Questions tagged [measurement]
For questions related to measurement and its effects as relevant to quantum computation and quantum information.
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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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If a quantum algorithm requires a measurement, how can we use that as a subroutine in another quantum algorithm?
Some algorithms (like period finding), use one or more measurement step. The post measurement state is then acted upon by another set of gates to complete the algorithm.
If I imagine this as blackbox ...
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What is the cost of measurement?
I am exploring a quantum algorithm to solve a partial derivative equation with time derivative. It performs the same entangling unitary to advance the solution by one time step.
Is it more efficient ...
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Qiskit - Statevector measurement of single qubit in GHZ state collapses the entire state
I have a GHZ state. I want to measure the third qubit in Hadamard basis, after which the state left behind should be a maximally entangled state as mentioned here.
But when I measure the third qubit, ...
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How does Quantum Simulation actually solve the problem it poses?
The problem of quantum simulation is below:
Given a Hermitian matrix, $H$, compute the unitary $e^{-iHt}$ for any $t > 0$. Using this computed unitary, calculate $e^{-iHt}\psi$ for any given $\psi$
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How is phase kickback possible if qubits are unentangled?
If I have two independent (unentangled) qubits, let's say one in state |1> and the other one in some superposition state with equal amplitudes and arbitrary phases. If I measure the qubit that is ...
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How to perform the measurements on a quantum circuit in W state basis?
I need to perform the measurements on a quantum circuit in the basis $\{ \eta^\pm,\zeta^\pm \} $. Where $ \eta^\pm,\zeta^\pm $ are given as follows:
$$\eta^\pm = \frac{1}{2}|001\rangle + \frac{1}{2}|...
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How are measurements done exactly on IBM cloud computers?
A quantum cloud server like from IBM typically returns a string of 0's and 1's such as 0010.
How is this measurement done exactly? I realize that the IBM cloud computers are transmon devices based on ...
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How to use more than 3 classical registers in a single quantum circuit in Qiskit without getting error: not enough memory slots?
I'm trying to run a quantum circuit on qasm simulator which has more than 3 classical registers. It gives error when I try to execute it. The circuit looks ...
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Measure or Amplify the least probable state
Qubits can be represented by a state vector $\psi \in \mathbb{C}^{2^N}$, where $N$ is the number of qubits.
The higher $| \psi_i |$ is, for any index $i$, the more likely it is to be measured. But is ...
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How we can perform measurements on an X, Y or Z basis in cirq?
How we can perform measurements on an X, Y or Z basis in cirq? Is there any function where we can give the list of qubits and measurement basis as an argument and get the output?
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Azure backend ignoring meas_level=2
I'd like to retrieve from IonQ QPU provided by Azure the per-shot measurements.
Azure recommends the results are retrieved via Qiskit.
The standard Qiskit command for that is: ...
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Computing gradients in parallel with cost from probs (Pennylane-Braket)
Do circuits that measure probabilities instead of expectation values benefit from parallel execution?
The Computing gradients in parallel with Amazon Braket tutorial shows how the multiple device ...
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How to write post-measurement states when the measurement apparatus measures one of two observables?
If I want to measure an observable $A$ but the measurement apparatus has $(1-p)$ probability of measuring the observable $B$ and probability $p$ that a measurement of $A$ would be done. So how can I ...
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Is it possible to generate a deterministic state after measurement after using QASM simulator in Qiskit?
I have a little naive question. We know that quantum state is probabilistic and we can the count result from QASM simulator to know the distribution of various state a qubit can be in. Is there any ...
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If measurement collapses the information and we lose information, what's the point of using a qubit?
It's a basic question, I'm new to the domain and still studying qubit.
To my knowledge, One of the most important advantages of a qubit over a classical bit is that it can store more information than ...
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How do I get correct measurement probabilities in ZX calculus?
I'm learning ZX-calculus, but I'm getting confused when trying to obtain some simple results to compute probabilities for different outcomes.
Here's a simple example where I'm getting lost. Here, <...
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Projective measurement operation in Qiskit
I would like to implement the operation $\pi = \begin{bmatrix}
1 & 0 \\
0 & 0
\end{bmatrix}$
on qiskit but I don't know how to do that.
If I use the reset ...
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Is there an alternative algorithm to extract a probability of states of qubit after measuring?
Let a simple quantum circuit consist of one qubit and one classical bit. Initially, a qubit has the $|0\rangle$-state and then goes through some sequence of quantum gates, see the circuit below.
The ...
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qiskit : how to measure multiple pauli strings
This seems like a basic operation, but I can't see how it's done in qiskit.
The solution here
Measuring tensor products of Pauli operators doesn't work anymore.
I get an error "qiskit has no ...
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Formal measurement of the probability of an outcome of a Qubit in the hadamard base
I am fairly new to Quantum Computing and have a question which might be trivial for all of you, but I am really struggling with it.
From Quantum Computation and Quantum Information I have learned, ...
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Is a generalized 2D cluster state still a universal resource?
