Project Summary

This project will expand the capabilities of the open source Python library toqito for quantum state distinguishability, antidistinguishability, and classification. The core aim is to provide a unified, well-tested set of numerical tools that take ensembles of quantum states or channels as input and return optimal distinguishability or exclusion performance under a range of measurement constraints.

Building on toqito’s existing support for entanglement theory and nonlocal games, this project will deliver a consolidated module for quantum state and channel discrimination and exclusion (including figures of merit such as minimum-error and unambiguous discrimination), improved separability and symmetric-extension tools, and user-friendly documentation and examples. The result will be a “one-stop” numerical toolkit that researchers and students can use to study state distinguishability, antidistinguishability, and related classification problems in a reproducible, extensible way.

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

Goals

1. Unify quantum state distinguishability and exclusion in a single interface.  

   Provide a general module that accepts an ensemble of quantum states (or channels) together with a chosen figure of merit and returns optimal distinguishability or exclusion values, along with corresponding measurements when feasible.

2. Support multiple classes of measurements and figures of merit.  

   Handle global (positive), PPT, and separable measurement operators within a common API, and support at least the minimum-error and unambiguous distinguishability / exclusion paradigms, with room to extend to other figures of merit.

3. Strengthen separability and symmetric-extension tooling.  

   Improve and generalize separability tests and the symmetric extension hierarchy so that separable-measurement distinguishability becomes practical for a wider range of instances, including beyond strictly bipartite settings.

4. Extend to sequences and channels. 

   Add support for optimal discrimination and exclusion of quantum sequences and channels, including settings motivated by “quantum majority vote”, modality testing, and quantum cryptographic applications.

5. Provide robust documentation, tests, and examples.  

   Ensure that all new functionality is covered by tests, benchmarked on representative problems from the literature, and documented with examples that are accessible to both researchers and advanced students.

Plan to achieve these goals

Design and implementation.  

  - Define a core data model for “ensembles” of states, sequences, and channels, together with associated priors or weights.  

  - Implement a unified entry point (for example, a distinguish / exclude style interface) that dispatches to appropriate semidefinite programs or analytic criteria depending on the chosen figure of merit and measurement constraints.  

SDP-based optimization back end.

  - Extend existing toqito routines for state distinguishability and exclusion to support a broader range of measurement families and problem variants.  

  - Integrate with standard Python SDP/convex-optimization libraries and benchmark different back ends to identify sensible defaults and document trade-offs.

Separability and symmetric extensions.  

  - Refactor and extend the is_separable and symmetric extension hierarchy implementations to improve clarity, generality, and performance.  

  - Replace hard-coded assumptions about system structure with dynamic handling of multipartite settings, enabling use beyond strictly bipartite scenarios.  

  - Identify bottlenecks and introduce vectorization, symmetry reductions, or other improvements where they offer concrete gains.

Sequences, channels, and generalizations.

  - Implement tools for discrimination and exclusion of quantum sequences and channels, based on ongoing and recent research that I am directly involved in.  

  - Add support for generalized “m-out-of-n” distinguishability and exclusion tasks, once the underlying optimization problems are fully specified in ongoing work.

Testing and documentation. 

  - Add comprehensive unit and integration tests, including regression tests derived from published examples.  

  - Create worked examples and short “recipes” to show typical usage patterns, for example: checking antidistinguishability from inner products, comparing PPT vs separable measurements, or exploring quantum sequence discrimination.  

How will this funding be used?

I am requesting **9,600 USD** to support approximately two months of focused part-time development and maintenance work on toqito related to quantum state and channel distinguishability, antidistinguishability, and classification.

The funds will be used roughly as follows:

Core development and research time (about 70%) 

  - Designing and implementing the unified distinguishability/exclusion module for states, sequences, and channels.  

  - Enhancing and refactoring separability checks and the symmetric extension hierarchy for clarity, performance, and generality.  

  - Implementing additional analytic antidistinguishability and exclusion criteria (for example, inner-product-based checks) as fast pre-filters for large instances.

Testing, benchmarking, and documentation (about 20%)

  - Writing unit and integration tests, including regression tests against known results from the literature.  

  - Benchmarking different SDP back ends and profiling the symmetric extension hierarchy to identify and mitigate bottlenecks.  

  - Producing user-facing documentation, worked examples, and short tutorial-style guides.

Infrastructure and community support (about 10%)

  - Maintaining CI, dependency management, and release automation to ensure the new features are robust and easy to install.  

  - Reviewing community pull requests related to distinguishability, exclusion, and classification and integrating them into the expanded module.

All work will be carried out using existing compute resources and standard open source tooling; there is no hardware budget in this request.

