Quantum computing applications

You question is very wide, however, I can give you some examples:

• optimization tasks (mainly binary programming ones such as travelling salesman problem)
• Monte Carlo simulation in finance (credit risk analysis, pricing finacial instruments)
• portfolio optimization
• any problems dealing with solving systems of linear equations

However, bear in mind that these applications are currently only toy-models because of constraints imposed by imperfection of quantum hardware (shor decoherence times, sussceptibility to noise, lack of 1000+ qubits processors etc.)