# 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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### QuTiP VS RK45: Which one gives the correct results for time-dependent systems?

I am writing a code for a quantum thermal machine which includes both coherent and dissipative time evolutions in its different stages of operation. However, evolving the system with "mesolve&...
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### 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, ...
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### Universal resource for measurement based quantum computation

Consider universal resources for measurement based quantum computation, as defined here: We are now ready to formulate the following definition. A family $\Psi$ is called a universal resource for MQC ...
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### What is the largest number of stabilizers a pure state can have?

What is the largest number of stabilizers a pure state can have? Elaborately put: Let $P(n)$ denote the Pauli group. Given an arbitrary pure state $|\psi\rangle$, what is the upper limit on how many ...
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### What is the difference between quantum "system", "register" and "Hilbert space"?

As far as I can tell, these terms are interchangeable but I am not sure of this. What is meant by each of the terms "quantum system", "quantum register" and "Hilbert space&...
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### Are $(|00\rangle-|11\rangle)/\sqrt2$ and $(|11\rangle-|00\rangle)/\sqrt2$ the same quantum state?

The state $(|00\rangle-|11\rangle)/\sqrt2$ is an entangled state. If we think about the state $(|11\rangle-|00\rangle)/\sqrt2$, is this also entangled, but with maybe a phase change? The above two can ...
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### I am a beginner and therefore, these three H terms are confusing. "Hemitian", "Hamiltonian", and "Hilbert"

I am a beginner and therefore, these three H terms are confusing. "Hemitian", "Hamiltonian", and "Hilbert". Could someone give proper context and explain these terms . ...
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### How many minimum Quantum Rats are needed to figure out which bottle contains poison?

For the classical Poison and Rat puzzle, we need at least $\lceil\log_2({\rm bottles})\rceil$ rats to figure out the poisoned bottle. If we have Schrödinger’s quantum rats, can we use fewer rats(...
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### From the final quantum state to the quantum circuit composition

When I build a quantum circuit and my initial state is the one composed only by zeros ($|000\ldots 0\rangle$), I have a final state $|\psi\rangle$ that is the result of the application of the quantum ...
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### How do I construt a mixed state for an arbitrary symmetric matrix?

A symmetric matrix can be seen as a density matrix. If I have an arbitrary symmetrical matrix, can I use a quantum random access memory to construct a corresponding mixed state? What kind of quantum ...
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### Why can't we simulate a Qubit using classical computer?

I am completely a noob in terms of quantum computing, have watched several videos to understand what Quantum computers are trying to achieve. I am a programmer of classical computers. We have a ...
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### What are the typical gate times for single-qubit and 2-qubit gates for ion trap, superconducting, neutral atom, photonic, spin QC?

What are the typical gate times for single-qubit and 2-qubit gates for -- ion trap, -- superconducting, -- neutral atom, -- photonic, -- spin quantum computers based on today's technologies?
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### How many physical qubits are needed to encode a logical qubit on ion trap, superconducting, neutral atom, photonic QC?

How many physical qubits are needed to encode a logical qubit on an -- ion trap, -- superconducting, -- neutral atom, -- photonic, -- spin quantum computer based on today's technologies?
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### How to determine the threshold value of the quantum error correction code

How to determine the threshold value of the quantum error correction code, what is the specific method, such as surface code, how to determine the threshold value of the color code with a decoder, I ...
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### Are the first and second qubits of the state $| 111 \rangle + | 010 \rangle + | 101 \rangle + | 000 \rangle$ entangled with each another?

State of qubits: $\frac{1}{2} (| 111 \rangle + | 010 \rangle + | 101 \rangle + | 000 \rangle)$ Are the first and second qubits of this register entangled with each another?
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### How to tranfer given superposition to quantum circuit?

Let's say I have a superposition of qubit defined as $\frac{1}{2} (| 000 \rangle + | 001 \rangle + | 111 \rangle + | 110 \rangle)$ (as given in the answer here: Explanation of output produced by the ...
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### How to apply the Hadamard gate to a given qubit state?

I have this qubit state: $$H \left[ \frac{1}{\sqrt{2}} |0\rangle + \left( \sqrt{\frac{2}{7}}+\frac{1}{\sqrt{7}}i \right) |1\rangle \right]$$ How to solve this given Hadamard gate on qubit? Hadamard ...
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### Reduced density matrix of a Haar random state and its Schmidt decomposition

Consider a Haar random quantum state $|\psi\rangle$. Note that $$\rho =\mathbb{E}[|\psi\rangle\langle \psi|] = \frac{\mathbb{I}_{n}}{2^{n}}.$$ $\mathbb{I}_n$ is the identity operator on $n$ qubits. ...
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### What is the Schmidt number of generalized GHZ and W states?

Consider generalizations of the GHZ state and the W state to $n$ qubits. What is the Schmidt number of these two states for any bipartition $c n$ and $(1 - c) ~n$, for $c < 1$? Does it depend on ...
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### How to multiply two vectors (kets) in qiskit?

Hi does anyone know how i could write a program to get the product of something like |1>|0>|0>?
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### Applying CNOT in series to ancilla qubit

$\renewcommand{ket}{\left| #1 \right\rangle}$ $\renewcommand{bra}{\left\langle #1 \right|}$Suppose we have to qubits both in the state $\ket{+ }= \frac{1}{\sqrt{2}}(\ket{0}+\ket{1})$, and we ...
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### Why can the most general state of a qubit be written as $|\Psi\rangle=\cos(\frac\theta2)|0\rangle+e^{i\phi}\sin(\frac\theta2)|1\rangle$?

Why we can express a most general qubit as $|\Psi\rangle = \cos{\left(\frac{\theta}{2}\right)}|0\rangle + e^{i \phi} \sin{\left(\frac{\theta}{2}\right)} |1\rangle$? Is there any formal proof for this?
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### How to determine the basis state with maximum amplitude without measurement?

Suppose I have two quantum registers described respectively by the quantum states $| \psi_1 \rangle = \sum_i \alpha_i |i \rangle$ and $|\psi_2 \rangle = |0\rangle$. I would like to implement a CNOT ...
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### Eigenvalues and energy levels of 1D Heisenberg model using real Quantum Computers?

The 1D Quantum Heisenberg model is $$H_\textrm{Heisenberg} = -~J \sum_{\langle i\ j\rangle} \hat{S}_{i} \cdot \hat{S}_{j}$$ where each spin is an operator. For simple cases, for example, a system with ...
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### Show that $\langle v,O(v)\rangle= \mathrm{tr}(O|v\rangle\langle v|)$ for $v \in V$

I have a question regarding this exercise: Let O be an observable on V. Show that $\langle v,O(v)\rangle= \mathrm{tr}(O|v\rangle\langle v|)$ for $v \in V$. I thought that this exercise is quite easy ...
### Why can we write $\rho=\sum_\mu q_\mu|\varphi_\mu\rangle\!\langle\varphi_\mu|$ iff $q\preceq \mathrm{spec}(\rho)$?
Exercise 2.6 in Preskill's notes (chapter 2, around page 48, pdf available here) asks to prove that an arbitrary state $\rho=\sum_i p_i |\alpha_i\rangle\!\langle\alpha_i|$, where $p_i$ and \$|\alpha_i\...