Questions tagged [quantum-state]

Quantum systems can mathematically be described by their 'quantum state'. When the system is closed/isolated, the state is 'pure' and can be written as a sum (i.e. 'superposition') of basis vectors. When the system is a subsystem of an open system, the state is instead usually 'mixed' and cannot be written as a pure state, so has to be written as a density matrix. Consider using the density-matrix tag when relevant

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What can be inferred about the closeness of reduced qubit states from the closeness of the bipartite quantum state?

Given a qubit state $|\psi\rangle \in \mathcal{H}$, and two bipartite general mixed states $\rho$ and $\sigma$, such that, $$\langle \psi|\otimes \langle \psi|\rho - \sigma |\psi\rangle \otimes |\psi \...
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Is the Hilbert-Schmidt probability simply zero that a generic rank-2 two-qubit (“pseudo-pure”) density matrix is separable?

The multifacted evidence is very compelling--although not yet presented in a formal proof--that the Hilbert-Schmidt probability that a generic (full rank/rank-4) two-qubit density matrix is separable ...
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Can you encode two values in a single qubit state, say its phase and orientation?

I had an interesting talk with someone who said that we can use a single qubit to encode two different values. We encode the first value in its orientation (up/down) of particle/wave (electron, photon,...
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Quantum-Assisted Neural Network Training (Is my design reasonable?)

I'm a college student with a slight interest in quantum mechanics. I think I have a decent understanding of the Copenhagen and Many Worlds interpretations of quantum mechanics, and was considering how ...
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How the simulator work?

Recently I focused on how to simulate in classical computer, and I found Qiskit offers qasmsimulator and statevector simulator. ...
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Are there any resources of lists of attempts at non-probabilistic models of quantum mechanics, with debunking?

For example, some introductory resource I was reading years ago (forget which one) brought up such an attempt: imagine if a qbit wasn't a complex state vector which collapses probabilistically on ...
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How can I represent mixed states in Q#?

I have a mixed state with a density matrices corresponding to $\rho=\sum_0^{2^n-1}p_i|i\rangle\langle i|$. How would i represent this in Q#? How would I go about applying Unitary Operations $U$ on ...
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Correct interpretation of a Quantum State

If a quantum system is described to be only in Quantum states $s_1$ and $s_2$ (described by computational basis $\vert {0} \rangle$ and $\vert {1}\rangle$) or a combination of both (for a qubit system ...
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How to prepare a quantum circuit for $\frac{1}{\sqrt{3}}(|00\rangle+|01\rangle+|10\rangle)$ starting from $|00\rangle$

How do I prepare a quantum circuit for $\frac{1}{\sqrt{3}}(|00\rangle+|01\rangle+|10\rangle)$ state starting from the $|00\rangle$ state? I have no clue how to do it. I tried with controlled Hadamard ...
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How to measure the sign of quantum amplitudes

I have a quantum state on $ n $ qubits ($ 2^n $ amplitudes) for which I know the amplitudes are real numbers. I want to take the state out as a vector. I can estimate the magnitude of the amplitudes ...
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Expectation value of an operator error: Composition is not defined over operators of different dimensions,

I am trying to calculate the expectation value of a customized operator on two similar but differently constructed states $\phi = \phi_2 =\frac{1}{\sqrt{2}}\left( |001⟩ + |011⟩\right)$ which consist ...
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What's the purpose of phases in quantum mechanics?

I know this it's perhaps, a little "stupid" question, but... What's the purpose of phase in Quantum? Per example, in quantum Computing, the phase don't seems to be very important in the ...
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How do we restrict to a limited number of dimensions, say 3 for qutrits, while using OAM states of light?

When a azimuthal phase $\mathrm{e}^{il\phi}$ is applied to gaussian beams having plane wavefront, they develop a corkscrew sort of structure and therefore possess an orbital angular momentum in ...
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Visualizing “interference” in Quantum Programs

I'd like to develop an intuition about interference in QC programs and was hopeful that some visualization vehicle (like the bloch sphere) would be available to assist in developing an intuition of ...
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Joint system of RAB after purification of A into R

Given a pure state $|\psi\rangle_{AB}$ on a joint system $AB$, we can consider the reduced density operator $\sigma_A = Tr_B(|\psi \rangle \langle \psi|)$ on $A$ and subsequently purify this state ...
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A question about how does the single qubit gate simulated in simulator?

I have found the procedure of simulation process as this picture : Image reference. So in the low-level compilers, all single-qubit gates are approximated by the universal gate set (CNOT, H, T, S). ...
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Creating a specific cluster state

I have a state $$\dfrac{1}{2}(|00000\rangle+|00111\rangle+|11101\rangle+|11010\rangle)$$ How does one create this state. In general, how does one create for instance an $n$-bit cluster state, is there ...
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Can we have multiple-state unit for quantum computer?

