Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

Questions tagged [state-preparation]

a procedure that outputs repeated examples of the same quantum system - particle or multiparticle system - in the same quantum state

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Are quantum states like the W, Bell, GHZ, and Dicke state actually used in quantum computing research?

I recently started studying quantum computing and learned about several well-known quantum states such as the W state, GHZ state, and Dicke state. I noticed that there are also some questions here on Stack Exchange regarding quantum state…
Jayce
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Is there an efficient circuit implementing the unitary $U|x\rangle|0\rangle=|x\rangle\Big(\sqrt{1 - x/2^n}\,|0\rangle+\sqrt{x/2^n}|1\rangle\Big)?$

Given an $n$-qubit register $|x\rangle$, does there exist an efficient circuit implementing unitary operation $U$ such that $$U |x\rangle|0\rangle = |x\rangle\Big(\sqrt{1 - x/2^n}\, |0\rangle + \sqrt{x/2^n}\, |1\rangle\Big)?$$ I've found this…
orlp
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Preparing a quantum state from a classical probability distribution

Suppose I have a black-box unitary $U_p$ which is described as follows: given a finite probability distribution $p:\{1,\ldots,n\}\rightarrow \mathbb{R}_{\geq0}$, where $\sum_{x=1}^n p(x)=1$, the action of the black box on a basis is given by…
Condo
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Can we distill magic states with arbitrary angle $\theta$?

There seems to be numerous work about the distillation protocol of the $T$-magic state $$ \frac{1}{\sqrt{2}}(|0\rangle+e^{i\pi/4}|1\rangle). $$ Similarly, I am wondering if it is possible to distill a $\theta$-magic…
Yunzhe
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Can we get access to the second-lowest eigenstate?

I'd like to know if there's anything that can be said about whether and when we can efficiently prepare a state corresponding to the second-lowest eigenvalue $|\lambda_1\rangle$ of a given Hamiltonian, or in any other way learn what this energy…
Mark Spinelli
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Forming states of the form $\sqrt{p}\vert 0\rangle+\sqrt{1-p}\vert 1\rangle$

I'm curious about how to form arbitrary-sized uniform superpositions, i.e., $$\frac{1}{\sqrt{N}}\sum_{x=0}^{N-1}\vert x\rangle$$ for $N$ that is not a power of 2. If this is possible, then one can use the inverse of such a circuit to produce…
Sam Jaques
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Is it known whether the Fermi-Hubbard ground state can be prepared efficiently or not?

Naturally, in general, ground state preparation is QMA-complete. There exists a paper by Andrew Childs, David Gosset & Zak Webb, which shows that ground state preparation for the Bose-Hubbard model is QMA-complete. However, is it known what the…
lm1909
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How many quantum gates are needed to prepare an arbitrary state?

In this paper there is this sentence: [...] the description of a $2^n\times2^n$ unitary matrix $U$ (which is a poly($n$)-size quantum circuit) According to the meaning of "which" in English, in contrast to "that", the sentence means that the…
Doriano Brogioli
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Making a superposition proportional to a 1-cosine envelope

Here is a simple circuit that produces a superposition proportional to a sine envelope $\sum_{k=0}^{n-1} \sin(\pi k/n)$: Is there also a simple circuit to prepare a 1-cosine envelope? A state proportional to $\sum_{k=0}^{n-1} 1 - \cos(2\pi…
Craig Gidney
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How instantaneous is state preparation in a quantum register, if all possible superpositions are to be initialized equally?

Before the start of a quantum algorithm qubits need to be initialized into a quantum register. How fast can a quantum register of length $n$ be initialized in a way that all possible superpositions of the $N=2^n$ basis states exist with equal…
linker
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How to add the basis state $\vert 0 \rangle$ to an arbitrary uniform superposition state?

There is an unknown uniform superposition state $$\vert \psi \rangle = \frac{1}{\sqrt{N}} (\vert k_1 \rangle + \vert k_2 \rangle + \cdots + \vert k_N \rangle),$$ where $$k_1 \neq k_2 \neq \cdots k_p \neq 0,$$ $k_i$ is unknown but $N$ is known. How…
Bingren Chen
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What's so bad about preparing magic states by measuring Clifford gates?

Suppose we want to perform a gate from the third level of the Clifford hierarchy for example $ T,CS, CCZ, CCX $. To implement such a gate using gate teleportation we need to take as an input certain ancilla states. For example, a $ |T\rangle $ state…
Ian Gershon Teixeira
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References for quantum state praparation: what states are easy to prepare and which ones aren’t?

I’m looking for references on quantum state preparation. I know there’s a plethora of papers on this topic but I don’t know how to narrow it down or figure out which ones to prioritize. In general, I’m interested in the question of: “which class of…
confusion
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Ansatz for VQE demonstrating Quantum Advantage

What would be a possible ansatz quantum state in VQE (variational quantum eigensolver [1]) that would demonstrate the quantum advantage of VQE over classic computers? More specifically, I see that VQE has a quantum advantage if my ansatz state is…
user20374
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Given a quantum state, can you generate a uniform superposition over its computational basis vectors with nonzero amplitudes?

Given an arbitrary $|\psi\rangle=\sum_{i=0}^n\alpha_i|i\rangle$, $K=\{i\mid \alpha_i\not=0\}$, and $k=\vert K\vert$, is it possible to generate the state $\frac{1}{\sqrt k}\sum_{i\in K}|i\rangle$? I feel like this isn't allowed by no-cloning, but I…
FlamtapShuckle
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