Questions tagged [measurement]
For questions related to measurement and its effects as relevant to quantum computation and quantum information.
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How to find that if two quantum states are entangled or not using quantum circuit?
Let us consider, we can easily prepare 2 distinct single qubit quantum states psi1 and psi2 in quantum registers (q1 and q2) in a quantum circuit. How to find out the entanglement status of these two ...
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What is the meaning of the bloch vector & how can i calculate the component of the vector?
I know that a density matrix can be represented linearly by a Pauli matrix using $\rho=1/2(I+\vec{r}\vec{\sigma})$. I also know the vector, $\vec{r}$, composed of coefficients, is called the Bloch ...
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Measurement in X basis
There is something I don't understand about measurement in other basis than the Z-Pauli Basis.
If measurement fixes the state of a quantum system thus destroying superposition, how can we get a ...
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Why for every state there is always a measurement that has a deterministic outcome?
The Qiskit Textbook on https://qiskit.org/textbook/ch-states/single-qubit-gates.html in section 4: Digression: Measuring in Different Bases, says –
Z-basis is not intrinsically special, and that ...
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circuit.measure() throwing error
I have circuit like this
when I try
circ.measure([0, 1, 2], [0, 1, 2])
It is showing the error
list index out of range
I have ...
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Effect of measurement error on surface code
In my understanding, surface code decoders detect measurement error by noticing that a flip of syndrome cannot be matched to another flip. But to what extent does measurement error rate affect the ...
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Why adding H-gate is referred as changing the basis of measurement?
I study Qiskit. When I measure a qubit by including qc.measure(qb,cb) instruction, I measure it in the computational basis. But if I apply the Hadamard gate adding <...
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How do you find the possible measurement values of an observable?
$\newcommand{\ket}[1]{\left|#1\right>}$
Note: I considered posting this as an update to a prior question, but it seemed like it should be it's own post.
So this is a very basic question, but one I'...
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Does applying an operator to a state have nothing to do with taking a measurement?
In class, it was mentioned that beginning students often mix up the application of an operator to a state with taking a measurement of that state, and that this is not the case. What's more, the TA ...
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How to measure an unknown state produced by a source of qubits?
What kind of experiment can allow me to measure an unknown state produced by a source of qubits? For example: the state of photon polarization. But it can be another one.
I have no information about ...
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How are logical operators performed and measured on the surface code, in a defect-free way?
I am reading about the surface code and I am still not sure how to perform and measure logical operators, such as $X_L$ or $Z_L$, without creating defects. Suppose I stabilise my qubit array into a ...
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Is $Tr[E_i E_j] \geq 0$ for $i\neq j$ and $\{E_k\}$ a POVM?
Suppose that $\{E_i\}$ form a POVM (i.e. a set of positive operators satisfying $\sum_{i} E_i = I$, where $I$ denotes identity).
Is it the case that $Tr[E_i E_j] \geq 0$ for all $i \neq j$?
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Numerical optimization over separable measurements
For a set of bipartite density operators $\{\rho_a\}_{a=1}^m \subset D(\mathcal{X} \otimes \mathcal{Y})$ each associated with a probability $p(a)$, an optimal separable measurement is a POVM $\{ \...
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How to derive the state of a qubit after a partial measurement?
I am trying to solve a problem from the course "Quantum Information Science I" of MIT Open Learning Library, but I get stuck.
Here is the problem. Consider the below circuit where the meter ...
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Qiskit: density matrix after measurement
I would like to find density matrix after the measurement. The toy code:
...
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Entanglement Measurement vs Observation
This is a very basic question. Consider an entangled pair |00> + |11> of two qubits $q_1$ and $q_2$. Now, we measure $q_1$ and its outcome is 0. I know that $q_2$'s state "collapses" ...
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Can two measurements be represented as a single measurement when they are acted upon sequentially?
Let two different POVM measurements represent as $\mathcal{M}_1=\{\Pi_i\}_{i=1}^k$ where $\Pi_i$ is element of the $\mathcal{M}_1$ measurement and $\mathcal{M}_2=\{E_j\}_{j=1}^n$ where $E_j$ is the ...
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How am I suposed to do a measurement in a quantum circuit?
