Questions tagged [superposition]

Quantum superposition is a fundamental principle of quantum mechanics. It states that, much like waves in classical physics, any two (or more) quantum states can be added together ("superposed") and the result will be another valid quantum state; and conversely, that every quantum state can be represented as a sum of two or more other distinct states. Mathematically, it refers to a property of solutions to the Schrödinger equation. (Wikipedia)

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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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Mark a state if it is part of another register

I am wondering something, especially about Grover algorithm: imagine I have a quantum register $a$ and a quantum register $b$ of equal length. Then, suppose I apply some algorithms on $a$ s.t. it is ...
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When physically implementing superposition in a Transmon, what is the actual driving amplitude used in the microwave pulses by Qiskit?

I had been playing around with Qiskit Pulse, and I managed to run several single qubit circuits, however throughout these processes, I recurringly came across the driving amplitude and the signal ...
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Given a quantum state, can you generate a uniform superposition over its computational basis vectors with nonzero amplitude?

Given an arbitrary $|\psi\rangle=\sum_{i=0}^n\alpha_i|i\rangle$, $K=\{i\mid \alpha_i\not=0\}$, and $k=\vert K\vert$, is it possible to generate the state $\frac{1}{\sqrt k}\sum_{i\in K}|i\rangle$? I ...
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Why use superpositions to write states even when they are not entangled?

I am reading book "Dancing with Qubits. How quantum computing works". I had learned the rule of entangled state: when quantum state is separable(i.e. it can be written as such a tensor ...
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Can you construct a 3-qubit XOR state?

I'm wondering if it is possible to build a 3-qubit quantum circuit that creates the following pure state: $$\frac{1}{2}\left(|000\rangle+|011\rangle+|101\rangle+|110\rangle\right)=\frac{1}{2}\left[1,0,...
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Does quantum superposition allow to apply an algorithm to all bits possibly in one shot?

From what I understood, quantum programming can solve some algorithm exponentially faster. Thanks to the superposition, unlike a classic bit, which can be either 0 or 1, a qubit can be both 0 and 1. ...
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How does superposition in a quantum register work?

When I put each single qubit within a quantum register using Hadamard gates in superposition, how does it work that the whole register quantum-state is in superposition? On the math-level the register-...
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Surface Code Eigenstates as Circles

I learned that logical $|0\rangle$ of surface code, is an eigenstate, where all stabilizers are +1 value, and since the z-stabilizer is enforcing an even amount of edged in each node, and the x-stab ...
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How to obtain the state $|0\rangle+|1\rangle$ from $|0\rangle$ via Pauli gates?

Could somebody explain in which way are we able to achieve superposition with Pauli $X$, $Y$, $Z$ matrices? In case of Hadamard gate $H$ we change coefficients to $1/\sqrt{2}$ directly, in case of $X$ ...
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Understanding phase kickback caused by the CNOT gate

Applying the CNOT gate to the state |+-⟩ would result in the state |--⟩ as per: What has occurred is a "phase kickback". The relative negative phase from the target qubit has transferred to ...
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Deutsch's algorithm makes no sense

Here are the 4 classical functions over $1$ bit we're examining, $f(x) = \{0,1\}, x \in\{0,1\}$: identity (balanced) -> $f(x) = x$: \begin{bmatrix}1&0\\0&1\end{bmatrix} negation (balanced) ...
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Implementing state which is a superposition of unitaries applied to the same reference

I was wondering if there is exists an (efficient) way to implement the state $$|\Psi\rangle=\left(\sum_i^N c_i|{\psi_i}\rangle\right)=\left(\sum_i^N c_i\hat U_i\right)|{0.....0}\rangle$$ where $\hat{U}...
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Calculating variance among the states under superposition

I wonder if it is possible to calculate (or estimates) variance among the quantum states under superposition, with respect to their values in the computational basis. For example, a simple 2-qubit ...
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Bias in the results of superposition measurements on IBMQ Backends, qiskit

Dear people on this forum, I was doing some research, and I created this circuit in qiskit Please bear in mind that I am really new to this field, and I do not retain much knowledge yet. Therefore I ...
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Does the X (NOT) gate affect superpositions at all?

Does "NOT" gate have any effect on qubit in superposition state? After applying Hadamard gate on qubit seems like the "NOT" gate doesn't have any effect on it. Could somebody ...
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Is it possible to recover a marked bitstring from a superposition?

Is it possible to recover a marked bitstring from a superposition? For example, consider the state $$\lvert \psi \rangle = \frac{1}{2}\left(\lvert 00 \rangle \lvert 0 \rangle + \lvert 01 \rangle \...
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If 3 polarizer experiment to teach quantum superposition can be explained classically, should it not be used to explain Quantum Mechanics?

