# 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)

97 questions
Filter by
Sorted by
Tagged with
60 views

### 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 ...
30 views

### 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 ...
1 vote
10 views

### 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 ...
72 views

### 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 ...
1 vote
82 views

### 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 ...
1 vote
65 views

71 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
31 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 ...
43 views

4k views

74 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 ...
35 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. ...
182 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 ...
78 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 ...
53 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, ...
132 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 ...