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Approximate Cloning
Question
Consider two single qubit states $\left\{|\alpha_0\rangle,|\alpha_1\rangle\right\}$ which are not orthogonal or parallel, i.e. $\left|\langle\alpha_0|\alpha_1\rangle\right|\ne0,1$. Additionally, consider the unitary operation:…
Chris Long
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Why is the complexity of $n$-qubit state tomography not upper bounded as $O(3^n)$?
Consider the task of fully determining an $n$-qubit state $\rho$ which can be written as
\begin{equation}\tag{1}
\rho = \sum_{p \in \{I, X, Y, Z\}^n} \text{Tr}(\rho P_{p}) P_{p}
\end{equation}
and each $P_{p} = P_{p_1} \otimes \dots \otimes…
forky40
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What is the role of entanglement in quantum-computational speed-up?
The way I see it, there are three main quantum properties utilized in quantum computing - superposition, quantum interference, and quantum entanglement. I'm looking to understand which one is responsible for the exponential speed-up that quantum…
Ognyan Tsvetkov
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What precisely is Reverse Annealing?
Quantum Annealing, (related questions Quantum Annealing, or hamiltonian related) is the process used in D-Waves' Quantum Annealer, in which the energy landscapes are explored, for different solutions, and by tuning a suitable Hamiltonian, zero in to…
user3483902
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Quantum chemistry: references
I have heard about Quantum chemistry as one of the main applications of quantum computers. However, I have not found concrete related articles with circuit-implementations for these applications.
Does anyone have articles on simulating molecules…
nippon
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Why or how is 'cat' state preparation via a C-not-not operation not fault tolerant?
On p490 of Nielsen and Chuang, 2010 the authors say that the preparation of the 'cat' state ($|000\ldots 0\rangle+|111\ldots 1\rangle$) is not Fault Tolerant. Below is my mock up of the diagram they draw for the preparation ($H$ and $C$-not-not *)…
Quantum spaghettification
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What is the maximum separation between two entangled qubits that has been achieved experimentally?
Considering two entangled flying qubits, as far as I know, there is no physical limit for separating them without losing quantum information.
See: Is there any theoretical limit to the distance at which particles can remain…
SalvaCardona
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Prove the fidelity can be written in terms of Pauli expectation values as ${\rm tr}(\rho\sigma)=\sum_k \chi_\rho(k)\chi_\sigma(\rho)$
I am reading through "Direct Fidelity Estimation from Few Pauli Measurements" and it states that the measure of fidelity between a desired pure state $\rho$ and an arbitrary state $\sigma$ is $\mathrm{tr}(\rho\sigma)$. It then describes a…
Quantum Guy 123
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Is there a practical architecture-independent benchmark suitable for adversarial proof of quantum supremacy?
Recent quantum supremacy claims rely, among other things, on extrapolation, which motivates the question in the title, where the word "adversarial" is added to exclude such extrapolation-based quantum supremacy claims.
To clarify the exact meaning…
fiktor
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Shor's algorithm caveats when $a^{r/2} =-1 \mod N$
For an integer, $N$, to be factorised, with $a$ (uniformly) chosen at random between $1$ and $N$, with $r$ the order of $a\mod N$ (that is, the smallest $r$ with $a^r\equiv 1\mod N$):
Why is that in Shor's algorithm we have to discard the scenario…
Tech Solver
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5 answers
Why can't quantum computation replace classical computation?
I am not a total novice of quantum computation (have read the first 6 chapters of Nielsen and Chuang, though not familiar with every part), but there are some fundamental questions that I don't know answers well.
One question that has bothered me is…
Liren Lin
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How do we understand Jordan's Lemma?
In quantum computing protocols, jordan's lemma keeps cropping up. See, for example, here: https://cims.nyu.edu/~regev/teaching/quantum_fall_2005/ln/qma.pdf
For any two projectors $\phi_1$, $\phi_2$, there exists an orthogonal decomposition of the…
snickers_stickers
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Prove that the singlet is invariant under $U\otimes U$
I have a Bell state ${\Psi}^{-}= \frac{1}{\sqrt2} (|01\rangle - |10\rangle).$
How can I prove that this state is invariant (up to a global phase), when doing the same unitary $U$ on each qubit?
That is, how can I show that, for all $2\times 2$…
arsene stein
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Are SU($n$) operations enough for quantum computation?
Usually we want a quantum computer that can perform all foreseeable unitary operations U($n$).
A quantum processor that can naturally perform at least 2 rotation operators $R_k(\theta)=\exp(-i\theta\sigma_k/2)$, where $\sigma_k$ are the Pauli…
Mauricio
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Does control and target matter in the CZ (Controlled-Z) Gate?
IBM Quantum Experience and other Algorithm Creators generally draw the CZ gates like this:
Does it not matter which qubit is the control and which is the target? If so why?
Jadon Erwin
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