Tests for small quantum devices

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

 

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.