Here is the link to the Dirac's three polarizer experiment. https://www.informationphilosopher.com/solutions/experiments/dirac_3-polarizers/ When a 90$^o$ and 0$^o$ polarizers are placed in front of ...
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How to create uniform superpostion of N states where N is not power of 2 [duplicate]

Many textbooks only consider superposition of N states where N is a power of 2. For example, H|0> is a uniform superpostion of |0> and |1> and N=2. How to construct quantum circuit for a ...
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Synthesize superposition state using generalized Grover algorithm

I'm following the paper by Grover (L. K. Grover, Phys. Rev. Lett., 85:2000) and trying to synthesize the following superposition state $$|\psi\rangle = \frac{2|00\rangle - 3|01\rangle - 4i|10\rangle + ...
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What does it mean to be in a superposition of eigenstates in a LC oscillator?

In superconducting qubits, we use a circuit with a specific type of inductor and quantize the Hamiltonian. Because it's an anharmonic oscillator, we say that it has states -- $|0\rangle$ and $|1\...
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Quantum algorithm to construct an arbitrary superposition of N integers?

Say for 3 qubits, I want a super position of 0 (000), 2 (010), and 7 (111). Is there a general algorithm for building this superposition? Or for an even super position of N integers? Part of me feels ...
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Is it possible to collapse a superposition into a preset state such that all entangled qubits collapse to the same state?

Ideally, I'd be able to apply an operation to qubit 0 that would collapse the superposition to a set state (say 1) on qubit 0 & 1. The operation applied to qubit 0 would be a one qubit operation (...
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Applying Hadamard gate to $\sqrt{3/4}|0\rangle + \sqrt{1/4}|1\rangle$

[I am just transferring this from Stack Overflow. It might need editing.] ———— [The reader can skip to “It all sounds fine…”, before the spreadsheet representation.] I am trying to figure out quantum ...
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Does the input of the quantum counting algorithm have to be a uniform superposition state?

Will the quantum counting algorithm work if the input is not a uniform superposition (even not a superposition of all basis states)? For example, if I use a state such as : $$\frac{1}{4}(2\vert 0000\...
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How can we keep Schrödinger's cat alive?

We know, Schrödinger's cat inside the box is in the equal superposition state of both alive and dead. We can express its state as $$|\text{cat}_\phi\rangle= \frac{|\text{alive}\rangle+e^{i\phi}|\text{...
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Derivation for the result of performing the Hadamard transform on $|0\rangle^{\otimes n}$ being $2^{-n/2}\sum_x|x\rangle$

It's said that the result of performing the Hadamard transform on n qubits initially in the all |0> state is $$ \frac{1}{\sqrt{2^n}}\sum_x|x\rangle $$ where the sum is over all possible values of x....
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Understanding the association rule between classical to quantum data $|x\rangle=\frac{1}{|\vec x|_2}\sum_{i=1}^d x_i|i\rangle$

I've been reading the paper on Quantum Hopfield Networks by Rebentrost et al. and I'm not sure to quite understand the association rule they mention on page 2. Here's what they say : Consider any $d$-...
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What is the role of entanglement in quantum-computational speed-up?

The way I see it, there are three main quantum properties utilized in quantum computing - superposition, quantum interference, and quantum entanglement. I'm looking to understand which one is ...
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How to derive $|0\rangle=\frac{1}{\sqrt{2}}(|+\rangle+|-\rangle)$?

When learning measurement basis, my teacher told us $|0\rangle=\frac{1}{\sqrt{2}}(|+\rangle+|-\rangle)$ and said that we can derive it ourselves. Along this, he also mentioned $|+\rangle=\frac{1}{\...
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How does superposition apply to quantum computing?

beginner here. I've always heard explanations on quantum computing, all about superposition, entanglement, etc. But how does superposition actually apply to quantum computing? Yeah, its "in ...
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What is the Schmidt decomposition for the 00 + 01 state?

If I try to write the two-qubit state $$ |\psi \rangle = \frac{|0 \rangle |0 \rangle + |0 \rangle |1 \rangle}{\sqrt{2}}$$ as $$ |\psi \rangle = \lambda_0 |\phi_0 \rangle |\phi_0 \rangle + \lambda_1 |\...
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How can one evaluation of $U_f$ in Grover's algorithm use only one query of $f$?

