Questions tagged [quantum-state]
Questions about or related to quantum states. Consider using the density-matrix tag when relevant.
1,452
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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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Proof of the 4.11 exercise in the Nielsen & Chuang book
In question 4.11 in Nielsen and Chuang's book, it states that there is a formula to describe any unitary matrix $U$ with two vectors $\vec{n}$ and $\vec{m}$ in the following way:
$$U=\exp(i \alpha) ...
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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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Rabi amplitude in theory vs practice
I am a bit confused with the definition of Rabi amplitude and how it relates to experimental values.
If I understand correctly, we can show a rabi driving (waveform) with the following formula:
$\...
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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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Complexity of the quantum circuits that are needed to implement communication protocol?
Consider the following simultaneous communication problem. Alice and Bob do not share any
entanglement or any common randomness, and cannot communicate directly with each other. As
inputs, x is given ...
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For tetrapartite state, and another way of decomposition, is the Schmidt basis separable?
Consider two tetrapartite quantum states $|\phi\rangle^{AA^\prime BB^\prime}$ and $|\psi_1\rangle^{AA^\prime}|\psi_2\rangle^{BB^\prime}$ in a finite dimentional Hilbert space $\mathcal{H}^A\otimes\...
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Does proximity of two bipartite states in a norm force high overlap between the elements of the Schmidt bases?
I want to know that there is a relation between the distance of two vectors and the corresponding elements of the Schmidt bases.
We assume that two bipartite vectors $|\phi\rangle^{AB}$ and $|\psi\...
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Sufficient conditions for a single-qubit unitary to be the identity
Say I have a unitary $U = e^{-iHt}$ where $H = \alpha X + Z$.
First, suppose $U = I$. Then it rotates a set of initial states to themselves. Say I'm working on a computational basis, then on the Bloch ...
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Can you twist a qubit?
Is it possible to operate on a single qubit by a map which has a nonzero degree?
Let $|c\rangle=c_0|0\rangle + c_1|1\rangle$ represent a qubit state where $c_0,c_1 \in \mathbb{C}$ and $|c_0|^2+|c_1|^2=...
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mechanics of expanding projector operator (two - qubits) in basis of traceless Hermitian Paul operators
I am currently on a set of lecture notes which says that for a state vector $| \psi \rangle_{AB}$ describing a tensor product state, its density operator $| \psi \rangle \langle \psi |_{AB}$ can be ...
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Statevector from Density matrix of non-pure state
I have a state vector of a 16 qubit system. I want to get the wave function (in the form of a state vector) for half and quarter of this system. When I try to make a ...
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How does error accumulate when entangling two distant qubits with limited connectivity?
My goal is to minimize accumulated error when entangling two qubits that cannot be entangled via a single native two qubit gate operation.
I have a coupling map/graph for the qubits of an IBM quantum ...
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Prove the fidelity equals $F( \rho , \sigma) = |\langle \psi_{\rho} | \psi_{\sigma}\rangle|^2$ for pure states
I am trying to learn by myself quantum computing and information and I have a very simple question concerning the demonstration of the following equality: $F( \rho , \sigma) = |\langle \psi_{\rho} | \...
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Upper bound on entanglement entropy of a Product State for any possible partition of the Joint System
Let $|\psi\rangle$ be an $n$ qubit quantum state on a line with Von Neumann entanglement entropy at most $r$ with respect to any bipartition of the qubits (does not have to be a contiguous bipartition)...
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Optimizing Selection of the Optimal Qubit in a 30-Qubit Quantum Circuit
I am working with a quantum circuit consisting of 30 qubits, and for each qubit, I have allocated a dedicated classical register to record individual measurement results. When I execute this circuit ...
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Half Adder using CNOT Gates
As per this schematic of qubits, how this explanation is correct --"If you look again at the four possible sums, you’ll notice that there is only one case for which this is 1 instead of 0: 1+1=10....