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

Team

- Vincent Russo — project lead and primary developer.  

  I will be responsible for the design, implementation, testing, and documentation of the new functionality.  

Community contributors and collaborators.  

  toqito already has over 50 unique contributors and an active user base. As with previous development cycles, I will collaborate with existing coauthors and contributors working on quantum state discrimination, antidistinguishability, and related problems. I expect some examples and documentation to be co-developed with students or collaborators, coordinated through GitHub.

Track record

- I am a quantum computing researcher and engineer with a PhD in computer science and 15+ years of experience building numerical tools and infrastructure for quantum information, quantum error mitigation, resource estimation, and post-quantum cryptography.  

- I am the **founder and lead maintainer of toqito**, which provides numerical tools for quantum states, channels, measurements, entanglement theory, and nonlocal games. The project has:  

  - 50+ unique contributors, 200+ GitHub stars, and 100+ forks.  

  - A peer-reviewed paper in the Journal of Open Source Software.  

  - Use in 10+ published research articles.  

  - Recognition as one of the top quantum software packages by QuantumInsider.  

- toqito has been repeatedly recognized and supported by the community:  

  - **First place** in the KaiCode open source contest, selected as the top project among 400+ submissions.  

  - **NumFOCUS affiliation**, reflecting its status as a mature, community-relevant scientific computing project.  

  - **Three microgrants** from the Unitary Fund that supported earlier rounds of development.  

  - Participation in **unitaryHACK** (2022, 2023, 2024, 2025), which has brought new contributors, features, and testing of the codebase.  

  - Participation in **Google Summer of Code 2025**, with a student project dedicated to enhancing toqito.

- Beyond toqito, I have led or contributed to several open source quantum software efforts:  

  - *mitiq** — co-developed new quantum error mitigation techniques (layerwise Richardson extrapolation) and implemented them as production-ready features, accompanied by large-scale experimental studies on multiple hardware platforms.  

  - *metriq-gym** — created a Python library that unifies execution of quantum benchmarks across heterogeneous hardware platforms and SDKs, enabling reproducible community benchmark submissions.  

This combination of domain expertise, open source experience, and existing infrastructure makes me well-positioned to deliver the proposed functionality reliably and on time.

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

Likely failure modes

1. **Technical difficulty of high-level SDPs and hierarchies.**  

   Some planned optimizations, especially around symmetric extension hierarchies and separable-measurement distinguishability, may be more challenging or resource-intensive than anticipated for very large instances or high hierarchy levels.

   - **Outcome:** The core unified interface and basic functionality are delivered and stable, but some advanced options (for example, very high hierarchy levels, very large ensembles, or highly constrained multipartite settings) remain slower or more memory-intensive than ideal. These limitations would be clearly documented.

2. **Scope creep from new ideas and variants.**  

   As the project progresses, it is likely that additional interesting problem variants will emerge (new figures of merit, cryptographic applications, generalized classification tasks).

   - **Outcome:** To protect the schedule, some of the most ambitious extensions—such as full-fledged channel exclusion in very general settings or sophisticated m-out-of-n generalizations—might be postponed to subsequent releases. The funded work would still deliver a coherent and useful subset that can be built upon later.

3. **Dependence on external optimization libraries.**  

   The performance and usability of the new features depend on third-party SDP/convex-optimization libraries and their solver back ends.

   - **Outcome:** Certain features may be tied to specific solvers or require users to install an optional dependency to get the best performance. Where necessary, fallback paths and clear installation instructions will be provided, and trade-offs documented.

In all cases, the failure modes are **partial rather than catastrophic**. The project is structured so that each month produces self-contained, releasable improvements. Even if some of the most advanced performance goals or generalizations are deferred, the community will still gain a significantly improved and unified toolkit for quantum state distinguishability, antidistinguishability, and classification.

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

In the last 12 months I have received modest but meaningful support related to toqito and closely aligned open source quantum information work. You can adapt the numbers below to your actual amounts:

- **Unitary Fund microgrant** supporting infrastructure and feature development in toqito.  

  - Amount: **8K USD**.  

- **KaiCode open source contest prize**, where toqito was awarded first place among 400+ projects.  

  - Amount: **5K USD**.  

- **Google Summer of Code 2025** support for a student project dedicated to toqito.  

  - Amount to the student: **7K USD** (paid directly to the student but resulting in direct improvements to toqito).  

Taken together, these sources represent **20K USD** of direct or closely targeted support over the last 12 months, in addition to significant in-kind contributions from toqito’s community of over 50 contributors through repeated participation in unitaryHACK and other events.