Space complexity describes the amount of memory space required by a deterministic Turing machine to solve a given computational problem with a certain algorithm. If necessary, also use the [memory-space] tag.
Questions tagged [space-complexity]
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Can we use quantum machines to reduce space complexity of deterministic turing machines?
Can we convert every algorithm in $\text{P}$ (polynomial time complexity for deterministic machines) into a quantum algorithm with polynomial time and $O(\log n)$ quantum bit?
Mohsen Ghorbani
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Is there a polynomial quantum algorithm for graph coloring?
Is there a polynomial time and polynomial space quantum algorithm for finding a 4 colouring of any loopless planar graph?
Learner
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Expressing a quantum state as a polynomial
Let us consider the state $\left|\psi\right>$ obtained by applying $m$ 1- and 2-qubit gates to $n$ qubits, starting from the state $\left|0,0,\dots\right>$. Let us express it as:
$$ \left|\psi\right> = \sum_{b_1, b_2, \dots} f(b_1, b_2, \dots)…
Doriano Brogioli
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What is the cost of implementing the Quantum Fourier transform in a classical computer?
What is the cost of implementing the Quantum Fourier transform (QFT) in a classical computer? We know we require at least $\log{n}$ depth quantum circuits to do a QFT in a quantum computer, with $n$ being the number of input qubits. Is there a…
BlackHat18
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Why does entanglement complicate quantum simulation?
To model a single qubit one would need enough memory for $2$ complex numbers. If we have an $N$ qubit system, we would have to store $2N$ complex numbers.
The general statement is that to store an $N$-qubit system, one would require memory for $2^N$…
Ognyan Tsvetkov
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How many real numbers are required to describe density matrix for $n$ qubits?
(All of these coming from the topic of simulation of quantum systems) A density matrix $\rho$ Which describe state of $n$ qubits will have $2^{n} \times 2^{n}$ size. We have couple of conditions like
$\mathrm{tr}(\rho) = 1$
$\rho$ is…
user27286
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