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Density matrix and State vector give different result in mesolve in QuTiP
qutip mesolve gives me different population evolve depending on that initial state is state vector or density matrix. And, in some situation, it gives me negative population. It doesn't make sense...
...
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Computing the evolution of expectation values of the Pauli observable
I have a quantum state described by $N$ qubits, and I don't know anything about this quantum state except the expectation value of the single-qubit Pauli observables of the $i$-th qubit ($\langle X_i \...
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How do I prove these gate identities?
How do I approach on solving the below two problems?
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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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How many dimensions does an n-qubit system have?
How many dimensions does an $n$-qubit system have?
What is definition of dimension for a quantum state? Is it related to the number of rows and columns of a density matrix?
My guess is that it has $2^...
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Problems trying to plot the classical Fisher information with Pennylane
I'm working with pennylane. My goal is to plot CFI(Classical Fisher Information)with following quantum state.
With the above equation I set gamma as 0. Then It becomes:
If gamma is not equal to zero,...
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How to design a circuit which produces the state $|\psi\rangle = \frac{1}{2}|{010}\rangle + \frac{\sqrt{3}}{2} |{101}\rangle$?
The quantum state to achieve is:
$$
|{\psi}\rangle= \frac{1}{2}|{010}\rangle + \frac{\sqrt{3}}{2}
|{101}\rangle
$$
So far I know how to produce the $$\frac{1}{2}|{010}\rangle$$ state in qiskit as ...
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Limited qubit number available in Aer Statevector simulator
I tried to run a calculation of 37 qubits with a Statevector simulator on Qiskit. The following is a demo code.
...
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Output of my quantum circuit to create 3-qubit GHZ-like state does not make sense mathematically
I want to create the GHZ-like state, $|\Psi\rangle = \frac{1}{\sqrt{2}} \left(|011\rangle - |100 \rangle \right)$.
I build my circuit in the following way.
apply the x gate to the first and third ...
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Is the inner product operation commutative or associative?
I am currently reading Quantum Mechanics The Theoretical Minimum by Leonard Susskind.
In the second lecture he says that for a given state of a spin $|A\rangle = a|u\rangle + b|d\rangle$: The ...
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Can quantum superposition be thought of as a quantized version of classical bits?
A classical bit is represented by either 0 or 1. However a superposition state is combination of 0 and 1 both with some probability ($|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$). Does it mean that ...
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RY rotation on a qubit
The classical representation of a state on the Bloch sphere is given by
$|\psi\rangle = \cos \frac{\theta}{2} + e^{i \varphi} \sin \frac{\theta}{2}$.
If I want to apply a rotation around the $Y$-axis, ...
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Plotting the Bell state on a Bloch sphere
How can you plot the bell state on a Bloch sphere?
bell = QuantumCircuit(2)
bell.h(0)
bell.x(1)
bell.cx(0,1)
Is there any good reference for understanding how ...
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Visualizing Y-gate operation to achieve quantum state
In the below snippet how qc.y(1) helps to achieve the quantum state $i|10\rangle$ ?
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Help to make the equations of state of qubits?
.., and find their cofacents, after H(q1) ->CNOT(q1,q2) -> H(q2)
On the website https://algassert.com/
The preparation is like this. I understand so far
The preparation is like this. I ...
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Given an observable $O$, what's the achievable maximum value of $\operatorname{Tr}(O\rho)$?
The maximum value of expectation value of an observable $O$ with respect to a density matrix $\rho$ can be computed by using Holder's inequality as follows:
\begin{equation}
\text{Tr}(O\rho) \leq \...
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Inverse channel of the Pauli 4 POVM
I'm currently grappling with a challenge in comprehending the inverse channel of the Pauli 4 POVM. The POVM elements are defined as follows:
$
M_0 = \frac{1}{3} |0\rangle\langle0|, \quad M_1 = \frac{1}...
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Schur's lemma for quantum states
I am trying to understand Lemma 2 in this paper.
