Not at all! What you're describing is whether there are problems with classical solutions that have also been solved via quantum computers in practice.
It depends how exactly you define a quantum computer, but for a long time D-Wave was making a number of splashy claims about how it had some large amount of entangled qubits in its "adiabatic quantum computer" and was using it to perform quantum annealing to solve various optimization problems. (Confusingly, despite the name, quantum annealing is a classical algorithm.) As part of the showcase, this system was used to solve a sudoku puzzle among other things.
There is no clear evidence that D-Wave's devices qualify as quantum computers (and if so, certainly not general-purpose ones capable of implementing Shor's algorithm), and that they achieved meaningful quantum speedup. But, they certainly did sell a handful of these devices for millions of dollars.
The general challenge with a "real" (more precisely: universal) quantum computer is that in order to get any useful computation out of them, you need a fair amount of entangled particles with high coherence times, and a fair amount of gates with high fidelity.
The wording of your question suggests that you're aware of the various implementations of Shor's algorithm and how the circuitry was designed with the answer in mind. So instead let me point you at https://en.wikipedia.org/wiki/HHL_algorithm which solves a certain family of systems of linear equations, which we can verify using classical algorithms like Gaussian elimination or LU factorization.
Not at all! What you're describing is whether there are problems with classical solutions that have also been solved via quantum computers in practice.
It depends how exactly you define a quantum computer, but for a long time D-Wave was making a number of splashy claims about how it had some large amount of entangled qubits in its "adiabatic quantum computer" and was using it to perform quantum annealing to solve various optimization problems. (Confusingly, despite the name, quantum annealing is a classical algorithm.) As part of the showcase, this system was used to solve a sudoku puzzle among other things.
There is no clear evidence that D-Wave's devices qualify as quantum computers (and if so, certainly not general-purpose ones capable of implementing Shor's algorithm), and that they achieved meaningful quantum speedup. But, they certainly did sell a handful of these devices for millions of dollars.
The general challenge with a "real" (more precisely: universal) quantum computer is that in order to get any useful computation out of them, you need a fair amount of entangled particles with high coherence times, and a fair amount of gates with high fidelity.
The wording of your question suggests that you're aware of the various implementations of Shor's algorithm and how the circuitry was designed with the answer in mind. So instead let me point you at https://en.wikipedia.org/wiki/HHL_algorithm which solves a certain family of systems of linear equations, which we can verify using classical algorithms like Gaussian elimination or LU factorization.