

The completed work includes mixed-state tests, ordered subsystem operations, environment-aware local-recovery calculations, environment-aware causal-distance calculations, and an end-to-end rank-four mixed-environment test for the current theorem model.

The project is therefore no longer only an idea. It already has working software, tests, packages, release records, and research documents.

The repositories remain private while intellectual-property and licensing questions are reviewed.

This proposal does not require every private component to be published.

The funding would support a separate public-benefit part of the project. This would include independent scientific review, clear scope documentation, reproducible examples, a registered benchmark, and non-confidential verification materials.

What are this project's goals? How will you achieve them?

The first goal is to obtain an independent technical review.

The current CRA model has been developed and tested in a documented single-step setting.

Before extending it to more general composed quantum channels, I need to understand whether the present mathematical structure remains valid.

The main question concerns the relationship between a single joint Stinespring dilation and sequential dilations that use fresh environments.

The review should examine the following questions:

Under what conditions can the joint and sequential models be considered equivalent?

Which CRA quantities remain unchanged when different dilation representations describe the same reduced quantum channel?

Can the current result be extended only under restricted assumptions?

Is there a counterexample showing that a general extension would be incorrect?

The purpose of the review is not to obtain an endorsement.

A negative result, a restricted theorem, or a counterexample would also be useful. It would show the correct scientific boundary and prevent unsupported claims from being added to the software.

The second goal is to complete a clear scope and limitations document.

This document will explain where the current theorem applies, which systems may be controlled, which environment remains untouched, which results are mathematically certified, which results are only numerical estimates, and which conclusions cannot yet be made.

The third goal is to complete and freeze a preregistered CRA and zero-noise extrapolation benchmark.

The benchmark will test whether there is a meaningful relationship between the CRA Recovery Gap and the residual error remaining after zero-noise extrapolation.

The aim is not to claim in advance that CRA is better than zero-noise extrapolation.

The aim is also not to claim that CRA can certify the failure of an error-mitigation method.

The purpose is to test whether the two measurements contain a meaningful relationship.

Before the results are examined, the following elements will be fixed:

The circuit families.

The random seeds.

The noise models and noise strengths.

The observables.

The exclusion rules.

The statistical procedures.

The robustness checks.

The rules for reporting negative or null findings.

The fourth goal is to produce an open reproducibility package.

The public package may include non-confidential example circuits, registered noise definitions, benchmark metadata, analysis scripts, result formats, verification instructions, and a public technical report.

Private source code, proprietary optimiser designs, unpublished proofs, and licensing-sensitive components will remain outside the public package.

The fifth goal is to make a clear decision about a possible CRA v0.4 release.

At the end of the project, one of the following decisions will be made:

Proceed with broader channel integration.

Proceed only under clearly stated restrictions.

Postpone the integration until more theory is available.

Stop the proposed generalisation because the evidence does not support it.

A decision not to continue with a proposed extension would still be a useful scientific result.

Work plan

The project is planned for six months.

During the first two months, I will organise the independent technical review, examine the relevant scientific literature, clarify the review questions, and revise the current theorem-scope document.

During the third month, I will freeze the benchmark design.

This will include the circuit-generation rules, random seeds, noise definitions, observables, exclusion rules, statistical procedures, and reporting rules.

The analysis code will first be tested using synthetic data. This will be done before the actual benchmark results are inspected.

During months four and five, I will implement and run the reproducible benchmark pipeline.

I will record errors, exclusions, failed runs, limitations, and deviations from the original plan.

Negative or null findings will be reported. The original question will not be changed after seeing the results in order to make the project appear successful.

During the sixth month, I will prepare the final technical report, the non-confidential reproducibility package, the reviewed scope document, and the decision record for a possible v0.4 release.

How will this funding be used?

The minimum funding required is USD 5,000.

At the minimum level, the funding will be used in the following way:

USD 2,000 for an independent review by a specialist in quantum information theory, quantum channels, Stinespring dilation, or open quantum systems.

USD 1,600 for implementation, testing, documentation, and preparation of the reproducibility package.

USD 700 for computing, storage, testing, and software infrastructure.

USD 500 for licensing, accounting, and grant-compliance advice.

USD 200 for transfer and administrative expenses.

The maximum funding target is USD 12,000.

Funding above the minimum would allow a more complete six-month implementation.

It would support broader benchmark coverage, more computing capacity, additional reproducibility tests, independent quality checking, better public documentation, and maintenance of the public verification materials after the first release.

No expense will be funded twice.

If another pending application is approved, I will disclose the award and revise the Manifund scope and budget before accepting overlapping funds.

Who is on your team? What is your track record on similar projects?

The project is currently led and implemented by me, Ali Özdemir, an independent developer based in Türkiye.

I have been involved in CRA's practical development from its early stages.

My work has included implementation, testing, packaging, clean-install verification, release management, documentation, GitHub operations, and the practical organisation of the development process.

The existing project evidence includes CRA Core v0.3.0 with 48 passing tests and CRA-Qiskit v0.3.0 with 33 passing tests.

There are 81 passing tests in total.

The packages have verified wheel and source distributions.

Clean-install verification has been completed.

Release manifests and SHA-256 integrity records have been prepared.

The project also includes mixed-state consistency tests, ordered subsystem operations, environment-aware local-recovery analysis, environment-aware causal-distance analysis, and an end-to-end rank-four mixed-environment theorem test.

Three research documents have also been prepared.

These are a theorem-scope and limitations document, a joint-versus-sequential dilation review brief, and a CRA-ZNE benchmark preregistration draft.

Selected technical documents, release artifacts, and relevant commit references can be shared confidentially with qualified reviewers.

What are the most likely causes and outcomes if this project fails?

The main scientific risk is that CRA may not generalise cleanly from the current single-step model to composed quantum channels.

The independent review may find that the relationship between joint and sequential dilations only holds under narrow conditions.

It may also identify a counterexample showing that a broader generalisation is not valid.

This would limit future development, but it would also provide a useful scientific result.

It would show where the current method ends and prevent unsupported claims from being built into a future release.

Another risk is that the benchmark may show no meaningful relationship between the CRA Recovery Gap and the residual error after zero-noise extrapolation.

Such a result would be reported as a null result.

It would not be rewritten or presented as a success.

Other risks include difficulty finding a suitable independent reviewer, delays in licensing decisions, limited computing resources, and delays during benchmark implementation.

These risks will be reduced by keeping the scientific question narrow, separating public outputs from private intellectual property, fixing the benchmark rules before the results are inspected, and preparing both minimum and expanded versions of the work plan.

Even if the proposed generalisation fails, the project can still produce useful public outputs.

These outputs would include a reviewed scope and limitations document, a reproducible benchmark protocol, non-confidential verification materials, and a clear record of which conclusions are and are not supported.

How much money have you raised in the last 12 months, and from where?

No grant funding has been received by the project to date.

A USD 4,000 microgrant application is pending with the Unitary Foundation.

A separate USD 15,000 application for a six-month CRA scientific validation and reproducibility program is pending with Emergent Ventures.

No award decision or payment has been received from either program.

Any future award will be disclosed.

The Manifund budget and work plan will be revised where necessary to prevent duplicate funding.