millennium problems in electronics

Electronic materials

Can a stable material carry current without electrical resistance at room temperature and ordinary atmospheric pressure?

Superconductivity is well established at low temperatures, and extreme pressure has opened new routes to higher transition temperatures. A reproducible material that superconducts at everyday conditions remains elusive. Finding one requires understanding which electronic interactions and crystal structures can sustain that state.

Such a discovery could reshape interconnects, power equipment, and magnetic devices. The first question is whether the material can exist. Making it useful would also require adequate current capacity, tolerance of magnetic fields, and a practical way to manufacture it.

Superconducting electronics

What microscopic processes produce the persistent low-frequency magnetic noise in superconducting circuits?

This noise, often called 1/f flux noise, limits sensitive magnetic detectors and disrupts superconducting qubits. Surface spins are a leading explanation, but a complete account of their identity, interactions, and dynamics is still missing.

The challenge is a theory that predicts how the noise changes with materials, surface treatment, temperature, and device geometry. Connecting those predictions to measurements would give engineers a firmer basis for making quieter circuits.

Communications and information theory

How much information can two transmitters send reliably when each interferes with the other’s receiver?

Even the standard two-user Gaussian interference channel has no complete, exact capacity region: the set of rates both links can sustain at once. Some regimes are solved, and powerful approximations exist. The general answer across signal strengths, interference levels, and power limits remains open.

Resolving it means finding transmission strategies that reach the limit and proving that higher rates are impossible. It would settle a basic question behind shared radio spectrum and interference between electronic links.

Control theory

How should two controllers cooperate when they see different information and an action also serves as a signal?

Witsenhausen’s counterexample, introduced in 1968, captures this difficulty in a two-stage system. The first controller observes a state and changes it; the second sees a noisy version and acts again. Nonlinear strategies can outperform every linear strategy, yet the exact optimum across all parameter choices remains unresolved.

The open problem is to determine the best strategies and prove their optimality. It exposes a fundamental obstacle in decentralized control: choosing an action requires considering both its physical effect and what another controller can learn from it.

Quantum information and hardware

How much quantum information can survive a channel that randomly applies each of the three basic qubit errors with equal probability?

This is the quantum capacity problem for the qubit depolarizing channel, a standard model of quantum noise. Its exact capacity remains unknown in general, even when noise acts independently on each use. Encoding across many qubits can beat strategies that appear optimal when considered one use at a time.

The question is the highest rate of reliable quantum transmission without a separate assisting channel or preshared entanglement. An exact answer would establish what error correction can ultimately preserve under this model, and where recovery becomes impossible.