Testing physics with small quantum computers

This colloquium will be given by Ben Reichardt of the University of Southern California.

Reliable qubits are difficult to engineer. What can we do with just a few of them? Here are some ideas:

1. Dimension test. An n-qubit system should have 2^n dimensions, but systems with just polynomial(n) dimensions can look like they have n qubits. Is nature really exponential? We give a test for verifying that your system has 2^n dimensions.

2. Entanglement and nonlocality tests. A Bell-inequality violation establishes that your systems share some entanglement. We give a test to show that your systems share lots of entanglement. Additionally, we give a test to eliminate non-signaling correlations (like the Popescu-Rohrlich nonlocal box), giving a way to check whether multi-party entanglement breaks down.

3. Error test. Error correction will be needed for scalable quantum computers. But high qubit overhead makes it impractical for small devices. We show that a seven-qubit computer can fault tolerantly correct errors on one encoded qubit, and that a 17-qubit computer can protect and compute fault tolerantly on seven encoded qubits.