I have a quantum circuit with 9 qubits. I have the matrix of the system. My question is how am I supposed to measure the final state of my first qubit? I know I need to apply a projection operator, ...
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Qiskit: Measure circuit until specific bitstring sampled
I'm implementing a quantum algorithm that involves measuring a circuit until a bitstring with a particular property is sampled. I want both the bitstring and the number of measurements it took until ...
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how does one get native 2-body measurements?
How are Majorana-based architectures able to possess native 2-body measurement operations? Could anyone provide an appropriate reference explaining that?
Are those native measurement operations ...
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Is a diagonal matrix with one non-zero element a measurable observable?
The HHL algorithm prepares the output state $|x\rangle$. However, we cannot efficiently measure the state directly to get its components. Instead, we can construct an operator $M$ to find $\langle x|M|...
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Quick conditions to see that $I - E_1 -E_2$ is positive for $E_1, E_2$ positives (example from Nielsen and Chuang)
In the Nielsen and Chuang ("Quantum Computation and Quantum Information"), section 2.2.6 POVM measurements, they define these three operators:
$E_1 = \frac{\sqrt{2}}{1+\sqrt{2}} |1\rangle \...
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What are examples where the quantum discord is achieved by a non-projective POVM?
Consider the (asymmetric) quantum discord, defined as (borrowing notation from Eq. 4.13c of Zurek's review):
$$\mathcal D(\mathcal S:\mathcal A) = I(\mathcal S:\mathcal A) - \chi(\rho_{\mathcal A}),$$
...
glS♦
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Prove that the square root measurement $\Lambda_y=\frac14(\rho_{B^3})^{-\frac12}|\psi_y\rangle\langle\psi_y|(\rho_{B^{3}})^{-\frac{1}{2}}$ is a POVM
Consider $\textit{X}\sim \mathrm{Unif}([0,1,2,3]), |\mathcal{Y}|=|\mathcal{X}|=4$. Also for every random variable realization {\it x} we use three parallel quantum channels like the one employed ...
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How to get exact measurement probabilities when having intermediate measurements with Qiskit?
Suppose we have a circuit with two qubits, A and B. Both are initialized to $|0\rangle$. Over qubit A we apply a single rotation gate (e.g. $R_y$) with an angle given by $x_0$, and then we entangle ...
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AerSimulator measurements
When I use the simulator
Aer.get_backend('aer_simulator')
and the circuit contains measurements at the end, how do Qiskit performs these measurements?
I thought ...
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Simultaneous measurements and Bell basis measurements to estimate $\lvert\text{Tr}(\sigma \rho)\rvert^2$ in Huang et al. paper
Theorem 2 of this paper says if one is able to prepare $\rho^{\otimes k}$ then it is possible to predict expectation values of all $n$-qubit Pauli observables using $O(n)$ number of copies of $\rho$. ...
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Reduced density matrix accuracy in amplitude estimation
I am implementing QAE (Quantum Amplitude Estimation), which is very similar to QPE (Quantum Phase Estimation) with a Grover Operator as the U matrix of QPE.
I want to check my results, in the outputs ...
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Writing a state respective to the eigenbasis of an observable
Problem:
When people say that a state $|\mathcal{A}\rangle$ can be expressed in respect to the eigenbasis of an observable $A$, they provide $p_{\mathcal{A}}(a)$, which apparently gives the ...
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How does Qiskit Primitives Estimator compute expectation values?
The Qiskit Primitives Estimator class is implemented to work in two different ways depending on the shots parameter nature:
...
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Measurement of readout errors for error mitigation algorithms
I am using an error mitigation algorithm that uses the readout errors p(0|1) and p(1|0) to correct the errors due to noise in my original circuit. I am trying to measure the readout errors in the same ...
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Given a POVM, what's the channel that optimally preserves coherence in the post-measurement outcomes?
It is well-known that a POVM $\boldsymbol\mu\equiv (\mu_a)_{a\in\Sigma}$ describes outcome probabilities, but not post-measurement outcomes, which in many scenarios exist and are of interest.
To ...
glS♦
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Can qubit ever be in non-superposition state other than the instance its measured?
For a qubit to be in "actual state" $\psi=\alpha_0|0\rangle+\alpha_1|1\rangle$ cannot be viewed as the qubit is either in $|0\rangle$ or $|1\rangle$ with probability of $|\alpha_0|^2$ or $|\...
