What Problem Does A Variational Quantum Eigensolver Solve?
You don’t need to be a physicist to understand it
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The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm. It aims to find an upper bound of the lowest eigenvalue of a given Hamiltonian.
Don’t get scared, even if you’re not a physicist. This post provides a high-level overview. The Hamiltonian is a quantum operator that corresponds to the total energy of a physical system. It is the central part of Schrödinger’s equation.
Schrödinger’s equation says that the energy (𝐸) — a scalar value corresponds to 𝐻 — an operator. A quantum operator is a linear mapper that turns one quantum state vector into another one — it is a matrix.
So, of course, a scalar value is not a matrix. In fact, we’re not saying this. Because 𝐻̂ is an operator on Ψ, it doesn’t work without it. And, so, 𝐸 is the wave’s energy — it is a characteristic of the wave. It doesn’t mean anything without it. For that reason, we can’t cancel Ψ from the equation.
So, when 𝐸 and 𝐻̂ are not equal, how do they relate?