Let $G = (V, E)$ be a $\sqrt{n} \times \sqrt{n}$ grid graph. Consider preparing a 2D cluster state as follows.
$$|\psi_{\mathsf{C}}\rangle = \underset{(i, j) \in E}{\Pi} (\mathsf{CZ})_{i, j} | + \...
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Is the post-measurement state always pure after a partial measurement?
Imagine I have two potentially entangled qudits and measure the first one using some Hermitian operator $M$ that has only one eigenstate per eigenvalue and get some outcome $m$. Can I know for sure ...
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How can you extract all the state probabilities in e.g. Grover's search?
In the Qiskit tutorial for e.g. Grover's algortihm, there is a 3-qubit implementation on a real quantum computer
https://qiskit.org/textbook/ch-algorithms/grover.html#3.1.2-Experiment-with-Real-...
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How can one impliment Bennett's partial measurement onto a binomial subspace for state distillation?
I'm reading the seminal paper on entanglement distillation by Bennett et. al.
The idea is that Alice and Bob have $n$ identical copies of an imperfect (but pure) Bell state. The initial state is ...
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Going from projective measurement to unitiary operators for qiskit
I have a solution to the Peres-Mermin magic squares game (Wikipedia quantum pseudo-telepathy)
I simulate the six measurements using projective (non-unitary) measurement operators like in Nielson and ...
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If $[M,N]=0$, is the probability distribution obtained measuring $M$ after $N$ the same as the one obtained measuring $N$?
Let $|\psi\rangle$ be a fixed state and $M$ and $N$ two commuting operators corresponding to projective measurements. Consider the probability distribution $p$ obtained by measuring $N$ on $|\psi\...
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How to compute projective probabilities of a given measurement outcome using Stim?
I am looking to calculate the projective probabilities for each measurement outcome in a Clifford circuit and then output its corresponding tableau state. I am performing the measurement in the Z ...
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CNOT entangling a third qubit and how measurement impacts entanglement
I'm trying to understand entanglement, superposition and the effects of measurement on entangled qubits a bit better.
About entanglement:
I know that the circuit below will entangle the two qubits:
...
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Measuring qubits vs measuring operators
I'm having trouble unifying these two ideas. When I read examples using, say, qiskit, it's typical to measure a qubit, so that to find the probability of measuring a state $|\psi \rangle$ in the state ...
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Exact Probabilities of Outcomes for Clifford Circuits with Mid-Circuit Measurements Using Stim
I am trying to find the exact probabilities of specific measurement outcomes for Clifford circuits with mid-circuit measurements. Essentially, I am looking for a function that takes an arbitrary ...
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Swap test vs measurement in a specific basis
I have two states $|\psi\rangle$ and $|\phi\rangle$. The swap test allows to estimate $|\langle \psi | \phi \rangle|^2$ by using the controlled SWAP gate and a couple of Hadamard gates. To obtain the ...
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What is the most general way to describe post-measurement states?
Background
Generally speaking, the description of post-measurement states associated with a POVM seems to always pass through, in some form or another, the formalism of Kraus operators. For example:
...
glS♦
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Given a state $\rho$ and operator $0\le \Lambda\le I$, what does $\sqrt\Lambda \rho \sqrt\Lambda$ represent?
An expression that is found in a good number of results is $\sqrt\Lambda\rho\sqrt\Lambda$, for some pair of positive semidefinite operators $\rho,\Lambda\ge0$. For example, in the gentle operator ...
glS♦
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How does interference help to bias the measurement of a qubit towards a desired state?
I just read that :
A fundamental idea in quantum computing is to control the probability a system of qubits collapses into particular measurement states. Quantum interference, a byproduct of ...
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Why after breaking the entanglement does the phase disk in the second qbit not match the result?
I am new in IBM composer quantum and I have a doubt.
I have the next circuit
After reinitializing q0 and reading it. (breaking entanglement) The phase disk for qubit q1 says that 100% is 0, but the ...
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In a state $\alpha \vert HL \rangle + \beta \vert VR \rangle$ can a particle be measured in the $\{|L\rangle,|R\rangle\}$ basis?
Given a pair of entangled particles:
$\alpha \vert HL \rangle + \beta \vert VR \rangle$
where:
$\alpha^2 + \beta^2=1$
$H$ and $V$ are orthonormal vectors.
$L$ and $R$ are orthogonal vectors (but not ...
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What projective measurement discriminates between a set of pairwise orthogonal states?
If we know a set of $K$ states $\{\lvert\psi_j\rangle:j\in[K]\}$ such that they are pairwise orthogonal, and we are given an unknown state $\lvert\psi_i\rangle$, what sort of projective measurement ...
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Finding the Exact Probability Distribution for the Outcomes of a Quantum Circuit with Mid-Circuit Measurements
I would like to find the exact probabilities of the possible outcomes of a circuit that includes mid-circuit measurements.
So, as a specific example, consider the following circuit:
I would like to ...
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Quantum instrument vs POVM
In the Wikipedia article https://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics#Generalized_measurement_(POVM)
They say that the Kraus decomposition of the POVM operators is needed to express ...
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