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Do SIC-POVM elements for $d=2$ sum up to the identity?
I am studying SIC-POVM in dimension two and I want to check that the elements sum up to identity.
$$\begin{aligned}
& \left|\psi_1\right\rangle=|0\rangle \\
& \left|\psi_2\right\rangle=\frac{1}...
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Is there a way to access the value of a classical bit after measurement and store it as a variable (qiskit)?
I am trying to implement the one-qubit Approximate QFT for Shor's Algorithm in qiskit as described in this paper, which requires the gate
$$
R_j^{\prime}=\left(\begin{array}{c}
1 \hspace{0.5em} 0 \\
0 ...
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How to increase the probability of successful measurement to find out the largest amplitude?
I have built a state
$$A|0\rangle = |\Psi \rangle = \sum _n c_n |n\rangle$$
Where $A$ is a circuit.
And I need to known, where is the largest $|c_n|$.
I find out that, I can simply do many ...
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Significance of angle $\phi$ on bloch sphere
So far I learned that a qubit can be written as $| \psi \rangle = \alpha | 0 \rangle + \beta | 1\rangle$ with $|\alpha|^2 + |\beta|^2 = 1$ and reparametrized as $| \psi \rangle = cos( \theta / 2) + e^{...
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De-coherence and Wigners friend?
So in the thought experiment Wigners friend the paradox is ultimately due to a difference of descriptions of density matrices.
If the physical variable that is measured of the spin system is denoted ...
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How and how much do fabrication defects affect superconducting qubit coherence time?
I used simulations to calculate T1 time of a transmon qubit, but the result is much longer than the lab data. I suspect it was because simulation does not consider fabrication defects. May I ask if ...
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What does "commuting operators can be measured simultaneously" mean?
I want to understand better what it means by any commuting set of operators can be measured simultaneously.
Suppose I have an $n$-qubit arbitrary pure state $\rho = \lvert \psi \rangle \langle \psi \...
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Why do quantum computing simulators have the measurement function?
Quantum computing simulators like qasm_simulator in Qiskit Aer have a function to simulate quantum measurements (for example, the command of ...
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What is a POVM?
I am having a hard time understanding what exactly a Measurement is by its definition? What I read is that a POVM $M$ is defined by its set of elements $M_i$. So is $M$ itself an operator? In circuit ...
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Applying Clifford Gate before a Pauli Measurment
I am reading a paper where they describe different randomised measurement protocols. I am confused about a simple case of this protocol that they discuss.
The link of the paper is here , and I am ...
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How to get the group of qubits which are on the same port of measurement?
From IBMQ's quantum computer, we know that logical qubits are mapped to their computers' physical qubits, and then they are measured to get classical bits (0 and 1). For instance, a 27-qubit ...
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How does a quantum system identify hermitian and unitary matrices?
I am a beginner in quantum computing. I know that multiplying a state $|u\rangle$ with a hermitian matrix $M$ yields spectral decomposition and multiplying $|u\rangle$ with a unitary matrix yield an ...
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Expectation value of Pauli Z for locally rotated Bell state
Suppose we have a Bell state $\frac{\lvert 00 \rangle + \lvert 11 \rangle}{\sqrt{2}}$. The expectation value of the Bell state with respect to $Z \otimes I $ is $\langle Bell|Z_1|Bell\rangle = 0$. Now,...
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Simultaneous measurements of Pauli observables and number of copies required
Does simultaneous measurement imply that we can only use $1$ copy of quantum state to measure any set of commuting observables? For example, suppose we have a Bell state $(\lvert 00 \rangle + \lvert ...
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Is Shor demonstration wrong?
in Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer by Peter W. Shor (also in Algorithms for quantum computation: discrete logarithms and factoring).
In ...
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Expectation value of a time evolved circuit in the non-Z basis
I am new to qiskit and have hit a roadblock in my calculation. Given the following circuit:
...
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How many measurements are needed to distinguish two fixed density matrices?
Suppose there are two fixed density matrices $\rho_1$ and $\rho_2$ are prepared for equal probability. Can we say something about the minimum number of measurements required to distinguish the two ...
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