Quantum Computation

Quantum Computation

How do quantum systems use quantum properties to compute?This question can be split into two parts:

• How are algorithms developed for the quantum computers available today?
• How do people create algorithms for future “fault tolerant” quantum systems that are still theoretical?

Many algorithms for near-term quantum hardware require you to find the “best” solution from among many possible solutions, such as finding the lowest energy state of a molecule among various possible molecular bond lengths. For each possible bond length, you represent parts of the energy on a quantum processor, and then measure the energy directly. Trying various solutions eventually leads to the bond length with to the lowest energy state, which represents the equilibrium molecular configuration. More information can be found here.

Algorithms for the kinds of quantum systems we hope to have in the future, called fault tolerant universal quantum computers, were among the first to be developed in the field. This includes some of the most well known examples: Shor’s factorization algorithm and Grover’s algorithm for unstructured search. While near-term algorithms involve relatively few qubits and operations, and errors can be compensated by running the algorithm many times to get an average value, fault-tolerant algorithms require extremely long gate sequences and high gate fidelities to perform well. The quantum hardware needed for fault-tolerant algorithms is still being developed; however, they demonstrate that certain quantum algorithms can outperform their classical counterparts, given the right quantum system.