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1500 questions
24
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4 answers
Why is it crucial that the initial Hamiltonian does not commute with the final Hamiltonian in adiabatic quantum computation?
I've read in many sources and books on adiabatic quantum computation (AQC) that it is crucial for the initial Hamiltonian $\hat{H}_i$ to not commute with the final Hamiltonian $\hat{H}_f$, i.e. $\left[\hat{H}_i,\hat{H}_f\right]\neq 0$. But I've…
Turbotanten
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24
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What is the purpose of a quantum RAM in quantum algorithms?
I see many papers (e.g. Quantum principal component analysis) in which the existence of qRAM is necessary. What's the actual purpose of qRAM in quantum algorithms?
Anton Karazeev
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24
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How does the Grover diffusion operator work and why is it optimal?
In this answer, Grover's algorithm is explained. The explanation indicates that the algorithm relies heavily on the Grover Diffusion Operator, but does not give details on the inner workings of this operator.
Briefly, the Grover Diffusion Operator…
Discrete lizard
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24
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What makes quantum computers so good at computing prime factors?
One of the common claims about quantum computers is their ability to "break" conventional cryptography. This is because conventional cryptography is based on prime factors, something which is computationally expensive for conventional computers to…
Paul Turner
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23
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What's the difference between T1 and T2?
I learned that T1 is relaxation time (time from $|1\rangle$ to $|0\rangle$) and T2 is coherence time.
The relaxation is a specific case of decoherence.
What's the difference between them and what's the exact meaning of coherence time T2?
peachnuts
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Is there a list of accessible open problems in quantum computing from a theoretical computer science perspective?
(Classical) theoretical computer science (TCS) has a number of outstanding open problems that can easily be instantiated in a manner that is accessible to a wider general public.
For example, questions about $\mathrm{P}$ vs. $\mathrm{NP}$ can…
Mark Spinelli
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23
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4 answers
Why can the Discrete Fourier Transform be implemented efficiently as a quantum circuit?
It is a well known result that the Discrete Fourier Transform (DFT) of $N=2^n$ numbers has complexity $\mathcal O(n2^n)$ with the best known algorithm, while performing the Fourier transform of the amplitudes of a quantum state, with the classical…
glS
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23
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2 answers
What is the difference between transmon and Xmon qubits?
Transmon and Xmon qubits are two types of superconducting charge qubits that seem to be often used in superconducting quantum devices.
However, I wasn't able to easily find direct comparisons between them.
The Xmon architecture seems (1304.2322) to…
glS
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22
votes
4 answers
Can we combine the square roots inside the definition of the fidelity?
The (Uhlmann-Jozsa) fidelity of quantum states $\rho$ and $\sigma$ is defined to be
$$F(\rho, \sigma) := \left(\mathrm{tr} \left[\sqrt{\sqrt{\rho} \sigma \sqrt{\rho}} \right]\right)^2.$$
However, as discussed here, the cyclical property of the trace…
tparker
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What does Google's claim of "Quantum Supremacy" mean for the question of BQP vs BPP vs NP?
Google recently announced that they have achieved "Quantum Supremacy": "that would be practically impossible for a classical machine."
Does this mean that they have definitely proved that BQP ≠ BPP ? And if that is the case, what are the…
Alex Kinman
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What is a "barrier" in Qiskit circuits?
I just started studying IBM Qiskit, and cannot find details about the barrier method on the QuantumCircuit class. It is shown in the circuit drawing, but I never heard about it after reading quantum computing text books. Is it a unitary gate? If so,…
czwang
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22
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3 answers
Toffoli gate as FANOUT
I was searching for examples of quantum circuits to exercise with Q# programming and I stumbled on this circuit:
From: Examples of Quantum Circuit Diagrams
- Michal Charemza
During my introductory courses in quantum computation, we were taught…
D-Brc
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22
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1 answer
An impossible quantum adder claimed by a journal article?
In Quantum adder of two states that are themselves superpositions, I asked:
I have two states $|a\rangle = \frac{1}{\sqrt N}\sum_{i=0}^{N-1}|i\rangle|a_i\rangle$ and $|b\rangle = \frac{1}{\sqrt N}\sum_{j=0}^ {N-1} |j\rangle|b_j\rangle$,…
Paulske
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5 answers
How can I build a circuit to generate an equal superposition of 3 outcomes for 2 qubits?
Given a $2$ qubit-system and thus $4$ possible measurements results in the basis $\{|00\rangle$, $|01\rangle$, $|10\rangle$, $|11\rangle\}$, how can I prepare the state, where:
only $3$ of these $4$ measurement results are possible (say,…
weekens
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What is the use of categorical quantum mechanics?
I recently noticed that Oxford's computer science department has started offering a grad course on categorical quantum mechanics. Apparently they say that it is relevant for the study of quantum foundations and quantum information, and that it uses…
Sanchayan Dutta
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