All quantum computers now are working with qubit which is zero or one. Can we have quantum computer with multiple-state unit? Such as trit (trinary, 3 states), digit (10 states) instead of qubit (2 ...
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Are quantum operations reversible?

If We perform some unitary operations on a Quantum State $|A\rangle$ after which it becomes$|A'\rangle$. Then if we perform the inverse of all those unitary operations on the state $|A'\rangle$ in ...
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Are separable, orthogonal states LOCC distinguishable?

Consider two states $\sigma_0,\sigma_1\in\text{L}(\mathcal{H}_{AB})$, and suppose $\sigma_0,\sigma_1$ are separable and orthogonal. Is it possible to distinguish between $\sigma_0,\sigma_1$ through ...
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How do I encode a classical vector into the input qubits?

Does anyone know how to encode a classical vector into a quantum state? For instance, I would like to encoder a classical vector $(0, 0.1, 0.4, 0.9)$ into 2 qubits by adding some quantum gates on 2 $|...
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How can I print out a state vector of a specific wire?

Suppose we start from 2 wires (q0 and q1) and through some quantum gates, suppose we measure q1 wire only. As we measure the q1 wire, the state vector of this quantum state would be determined ...
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If two reduced density matrices are equal, does that mean that the two subsystems are the same?

Suppose we have a $3$-qubit system at time $t_0$ in the state $$\vert{\psi(t_0)}\rangle= \vert{q_0}\rangle \otimes \vert{q_1} \rangle \otimes \vert{q_2}\rangle. $$ We want to check if, for instance, ...
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Density matrix of spatially (i.e., at the same time instant) vs. causally ( i.e., one evolves into the other) correlated quantum systems

In the classical case, if Y is the output of a classical channel whose input is X, it makes sense to speak of a joint distribution $P_{XY}$. In the quantum case, if a state $\rho_A$ is input to a ...
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Finding phase angle in Q#

I've trying to measure the phase angle from X axis of a qubit, but unable to find any function in Q# documentation, can anyone help me with this?
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What is the shortest sequence of decomposition a given single-qubit unitary gate

Given a single-qubit unitary matrix, can we find the shortest sequence of Clifford + T gates that correspond to that unitary? According to Fast and efficient exact synthesis of single qubit unitaries ...
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How can I create a basis state of $n$ qubits in Q#?

I would like to create a set of basis qubits. For example if I have $n=2$ I should get 4 states being 01 10 11 00. Generalized for $2^n$. Is there a way to do this in Q#?
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Confusion over HSW theorem depicted in Nielsen and Chuang

On page 560, it states that $$C^{(1)} \geq S(\frac{\varepsilon(|{\psi}\rangle\langle{\psi}|) +\varepsilon(|{\varphi}\rangle\langle{\varphi}|)}{2} - \frac{1}{2}\varepsilon(|{\psi}\rangle\langle{\psi}|)-...
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Are Bell states distinguishable through LOCC?

Define $|\psi^{00}\rangle = \frac{1}{\sqrt2}(|00\rangle + |11\rangle)$ and $|\psi^{01}\rangle = \frac{1}{\sqrt2}(|00\rangle - |11\rangle)$, and consider the state $$ |0\rangle\langle 0|^C\otimes |\psi^...
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Indexing an “unknown” quantum state

Assuming I have a state $$|x\rangle = \frac{1}{\sqrt{n}}\sum_n |x_n\rangle$$ where $|x_n\rangle$ are quantum state vectors $$|x_n\rangle = \frac{1}{\|x_n\|}\sum_i x_{in}|i\rangle$$ and that I have a ...
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How to prepare an arbitrary two-qubit state?

I know that to prepare a Bell state say $|\phi^+\rangle$, we need to initial state $|0\rangle,|0\rangle$ and then perform a Hadamard on the first and then use it as control to do a NOT gate on the ...
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Why do I get positive amplitudes when I create a qiskit StateVectorCircuit from only negative amplitudes?

I am using amplitude encoding to encode my features in a quantum circuit. With this I expect to encode e.g. 32 features in five qubits. For the encoding I use qiskit's ...
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What can be said about the closeness of two states if the difference of their fidelity measured with respect to a fixed state is close to 0?

Suppose I have two states $\rho$ and $\sigma$. We are given that, $$Tr((\rho - \sigma)|\psi\rangle\langle\psi|) \geq \epsilon$$ where $|\psi\rangle$ is a fixed state and $\epsilon \rightarrow 0$, ...
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How to apply the Schmidt Decomposition to a Bell state?

