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# Questions tagged [quantum-state]

Questions about or related to quantum states. Consider using the density-matrix tag when relevant.

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### What is the value of a control qubit as a Controlled-X Gate or Tofolli Gate parameter?

For example in a Controlled-X or Tofolli gate, qubits can be assigned as control bits. But before the measurement ; what are the values of these qubits in the gate tensor since they can not be 1 or 0 ?...
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### Quantum gate count minimization

In classical digital logic, we have K-map and Quine–McCluskey algorithm for minimizing boolean equation, thereby reducing the number of logic gates needed. Is there such a thing in quantum computing?. ...
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### It is possible to obtain amplitudes from superposition with certain probability?

In many papers and books on quantum theory it is written that it is not possible to obtain amplitudes exactly when we have a qubit in superposition. In a course we said that actually it is possible, ...
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### Is there any way to always output |1> if the measurement has a probability to output 1?

Let's say I have an oracle that outputs 1 on a specific input (there can be multiple inputs x so that f(x)=1), else it outputs 0. If there is no such input so that f(x)=1, the quantum state of the ...
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### Set relative phase of qubit to zero without measurement?

Is there a quantum way to set the unknown relative phase of a qubit (assumed in a pure state) to zero, without measurement? The relative phase is not known, otherwise I would subtract it using a phase ...
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### A doubt regarding Mach-Zehnder Interferometer functioning

I am tying to understand the working of Mach-Zehnder Interferometer in the physical sense (how it behaves and why it does so etc.). The source I am referring to is this: (https://www.cs.princeton.edu/...
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### Why can two atoms can be entangled?

As a qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in ...
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### Performing QN-SPSA on hybrid quantum-classical neural networks

I had a question on the TorchConnector module in qiksit_machine_learning (based on this tutorial). If I'm not wrong, is ...
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### When we say that 4 qubits can represent $2^4$ binary bit sequences, how do we iterate to the desired bit sequence?

Being new to QC, always heard that $n$ qubits can represent $2^n$ unique combinations of equivalent binary bits at the same time. We can also say that if we have $n$ data lines, we can pass $2^n$ ...
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### Alternative measurements cost

Most of QKD protocols depends on performing measurements on different basis: Some performs the measurements on two basis (standard basis (Z) and the Hadamard basis (X)). some performs the ...
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### How to get statevector of qubits after running quantum circuits on IBMQ real hardware to calculate the fidelity of all qubits individually?

Is it possible to get the statevector while running quantum circuits on IBMQ real hardware? If getting the statevector is not possible can I still calculate the fidelity of a qubit somehow?. What I ...
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### What is the actual Hilbert space of a $N$-qubit system?

This question seems slightly naive. The Hilbert pace of any 2-level quantum system is given by the Bloch sphere and the algebra of observables arises from $SU(2)$, the Lie group generated by the three ...
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### How does a Hadamard gate impact the initial/previous values of a Qubit? [closed]

I've been studying Quantum Computing and one thing that intrigued me is: given a qubit q1 with an initial value x, when I apply a Hadamard gate on it, then it goes to superposition, so the probability ...
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### Cirq: Getting The Instances (samples) of a Quantum Circuit with Probabilistic Unitaries or Mixtures

The wavefunction simulator in Cirq uses a Monte Carlo approach to simulate a certain subset of quantum noise channels, namely through probabilistic/stochastic application of unitary gates. These are ...
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### How to find initial quantum states from the density matrix?

Recently, I came across density matrix. Given a qubit $|\psi \rangle = \alpha |0\rangle + \beta |1\rangle$, we can find its density matrix by computing $\rho \equiv |\psi \rangle \langle \psi |$. My ...
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### Can a polynomial-sized superposition of computational basis states be prepared with a polynomial-sized quantum circuit?

Suppose I am working with a class of states which consist of a superposition of $O(\text{poly}(N))$ computational basis states on $N$ qubits. Examples of this would be the subspace of states of fixed ...
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### In what contexts are different notations used for indicating measurement outcomes?

I have seen a few different notations for denoting measurement outcomes. Does anyone know of which notation is more widely used in various contexts? For instance, I like referring to this Wikipedia ...
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### Can someone explain to me what is T gate and tdg like im five?

I'm newbie to quantum computing, i read about these two gates on IBM quantum computing docs, but I can't seem to understand what is t-gate and tdg or t-dagger, can someone give me a simple explanation ...
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### what does it mean to "measure a qubit" if measurement is defined on operators

As far as I know "measurement" depends on the two variables : state and operator. So what exactly does measuring a qubit mean? is it implied that the operator is the $Z$ operator on that ...
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### Difficulty of creating arbitrary amplitude-encoded quantum states

Let $b \in \mathbb{C}^N$ be some vector, which we want to encode as a quantum state $\sum_{j=0}^{N-1} b_j |j \rangle$. The problem of achieving this encoding seems to be difficult in many cases, ...
I found this MCQ in a book that my friend gave me. Not entirely sure about this question. When starting from Qubit State $|0\rangle$, which operations when applied (from right to left) will result in ...