Consider a state $\tau_{H^n}=\int \sigma^{\otimes n}_{H} \mu(\sigma)$ where $\mu(\sigma)$ is the measure on the space of density operators on a single ...
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Is unambiguous discrimination between $|+\rangle,|0\rangle,|1\rangle$ possible?
I have a quantum state that is either $|{+}\rangle$ or it is $|{0}\rangle$, $|{1}\rangle$. Is there a way to determine this with a single measurement?
I am assuming not since $|{0}\rangle$, $|{1}\...
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In Deutsch–Jozsa algorithm, why one can safely ignore the last qubit of oracle output?
Wikipedia article about Deutsch-Jozsa algorithm says, under the section Algorithm, that:
At this point the last qubit, $$\frac{|0\rangle - |1\rangle}{\sqrt{2}}$$ may be ignored.
Does it mean that, ...
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What is $O$ such that measuring $O(|\phi\rangle\otimes|0\rangle)$ gives $\langle\phi|H|\phi\rangle$ for $H=\frac13 X+\frac12 I$?
Can someone help me with the following question:
Consider a one-qubit Hamiltonian $ H = \frac{1}{3}X + \frac{1}{2}I $. Give a two-qubit operator $ O $ such that when $ O $ is applied to $ |\phi\rangle ...
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What are the theoretical minimum times for quantum and classical logic gates?
I'm interested in better understanding the ultimate limits on how fast quantum and classical logic gates can be performed. Based on principles like the time-energy uncertainty relationship, there ...
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Is fidelity of mixed $\sigma$ and pure $|\psi\rangle$ equal to $\||\psi\rangle\langle\psi|\sigma\|_1$?
The quantum state fidelity between a pure quantum state $\rho:= \vert \psi \rangle \langle \psi \vert$ and a state $\sigma$ is
\begin{align}
F(\rho, \sigma):= {\rm Tr}[\sqrt{\sqrt{\rho}\sigma\sqrt{\...
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Unambiguous State Discrimination
I have a collection of possible states that are not necessarily orthogonal to each other -- suppose $A_1, A_2, ... A_N, B_1, B_2... B_N$. I get a new state $C$, and I want to determine whether its in ...
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Does integrating w.r.t. the Haar measure commute with taking partial trace?
Consider a density matrix $\rho(U)$ which depends on $U \in SU(2^n)$, corresponding to a state of a composite, finite-dimensional Hilbert space $\mathcal{H} \cong \bigotimes_{i=1}^{2^n} \mathbb{C}^2$ ...
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Understanding quantum computing power of entanglement
I read here that the power of quantum computing lies in the fact that the Hilbert space size of a $n$ qubits register grows exponentially with $n$, but only when entangled.
I would like to understand ...
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How to get resultant statevector after applying parameterized gates in qiskit?
I want to check the expressibility of my ansatz and calculate the resultant statevector on paper seems difficult. Is there a way I can do this in qiskit? I have the circuit for the ansatz which has ...
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Do power laws work for kets and bras?
We know for two real numbers a and b
$$a^3 \times b^3=(ab)^3$$
What if a and b are ket and bra, respectively?
Can i write the below formula?
$$(|0\rangle+|1\rangle)^2(\langle0|+\langle1|)^2=(|0\rangle\...
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Defining quantum memory mathematically
Is it possible that we may define the notion of quantum memory in abstract manner, that is, mathematically? A definition which is hardware independent that may be treated as a mathematical object. We ...
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Implementation of two qubit gate decomposition in local operations
My questions is regards to this paper: https://arxiv.org/abs/1909.07534
The above is the decomposition of a two qubit gate into local operations. Please note they are using a Super Operator formalism....
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Is it possible to distinguish a pure state from a "partially uniform" state?
Let $f$ be a random function mapping $n$ bits to $m$ bits. Let $|\phi\rangle$ be a state that is whether (1) $\sum_x2^{-n/2}|x,f(x)\rangle$ or (2) a pure state $|x,f(x)\rangle$ for some random and ...
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