I am trying to understand the Schmidt Decomposition, currently in my QC class. We had a tutorial where we were told if $|\psi\rangle$ is a pure state of a composite system A then there exists $|i_A\...
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Why is the function $f_s(x)=\sum_i x_i s_i \pmod 2$ balanced?

A parity function $f_s:\{0,1\}^{n}\rightarrow\{0,1\}$, for some $s\in \{0,1\}^n$, is a function of the form $f_s(x) = x \cdot s$, where the inner product is taken modulo 2. Show that $f_s$ is a ...
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A question about a real programmable quantum computer

In the theory of universal quantum gates,I have known a common universal gate set is the Clifford + T gate set, which is composed of the CNOT, H, S and T gates. Then there is a concept called "...
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How many samples are required to estimate the probabilities of a state?

Suppose that we have a quantum state of the form: $$|\psi\rangle = \sqrt{p}|0\rangle + \sqrt{1-p}|1\rangle$$ In order to get an estimate of the probability of reading $|0\rangle$ or $|1\rangle$, we ...
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Find the probability of a measurement outcome in terms of the coefficients of the state

Suppose we have a quantum state $|\psi \rangle$ of $n$ qubits, where $|\psi\rangle=\sum_{x∈\{0,1\}^n}\alpha_x |x\rangle$,and we measure the first qubit of $|\psi\rangle$ in the computational basis. ...
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Computing variance under the action of a unitary operator

I wish to calculate the expectation and variance for an observable on a particular qubit of a multi qubit quantum state. I'm using a quantum computing simulation library which allows me to apply ...
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Understanding global phase

I have looked at the following: What is the difference between a relative phase and a global phase? In particular, what is a phase? Global and relative phases of kets in QM Global phases and ...
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Example of a quantum algorithm better than its classical counterpart which involves only $1$ qubit?

I was reading over the proof of the Deutsch-Jozsa algorithm, which in its simplest case, involves at least 2 qubits. Is there an example of a quantum algorithm that is better than it's classical ...
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What is the physical meaning of the Hamiltonian $H = \alpha ( |01 \rangle \langle10| + | 10 \rangle \langle 01| )$?

In natural basis $| 0 \rangle = \begin{pmatrix} 1 \\0 \end{pmatrix}$, $| 1 \rangle = \begin{pmatrix} 0 \\ 1 \end{pmatrix}$, what physical situation/model does the following Hamiltonian represent: $H = ...
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A question about how to emulate quantum states and computation on classical computer

I have understood the concept of "universal quantum gates" in real quantum computer, and the quantum gates and states can be emulated as matrix in classical computer, and the matrix operation can be ...
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How can I initialize a state with chosen amplitudes in Qiskit?

I was trying to initialize to an arbitrary state of n qubits with the initialize() from Qiskit but it doesn't generate a state with the same amplitudes passed as an ...
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How to decompose a unitary single qubit gate by universal quantum gate set?

How to decompose a unitary single qubit gate? I have read some paper or books, which told me a unitary single qubit gate could be decomposed by universal quantum gates set. For example {phase gate, ...
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Bipartite states whose coefficients are entries of a unitary matrix

I've been trying to solve this question It seems that in order to show it has unit length, we must show that $$ \frac{1}{d} \sum_{m, n=0}^{d=1} \lvert U_{m, n}\rvert ^2 = 1 $$ I've tried searching ...
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What are the possible qubit states?

For a quantum state on the form $$|\psi \rangle = \alpha |0 \rangle + \beta |1 \rangle$$ which possible qubit states can you construct from this? I know that $\alpha$ and $\beta$ must satisfy $$|\...
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Find the number of elements in the Schmidt decomposition of a pure state

Consider a pure state $\boldsymbol{\eta} \in \mathcal{H}_{AB}$. There exist orthonormal sets $\{\alpha_1, \alpha_2 \dots \alpha_i\} \subset \mathcal{H}_A$ and $\{\beta_1, \beta_2 \dots \beta_i\} \...
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How to simulate master equation with a term of “cascaded formalism” with QuTiP?

I would like to simulate this master equation with QuTiP. The term in the second line is the so called "cascaded formalism" used for eliminates any feedback from system to the input nodes. But the ...
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Show that $I = \frac{\rho + \sigma_x\rho\sigma_x +\sigma_y\rho\sigma_y + \sigma_z\rho\sigma_z}{2}$ for all states $\rho$

I am trying to show that for any qubit state p, the following holds: $$I = \frac{\rho + \sigma_x\rho\sigma_x +\sigma_y\rho\sigma_y + \sigma_z\rho\sigma_z}{2}$$ I have tried different manipulations,...

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