Open Problems: Find a Question by Method
An open problem becomes a research project only after its statement, assumptions, available method, and success criterion are precise enough to guide work. This finder organizes questions by the kind of contribution needed. The linked topic assessments own the scientific evidence and the status of particular problems.
Choose the kind of work you can contribute
Section titled “Choose the kind of work you can contribute”| Your intended contribution | Problem guide | What the proposal must specify |
|---|---|---|
| Clarify an inference about quantum theory | Foundational questions | Operational predictions and the additional premises being tested |
| Prove a theorem or find a counterexample | Mathematical questions | Exact quantifiers, hypotheses, and the restricted class to attack |
| Distinguish physical mechanisms with data | Experimental questions | Signal, controls, nuisance models, and attainable sensitivity |
| Extend a reliable calculation | Computational questions | Observable, baseline, convergence, and computational resources |
| Integrate components into a delivered capability | Engineering questions | Interface contracts, latency, yield, and complete task metrics |
| Transfer a method across disciplines | Cross-disciplinary questions | Both fields’ baselines, terminology, and standards of evidence |
Several methods can address the same physical question. A failure to distinguish two phases may call for a better experiment, a new observable, a rigorous obstruction, or a more reliable calculation. Choose the contribution that can remove a specific uncertainty with your resources.
Separate a grand problem from a first project
Section titled “Separate a grand problem from a first project”“Understand high-temperature superconductivity” identifies a major scientific ambition. A first project might compare two candidate mechanisms against a specific response function in a controlled model. “Build a quantum internet” becomes a measurable question about entanglement rate, memory lifetime, loss, or protocol verification. The large ambition supplies motivation; the smaller question supplies a test.
The direction-selection guide asks for a baseline reproduction and a bounded deliverable. A project can produce a useful negative result, such as a counterexample, an identified noise floor, or a demonstration that available finite sizes cannot discriminate two hypotheses.
Check that the gap is real and still relevant
Section titled “Check that the gap is real and still relevant”Read an authoritative review to learn the formulation, then the closest primary result and later work that addresses its limitation. Search alternative terminology and ask a specialist. An old statement that a question is open does not prove it remains open. Conversely, a new theorem may settle a special case while leaving the physically relevant regime untouched.
Record the exact gap you intend to address. If a paper claims to solve it, compare assumptions, error guarantees, input models, and limits before abandoning or continuing the project. Source monitoring gives a claim-centered workflow.
Design a decisive first check
Section titled “Design a decisive first check”For numerical work, return to Computational Quantum Mechanics and establish independent convergence. For device work, specify the trust model and comparator; Eisert et al. explain why verification is task-dependent. For proof work, seek the smallest nontrivial case and a counterexample to the most tempting overgeneralization.
The deliverable should let another researcher decide what to do next. A plot without an error budget, a theorem without its hypotheses, or a device metric without a denominator does not meet that standard. State what would change your mind before selecting the most favorable outcome.
References
Section titled “References”- J. Eisert et al., “Quantum certification and benchmarking,” Nature Reviews Physics 2, 382–390 (2020). DOI.
- C. P. Koch et al., “Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe,” EPJ Quantum Technology 9, 19 (2022). Preprint — an example of turning broad ambitions into theory and implementation questions.