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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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Qiskit general amplitude embedding leads to long circuits

I am trying to use Qiskit to simulate many-body systems. Hence I calculate the ground state of Hamiltonians a lot. There are 2 ways I do them. 1: Calculate the ground state classically, then do state ...
Deren  Liu's user avatar
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Can we use inverse transform sampling in probability loading process of quantum computing?

Recently, I read some papers about Quantum Monte Carlo (QMC), which can speed up the classical Monte Carlo quadratically. However, the efficiency of QMC largely depends on the probability loading ...
ddk's user avatar
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Is $\rho = \sum_{j} p_j|n_j\rangle\langle n_j|$ a valid construction for any mixed state?

I have a mixed state $\rho$ and its hamiltonian $H$. Firstly, I find the eigenvalues $\{p_j\}$ of $\rho$, and orthonormal basis of $H$. I write $\rho$ in terms of $H$'s eigenstates and $\rho$'s ...
Việt Nguyễn's user avatar
2 votes
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Quantum Information Retrieval from Bipartite Mixed States under LOCC: Maximizing Individual State Knowledge

In the context of Local Operations and Classical Communication (LOCC), given a bipartite mixed state represented as $\rho=\frac{1}{n}\sum_{i=1}^n|\psi_i\rangle\langle\psi_i|$, where $|\psi_i\rangle$ ...
Pratapaditya Bej's user avatar
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Can we create a W state of n qubits with constant circuit depth using mid circuit measurements?

I saw this post where the GHZ state with many qubits (here 6) can be made by performing some mid circuit measurements in constant circuit depth: Depth circuit optimization for 6-qubits GHZ state I was ...
ty.'s user avatar
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How to implement the state $|\psi\rangle = \frac{1}{\sqrt{2}}\left[|0\rangle \otimes |X_i\rangle + |1\rangle \otimes |X_j\rangle\right]$

I am trying to implement the quantum k-means algorithm proposed in https://arxiv.org/pdf/1909.04226.pdf. In the equation (8) of the manuscript we need to implement a state $|\psi\rangle = \frac{1}{\...
pablote's user avatar
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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 ...
Yunzhe's user avatar
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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 ...
Saul_better's user avatar
2 votes
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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?
Juweria sayed's user avatar
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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 ...
Cuhrazatee's user avatar
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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’...
confusion's user avatar
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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 ...
Qubii's user avatar
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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 ...
Benjamin's user avatar
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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 ...
user20374's user avatar
1 vote
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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's user avatar
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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. Question Is there anything special about ...
bubakazouba's user avatar
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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 ...
Jarek Duda's user avatar
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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 ...
Song of Physics's user avatar
2 votes
1 answer
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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 ...
Michael.Andy's user avatar
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1 answer
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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 $\biggl[ \frac{1}{\sqrt{3}}, \sqrt{\frac{2}{3}} \biggr]$. ...
3nondatur's user avatar
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1 vote
1 answer
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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 ...
bubakazouba's user avatar
2 votes
1 answer
275 views

Adding phases of two qubits

Imaging a system of two qubits which at a given step of evolution is in the state $|q_{1}(0)\rangle = |0\rangle + e^{-i\phi_{1}}|1\rangle$, $|q_{2}(0)\rangle = |0\rangle + e^{-i\phi_{2}}|1\rangle$, ...
Juan José Gálvez Viruet's user avatar
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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 ...
AMZ's user avatar
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3 votes
3 answers
351 views

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 "...
SimoneGasperini's user avatar
4 votes
1 answer
202 views

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 ...
lm1909's user avatar
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2 votes
1 answer
169 views

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 ...
Mark Spinelli's user avatar
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1 answer
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How to create an arbitrary state for debugging purposes in the local computer?

Is there a way to create an arbitrary state in Q# just for debugging purposes in the local computer via the quantum full state simulator?
Fabio Dias's user avatar
1 vote
1 answer
220 views

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 ...
DYLAN NICO AMBROSI's user avatar
2 votes
1 answer
88 views

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 ...
tomdodd4598's user avatar
4 votes
1 answer
290 views

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 ...
FlamtapShuckle's user avatar
2 votes
1 answer
288 views

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 ...
Yousef Zook's user avatar
5 votes
2 answers
610 views

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 ...
Doriano Brogioli's user avatar
3 votes
2 answers
484 views

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, ...
NaturalLog's user avatar
2 votes
1 answer
534 views

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\...
Masab Iqbal's user avatar
2 votes
1 answer
734 views

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 $n$...
M. L.'s user avatar
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2 votes
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208 views

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 $\rho$ ...
Kalle's user avatar
  • 21
3 votes
2 answers
359 views

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 ...
Emily's user avatar
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4 votes
0 answers
159 views

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 ...
Mark Spinelli's user avatar
3 votes
1 answer
183 views

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 ...
Thomas's user avatar
  • 279
10 votes
1 answer
365 views

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{...
orlp's user avatar
  • 211
5 votes
2 answers
141 views

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 ...
linker's user avatar
  • 181
-2 votes
2 answers
215 views

Complex conjugate state preparation

Good day, have you ever seen the preparation of the state $\langle\psi|$? Or any gates that can transform $|\psi\rangle$ in $\langle\psi|$?
Kim's user avatar
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0 votes
1 answer
428 views

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 $|\psi\rangle\langle\psi|=\displaystyle\sum_{i,j=0}^{2^N-1}|j\rangle\langle i|$...
Yitian Wang's user avatar
4 votes
0 answers
139 views

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 ...
QCQCQC's user avatar
  • 449
10 votes
1 answer
1k views

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 ...
Condo's user avatar
  • 2,068
3 votes
1 answer
287 views

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?
Yongsoo's user avatar
  • 31
7 votes
3 answers
462 views

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 ...
Sam Jaques's user avatar
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