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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What is the state of the art quantum state preparation algorithm?
Encoding classical information into a quantum computer is a bottleneck of quantum machine learning. I want to learn which algorithm for state preparation is the best (in complexity) currently. The ...
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What exactly does state preparation mean in quantum computing?
I want to know what exactly state preparation means in a quantum computing. Are preparing a quantum state by applying different operations on it or we are preparing by some other methods?
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Is there a known classification of quantum states on $n$ qubits preparable with O(1) circuit depth?
A lot of quantum algorithms start from the uniform superposition state, and then do some finagling to transform that state into the one they cared about. I was wondering if there is any advantage from ...
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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’...
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How to alter the result of (somewhat) randomly generated circuits?
I create randomly generated circuits by iterating through a list of the gate set (in my case [$CX,SX,RZ,X$]) and adding the gate to the circuit. (In the case of the $CX$ gate we look at the topology ...
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Adiabatic state preparation for quantum phase estimation
I'm trying to understand the problem of state preparation for quantum phase estimation (QPE). Specifically how states are prepared adiabatically.
I have a couple of questions:
1). Typically when one ...
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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 ...
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How does the uncomputation step work in the Grover-Rudolph scheme to prepare $\sum_i\sqrt{p_i}|i\rangle$?
In https://arxiv.org/abs/quant-ph/0208112, the authors discuss a scheme to, given a discrete probability distribution $\mathbf p\equiv (p_i)_i$, under some assumptions on $\mathbf p$, prepare the ...
glS♦
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Is efficient state preparation possible for binary states?
Binary Vector Definition:
A vector where each entry has one of 2 possible values: $\{0, \dfrac{1}{\sqrt{K}}\}$.
Where $K$ is the number of non zero entries.
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Is there anything special about ...
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Two-way quantum computers (like in Ising model) - are they possible? Could solve general NP problems? [closed]
Standard one-way quantum computers (1WQC) allow for e.g. Shor, Grover algorithms, however, general NP problems seem too difficult for them(?) - bringing an open question if they could be somehow ...
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The necessity of a qRAM-based state preparation in qSVT-type problems
I've been reading a couple of papers regarding qPCA and its dequantisation. In the course of my reading, it appears to me that one of the ingredients that makes this dequantisation meaningful is the ...
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Global vs local: global density matrix and all the reduced density matrix
I prepare a $n$-qubit quantum state $\sigma$ whose ideal state is $\rho$, then perform state tomography on all the $m$- qubit reduced states. Ideally, I find that all the $m$- qubit reduced states are ...
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Why don't I receive the output I expect?
I tried to test the Bitflip code using Qiskit. So, see my code below, build the circuit and initialised the first qubit in the state $\biggl[ \frac{1}{\sqrt{3}}, \sqrt{\frac{2}{3}} \biggr]$.
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How is the depth of a circuit creating "Constant size vector states" $O(\log b)$
In Prakash's thesis - (link to PDF), section 2.2.2 Constant size vector states:
We show that the vector state $|x\rangle$ for $x\in R^b$ can be created in time $\widetilde{O}(\log(b))$ using a ...
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Adding phases of two qubits
Imaging a system of two qubits which at a given step of evolution is in the state
$|q_{1}(0)\rangle = |0\rangle + e^{-i\phi_{1}}|1\rangle$,
$|q_{2}(0)\rangle = |0\rangle + e^{-i\phi_{2}}|1\rangle$,
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permutation representations of Quantum Ternary Benchmark functions
I recently studied this paper: http://www.informatik.uni-bremen.de/agra/doc/konf/SAT-based_Exact_Synthesis_of_Ternary_Reversible_Circuits_using_a_Functionally_Complete_Gate_Library.pdf
In this paper ...
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How to prepare all the computational basis states by running the same quantum ansatz with distinct $\theta$ values?
Given a 2-qubits system, the 4 computational basis states are $|00\rangle$, $|01\rangle$, $|10\rangle$, $|11\rangle$.
