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2

I guess a similar argument used in $\big[$ Marriot, Watrous $\big] $ [1] to prove QMA$_{log}$ $\subseteq$ BQP and in $\big[$ Fefferman, Lin $\big]$ [2] to prove QMA$_{exp}$ $\subseteq$ PSPACE does not carry over since for L $\in $ QMA$_{exp}$ = PreciseQMA you get $ x \in $ L $ \implies \text{tr}[Q_x] \geq c $ $ x \notin $ L $ \implies \text{tr}[Q_x] \...


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This is an interesting question. I was looking into optimize the number of samples needed in VQE as well. We know that that the number of samples in VQE to get accuracy error of $\epsilon$ scales as $O(1/\epsilon^2)$. To be more precise, if $$ H = \sum_{i=1}^N h_i P_i $$ where $P_i$ represent the pauli string then $$\langle H \rangle = \sum_{i=1}^N h_i \...


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Currently, I do not know of any quantum processor allowing to condition a quantum operation on results in a classical register. On IBM Q, it is possible to do so in simulator only. However, if you are dealing with quantum circuits like quantum teleportation or superdense coding, where you use such conditioning, you can simply use controlled quantum gates ...


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Let me consider this example: if we have $|01\rangle$ then the circuit should give us at the output $|11\rangle$. Here I will try to show why I think this is impossible (by assuming that we don't do any measurements). Let's assume that we have the desired gate and we want to apply it to this state $\frac{1}{\sqrt{3}}(|00\rangle +|01\rangle - |11\rangle)$: $$...


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The Grover search is applied to the randomness that's fed into Schoning's algorithm. The randomness could be a big list of random bits, or for simplicity just a seed for a PRNG. You're searching over the seeds for one that causes Schoning's algorithm to succeed. Given an oracle (Schoning's algorithm) which accepts $(3/4)^n$ of its possible inputs, you only ...


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I often wonder if the welded trees considered in the Childs, Cleve, Deotto, Farhi, Gutmann, Spielman [CCDFGS02] paper have any applicability to questions in (algorithmic) knot theory such as knot-identification or knot-canonization. For example, I envision labeling vertices of the welded tree with specific knot diagrams/grid diagrams, and labeling edges ...


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The code I'll be referencing here is Qiskit, IBM's Quantum SDK (Software Development Kit). First, you would have to make a circuit, so a good place to start is with the following code: import qiskit from qiskit import * qc = Quantum Circuit (n, m) where n is the number of qubits, or inputs (each the size of 1 bit) you need to do arithmetic operations on. m ...


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For 32 bit you only need 5 qubits not 32 qubits. $2^n=N$, where $n$ stands for number of qubits, and $N$ stands for number of bits.


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I think it is similar to how Neural Networks are also good at handling noise (up to a certain threshold). VQE uses parameterized quantum circuit and hence it has the ability to adjust its parameters to absorb some of the noise. This is like how neural networks adjust their weights to absorb noise in the training data.


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This is a misconception. For example, people tends to say the Shor's factoring algorithm help us to do prime factor exponential faster than classical computer because the quantum computer will try out all the possible factors simultaneously then it will tells us the right answer at the end. In reality, the power of shor's algorithm is more subtle than that. ...


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Grover's Algorithm uses 2 simple tricks to search an unordered database (like a phonebook that contains names and phone numbers but not in alphabetical order). It inputs an equal superposition of all possible entries and searches the database in one operation. When it finds the matching entry, it marks it by flipping the sign of the wavefunction of this ...


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