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Quantum Computing

Questions tagged [quantum-algorithms]

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For questions about quantum algorithms, that is, sequences of quantum gates, operations, and measurements, whose purpose which achieve some goal. Standard examples are Shor's and Grover's algorithms.

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1answer
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I have noticed a lot of quantum algorithms that do not output an exact answer generally scale as $O(\log(1/\epsilon))$ where $\epsilon$ is the error threshold. I initially thought that this is because ...
1vote
0answers
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I've been working on a VQE implementation to calculate the dissociation curve of the H₂ molecule using Qiskit. The simulated curve (using Aer) looks great and behaves as expected. However, when I ...
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1answer
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Implement the Quantum Phase Estimation (QPE) algorithm using the unitary operator S and the eigenstate∣1⟩ as the target qubit. Use 3 counting qubits and 1 target qubit.Assumptions / notation:Assume ...
2votes
0answers
48views

I would like to build a quantum circuit in Qiskit that initializes the state in a uniform superposition over all valid permutation encodings.Concretely, for $ n = 2 $, I want:$$|\psi\rangle = \frac{...
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Currently writing a QASM parser and wondering if this is the proper way to parse a program using a DAG (Deutsch's from QASMBench in this example).The output from Deutsch's would be:...
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Im making a quantum SVM with the quantum kernel using qiskit. Right now, im trying to implement the noise model using the fake provider....
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1answer
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I’ve recently written a short note proving a structural property of Shor’s factoring algorithm, and I’d like feedback from those more experienced in quantum algorithms.Key result:If a base a is ...
2votes
2answers
217views

I'm not big on computational complexity theory; I only know a little about classes like P and NP. I would appreciate it if someone could shed light on the idea behind the Quantum Merlin Arthur ...
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1answer
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I'd like to implement $e^{-iat}$ as part of an algorithm for hamiltonian simulation. This makes the operation:$$|a\rangle|0\rangle \rightarrow |a\rangle e^{-iat}|0\rangle$$According to Nathan ...
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1answer
83views

In the paper "Grand Unification of Quantum Algorithms", the following operator is introduced in eqn. (27) of said paper:$$\hat{\Pi }_{\phi } = e^{i\phi (2\hat{\Pi }-\hat{I})}$$The operator ...
1vote
3answers
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I have a block-encoded matrix $A$ (for example, a diagonal matrix) encoded in a unitary $U_A$. I would like to apply a Chebyshev polynomial to the singular values of $A$ using Quantum Singular Value ...
1vote
1answer
55views

Does designing a specific circuit for dividing a number of length n by two with a fixed depth of 9 count as an advancement in quantum computing?In practice and in real-world applications, which ...
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This question is similar to Hamming Weight algorithm , but the solutions to that question do not suffice to implement what i am looking for.Does anybody know the best bound for a quantum circuit / ...
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1answer
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By high-precision here I mean that the algorithm returns the first $n$ bits of the true answer with high probability. By tractable I mean that the algorithm can be implemented with $O(\mathrm{poly}(n))...
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In what follows, I am mostly interested in exact arbitrary-precision arithmetic. Quantum arithmetic is an active research topic. Of course any classical algorithm for arithmetic can be expressed as a ...

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