I am very much new to quantum computation and do not have a background in quantum mechanics, which I believe is at the root of my confusion around Grover's algorithm. Suppose that we have a search ...
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2 votes
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Gate Cost to Transform Superposition of Hamming weight 1 states to superposition of arbitrary basis states?

Say you have something like a general-coefficient $n$-qubit W-state, i.e., $$ |\psi\rangle\equiv\sum_{j=1}^n a_j X_{j}|0\rangle^{\otimes n} \ , $$ where $a_j$ are normalized complex coefficients. ...
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Does a CNOT quantum gate violate no cloning theorem? [duplicate]

I am a curious quantum computing learner. :) Once observe the CNOT gate: as you can see there it converts a |+> to |-> in the top or to say in another way it clones the |-> state. So does ...
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When writing data into qRAM, can I do it in a superposition state?

In general, quantum algorithms are said to be hybrid algorithms. Especially when storing data in qRAM, it seems to be done through classical calculations. Is it possible to write this part directly to ...
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Does Toffoli AND conjugate affect superposition if used in Shor's algorithm?

I have come across several papers that use Toffoli AND conjugate to minimize the T-depth. But since it contains a measurement, does it affect Shor's algorithm (in terms of interference, entanglement, ...
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In the hidden subgroup problem for finite Abelian groups, where does the state $\frac{1}{\sqrt{|G|}}\sum_{g\in G} |g,0\rangle$ come from?

I am new to the concept of HSP. Previously, I saw how to solve hidden subgroup problem over $\mathbb{Z}_2^n$, which was Simon's algorithm. Over there the first step was to apply $H^{\otimes n}$, which ...
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4 votes
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How to read a Q sphere representation?

I'm trying to understand the Q-sphere representation of a 3-qubit system. I get that the 3-qubits are in a superposition of 2 different states. The first qubit (rightmost) is in a superposition of <...
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How to get a qubit into superposition?

I have a qubit $$\left| \psi \right> = (\alpha_1 + i\alpha_2 ) \left|0\right> + (\beta_1 + i\beta_2 )\left|1\right>$$ so if i give values $\alpha_1 + i\alpha_2 = 1 + 4i$ and $\beta_1 + i\...
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Is it possible to tune the amplitude of superposition generated by Hadamard gates?

I had a question earlier about generating the superposition of all the possible states: Here. In that case, we could apply $H^{\otimes n}$ to the state $|0\rangle^{\otimes n}$, and each state has the ...
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How to distinguish between collapsed and uncertain qubits in a quantum circuit?

I have been through the Young's double slit experiment. It's a direct proof or instance of showing that a wave is collapsed via observation or measurement, and shows no interference patterns. I want ...
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How to describe the state of a qubit passing through two Hadamard gates? [duplicate]

Describe the state of the qubit at points A, B and C. How does this demonstrate that we need the “ket” (or the vector) representation of qubits, rather than just describing them in terms of ...
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What's the point of a measurement operator? [duplicate]

I was experimenting with quantum circuits in IBM Quantum Experience. I know that the Hadamard gate creates superposition in the qubit, so I created the following circuit: However, when I looked at ...
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Superposition of quantum gates

In the standard model of quantum computation a gate is a unitary that acts on a subsystem. Physically, it can be implemented by some device. Now, any device is also a part of our quantum world, thus ...
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How instantaneous is state preparation in a quantum register, if all possible superpositions are to be initialized equally?

Before the start of a quantum algorithm qubits need to be initialized into a quantum register. How fast can a quantum register of length $n$ be initialized in a way that all possible superpositions of ...
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Is there a way to create a superposition of all the possible states?

If there're four qubits in my circuit, how can I arrange my gates so that the final output state is a superposition of all the possible states of 4 qubits? (there're 16 of them in total). I've tried ...
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Superposition of quantum circuits

Given a quantum circuit $C_1$ that generates a state $\vert\psi\rangle$ and another circuit $C_2$ that generates $\vert\phi\rangle$, is there a way to construct a circuit that outputs $$\frac{1}{\sqrt{...
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Can a single qutrit in superposition be considered entangled?

Often in quantum computing the idea of quantum superposition is introduced well before the concept of entanglement. I suspect this may be because our conception of (classical) computing privileges ...
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Can I switch $\alpha_0$ and $\alpha_1$ conditionally to $\alpha_0>0$ in a state $\alpha_0|0\rangle+\alpha_1|1\rangle$?

I have a single qubit $a$ in state $$ |s\rangle = \alpha_0|0\rangle + \alpha_1|1\rangle $$ $\alpha_0$ may be 0 whereas $\alpha_1$ is always positive and above $0$. Almost always $$\alpha_0 << \...
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