Hilbert Space
The mathematical framework used in quantum mechanics to describe quantum states. The state of an n-qubit system resides in a 2^n-dimensional complex vector space, with dimensionality growing exponentially with the number of qubits.
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The Hilbert space of quantum many-body problems grows exponentially with the number of particles, and once it exceeds the capability range of exact methods, reference solutions need to be generated with approximate means (such as the density matrix renormalization group DMRG, variational Monte Carlo).
The wave function of N particles lives in a 3N-dimensional Hilbert space; this abstract mathematical space can have infinite dimensions, but it is a purely mathematical tool and not a physical space.
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The Hilbert space of quantum many-body problems grows exponentially with the number of particles, and once it exceeds the capability range of exact methods, reference solutions need to be generated with approximate means (such as the density matrix renormalization group DMRG, variational Monte Carlo).
50%UnverifiedThe wave function of N particles lives in a 3N-dimensional Hilbert space; this abstract mathematical space can have infinite dimensions, but it is a purely mathematical tool and not a physical space.
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