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)

Filter by
Sorted by
Tagged with
0
votes
0answers
37 views

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 ...
3
votes
1answer
55 views

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 ...
3
votes
2answers
379 views

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 ...
3
votes
1answer
115 views

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 \...
3
votes
1answer
57 views

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 ...
1
vote
0answers
26 views

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 ...
2
votes
1answer
36 views

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 + ...
4
votes
1answer
74 views

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\...
3
votes
1answer
170 views

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 ...
0
votes
1answer
42 views

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 (...
0
votes
1answer
64 views

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 ...
2
votes
1answer
93 views

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\...
15
votes
1answer
4k views

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{...
0
votes
1answer
46 views

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....
2
votes
1answer
44 views

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 $d$-...
4
votes
2answers
219 views

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 ...
3
votes
3answers
144 views

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}{\...
2
votes
2answers
166 views

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 ...
2
votes
1answer
183 views

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 |\...
3
votes
1answer
66 views

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 ...
2
votes
1answer
33 views

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. ...
0
votes
1answer
105 views

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 ...
3
votes
0answers
56 views

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 ...
1
vote
1answer
47 views

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, ...
3
votes
1answer
105 views

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 ...
3
votes
1answer
207 views

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 <...
1
vote
1answer
94 views

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\...
4
votes
1answer
89 views

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 ...
8
votes
1answer
285 views

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 ...
1
vote
2answers
232 views

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 ...
2
votes
1answer
77 views

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 ...
8
votes
4answers
450 views

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 ...
5
votes
2answers
92 views

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 ...
5
votes
1answer
445 views

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 ...
10
votes
3answers
494 views

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{...
3
votes
1answer
130 views

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 ...
1
vote
2answers
103 views

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 << \...
2
votes
2answers
61 views

Testing superposition states in Q#

I am learning Q# so, as I often do, I am writing some unit tests to play with quantum gates. I was able to write these tests for X gate: ...
0
votes
3answers
88 views

CNOT in reversible computing and entanglement

We have a classical reversible circuit $U$ implementing a classical boolean function $f: \left\{0, 1\right\}^n \to \left\{0, 1\right\}$, which also takes some $a$ ancilla bits, and has side effect of ...
0
votes
1answer
65 views

How to create a Quantum circuit to implement the generation of 3-qubit uniform superposition wavefunction

I want to know experimentally or circuit wise diagram to know how to create a circuit that will produce 3-qubit uniform superposition wave function Can somebody help me in that Thank you in advance
1
vote
1answer
98 views

Which entangled qubit is measured in this example?

Sorry, I am a newbie to quantum computing. I am reading an overview paper (released just a week ago) titled Advances in Quantum Deep Learning: An Overview (Garg & Ramakrishnan, 2020). I am stuck ...
2
votes
2answers
225 views

Are superpositions of an infinite number of states realizable?

I first encounted this idea in Constructing finite dimensional codes with optical continuous variables where it mentions "superpositions of an infinite number of infinitely squeezed states" in the ...
3
votes
1answer
47 views

What are the two measurements per box being done in the Bell Tests in the IBM Quantum Experience "Entanglement and Bell tests" Section

I am confused as to what is being measured in the boxes in the example drawings shown on the Entanglement and Bell Tests section in the IBM Q Experience: https://quantum-computing.ibm.com/docs/guide/...
1
vote
1answer
172 views

Effect of Pauli X gate on minus state using bloch sphere

As I understood, the X gate flips the state around : $X(|0\rangle) = |1\rangle$. It can also be visualized with a $\pi$ rotation around the $x$ axis in the Bloch sphere. I have no problem with that. ...
6
votes
2answers
321 views

Is it right to think of superposition as just angle?

Based on my current understanding, a qubit is represented as a vector $(a, b)$ which satisfy $a^2 + b^2 = 1$. Classical bit one can be represented as $(0, 1)$ and bit zero can be represented as $(1, ...
3
votes
3answers
214 views

Do any two distinct pure states form a basis?

$\newcommand{\bra}[1]{\left<#1\right|}\newcommand{\ket}[1]{\left|#1\right>}\newcommand{\bk}[2]{\left<#1\middle|#2\right>}\newcommand{\bke}[3]{\left<#1\middle|#2\middle|#3\right>}$ In ...
1
vote
1answer
78 views

Why don't I get what I expect when measuring with respect to a different basis?

$\newcommand{\bra}[1]{\left<#1\right|}\newcommand{\ket}[1]{\left|#1\right>}\newcommand{\bk}[2]{\left<#1\middle|#2\right>}\newcommand{\bke}[3]{\left<#1\middle|#2\middle|#3\right>}$ If ...
6
votes
2answers
696 views

Is a qubit always in superposition?

I am introduced to ancilla qubits which are usually initialized to $\vert 0 \rangle$. It seems that an ancilla qubit is equivalent to the $0$ bit in classical computing as it will evaluate to $\vert 0 ...
0
votes
3answers
132 views

Represent qubit in a superposition [closed]

How do we represent a qubit $\vert 1 \rangle$ and put in a superposition (in dirac)?
4
votes
1answer
188 views

Can Toffoli operate on a qubit in superposition?

I understand that CNOT and Toffoli (CCNOT) gates are not universal for quantum computation since they (alone) cannot create superposition. Moreover, it is totally possible to perform a CNOT operation ...