Quantum computing is showing significant promise, and research is beginning to move from the earliest stages to a deeper understanding of what works best commercially and why.
On paper, quantum computing algorithms are potentially revolutionary. They suggest a way to solve some problems more quickly and more accurately than conventional computers ever could. But out in the real world of practical systems, creating and preserving a superposition of quantum states is a constant struggle against entropy, where the uncertainties of our macroscopic world need to be restrained from asserting themselves.
One of the biggest challenges for quantum computers is error correction, which protects calculations from degradation due to noise. The most promising approach to quantum error correction requires multiple copies of the data, with hundreds or even thousands of physical qubits for each logical qubit. Even crude quantum computers are thus likely to require millions of physical qubits.
First the good news: quantum simulators, hybrid mode of operation with the quantum computer as a coprocessor, and quantum-inspired algorithms will enable the quantum approach to computation to advance much more rapidly than pure quantum hardware and pure quantum algorithms are currently advancing. The bad news is that quantum computers are advancing at too slow a pace and strictly quantum algorithms are extremely daunting, especially in the face of very limited hardware.
This informal paper will focus mostly on algorithms rather than hardware, but without the needed hardware, strictly quantum algorithms are at risk of being left high and dry — if not for simulators and quantum-inspired algorithms running on classical computers which continue to advance at a brisk pace.