Reliable qubits are difficult to engineer. What can we do with just a few of them? Here are some ideas:
U. Southern California
1. Memory/dimensionality test. An n-qubit system has 2^n dimensions---a big reason for quantum computers' exponential power! But systems with just polynomial(n) dimensions can look like they have n qubits. We give a test for verifying that your system really has 2^n dimensions.
2. Entanglement test. A Bell-inequality violation establishes that your systems share some entanglement (i.e., there's no classical explanation). We give a test to show that your systems share lots of entanglement.
3. Extended Einstein-Podolsky-Rosen (EPR) test. Classical hidden variables can't explain a Bell inequality violation, but another non-quantum theory could explain it: non-signaling correlations like the Popescu-Rohrlich nonlocal box. We give a test, using three spacelike-separated devices, to eliminate non-signaling explanations.
4. Error correction test. Error correction will be needed for scalable quantum computers. But high qubit overhead makes it impractical for small devices. We show that a 7-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.