Is it possible to prepare these states by a one-parameter quantum circuit "...
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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 ...
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How best to prepare a uniform superposition over all strings of balanced parentheses?
[0001] Consider the set $D_n\subset \{(,)\}^{2n}$ of all Dyck words of strings of balanced brackets or balanced parentheses of length $2n$. For example, for $n=5$, we have $\sigma=()()()()()$ is ...
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What actually StatePreparation perform in qiskit?
I used this method to initialize classical data in a circuit. I would like to know what's under the hood and the complexity of this procedure, but I can't find anything on the internet which suits my ...
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Confusion about Rodeo algorithm "spectral weight suppression" argument
In this first paper on the Rodeo algorithm, there is an argument on the second page about the suppression of "spectral weights" that I don't really understand.
In short, the algorithm is ...
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Given a quantum state, can you generate a uniform superposition over its computational basis vectors with nonzero amplitude?
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 ...
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What are the mathematics and theory behind Initializing a quantum state vector?
I do not understand how the initialize function in QiSkit is working. I know that it is used to put a qubit in a specific custom state.
My question is - how is it implemented or how to do such a thing ...
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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 ...
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How to create superposition of states with fixed parity with a quantum circuit?
I'm searching for a circuit to generate, starting from the $|00\, ...\,0\rangle$ state, an arbitrary superposition of all states with either even or odd parity. The gate choice is irrelevant for now, ...
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How to create known quantum state in Qiskit (or any other platform) comprising of two or more bits?
Is there there any way to create a known quantum state in Qiskit (or any other platform) comprising of two or more than two bit?
For example if I want to create $\frac{1}{\sqrt{3}}[|00\rangle+|01\...
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Is the CNOT in the standard three-qubit circuit for the GHZ state necessary?
This is a very basic question about the GHZ state. I know the standard construction:
A Hadamard on one qubit, and then CNOT gates with targets on all the other ones.
However, why can't I just have $n$...
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How can a density matrix be prepared on a quantum register?
I am currently trying to implement the VQSE algorithm.
There the biggest eigenvalues and their corresponding eigenvectors of a density matrix $\rho$ are computed.
In contrast to VQE, the matrix $\rho$ ...
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How to prove that EPR outcomes have equal probability no matter the basis?
Recently in class, we learned about the EPR state. I know that no matter what basis the first qubit is measured in, the two outcomes have an equal probability. However, how does one prove this? I ...
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If we can prepare a ground state efficiently, when can we prepare the second-lowest energy 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 of a given Hamiltonian, or in any other ...
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How to prepare a random 1-qubit superposition for data encoding
Let's assume we have a normalized data vector $\vec{x}= [x_1,x_2]$. How can I prepare a state $$|\psi\rangle = x_1|0\rangle+x_2|1\rangle$$
for any $\vec{x}$. I know that this state is in general not ...
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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{...
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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 ...
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Have you ever seen the preparation of the state $a^{*}|0\rangle+b^*|1\rangle$ and $a|0\rangle+b|1\rangle$ from one initial state?
Have you ever seen the preparation of the state $a^{\star}|0\rangle+b^{\star}|1\rangle$ and $a|0\rangle+b|1\rangle$ from one initial state?
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Produce a quantum state with its density matrix an identity matrix up to an constant
For a n-qubit quantum state $|\psi\rangle=\displaystyle\sum_{i=0}^{2^N-1}|i\rangle$, by definition it's density matrix is $|\psi\rangle\langle\psi|=\displaystyle\sum_{i,j=0}^{2^N-1}|j\rangle\langle i|$...
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What's the circuit to create superpositions corresponding to efficiently integrable probability distributions?
See article here: https://arxiv.org/abs/quant-ph/0208112
There are two steps in this procedure that I am curious about. First off, they suppose one can construct a circuit which efficiently performs ...
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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 ...
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How can I find the fidelity of the preparation operation $|0\rangle$ of IBMQ?
I want to know the fidelity (or error rate) of the preparation of $|0\rangle$. How can I obtain it?
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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 ...
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