As of May 31, 2023, we have updated our Code of Conduct.

# Questions tagged [quantum-state]

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

206 questions
Filter by
Sorted by
Tagged with
15k views

### What is the difference between a relative phase and a global phase? In particular, what is a phase?

I know that $re^{i\theta} = x + iy$ for any complex number $x + iy$ by Euler's formula. How do you calculate relative and global phase?
6k views

### What is the difference between superpositions and mixed states?

My understanding so far is: a pure state is a basic state of a system, and a mixed state represents uncertainty about the system, i.e. the system is in one of a set of states with some (classical) ...
2k views

### Find the $\theta$ and $\phi$ values on the Bloch sphere corresponding to the state $\frac{1+i}{2}|0\rangle+\frac1{\sqrt2}|1\rangle$

If I have the following state: $$\left| \varphi \right>=\frac{1}{\sqrt{2}}\left(\left(\frac{1+i}{\sqrt{2}} \right)\left| 0 \right> + \left| 1\right>\right)$$ How can I find the $\theta$ ...
4k views

2k views

### How can infinite information be theoretically encoded or stored in a single qubit?

I've just gotten started with Nielsen and Chuang's text, and I'm a little stuck. They mention that theoretically, it would be possible to store an infinite amount of information in the state of a ...
2k views

### What is the result of measuring $\sigma_x$ on the state $|01\rangle+|10\rangle$?

I confused about how to calculate the probabilities and getting a certain result of measuring Bell's states with Pauli matrices as the operator. When you measure something, the state involved would be ...
15k views

### What is meant by the term "computational basis"?

What is meant by the term "computational basis" in the context of quantum computing and quantum algorithms? 34k views

### What's the difference between a pure and mixed quantum state?

As per my limited understanding, a pure state is the quantum state where we have exact information about the quantum system. And the mixed state is the combination of probabilities of the information ...
6k views

### Why does the "Phase Kickback" mechanism work in the Quantum phase estimation algorithm?

I've probably read the chapter The quantum Fourier transform and its applications from Nielsen and Chuang (10 th anniversary edition) a couple of times before and this took this thing for granted, but ...
6k views

### How can I build a circuit to generate an equal superposition of 3 outcomes for 2 qubits?

Given a $2$ qubit-system and thus $4$ possible measurements results in the basis $\{|00\rangle$, $|01\rangle$, $|10\rangle$, $|11\rangle\}$, how can I prepare the state, where: only $3$ of these $4$ ...
882 views

### Preparing a quantum state from a classical probability distribution

Suppose I have a black-box unitary $U_p$ which is described as follows: given a finite probability distribution $p:\{1,\ldots,n\}\rightarrow \mathbb{R}_{\geq0}$, where $\sum_{x=1}^n p(x)=1$, the ...
356 views

### Help Identifying a Gate In Nielsen and Chuang

I am seeking help to identify the oracle gates listed in this example. I understand that the right-most one is a toffoli gate, but what are the other ones? Specifically, I do not understand what a ...
403 views

### How to implement the Circuit of Steane's code for Quantum Error Correction?

I have referred this same question here 'Circuit for implementing Steane's code for Quantum Error Correction' . But the answer discusses the circuit to compute the syndrome and not clearly the ...
2k views

### Quantum machine learning after Ewin Tang

Recently, a series of research papers have been released (this, this and this, also this) that provide classical algorithms with the same runtime as quantum machine learning algorithms for the same ...
3k views

### How does measurement of one qubit affect the others?

To represent a quantum computer's state, all the qubits contribute to one state vector (this is one of the major differences between quantum and classical computing as I understand it). My ...
8k views

### How to calculate circuit depth properly?

Is the circuit depth the longest sequence of gates applied on one of the qubits? Or is it something more complicated?
2k views

### No-cloning theorem and distinguishing between two non-orthogonal quantum states

I'm currently reading Nielsen and Chuang's Quantum Computation and Quantum Information and I'm not sure if I correctly understand this exercise (on page 57) : Exercise 1.2: Explain how a device which,...
2k views

389 views

### Simulate a quantum channel with a certain fidelity

I am looking for an easy-to-use framework for simulating a quantum channel that can accept the desired average fidelity of the channel as input. For example, if I want a channel with 98% average ...
3k views

### Why do computer scientists care about the phase of qubits?

When I design some classical register, flip-flop, binary counter, small byte of RAM, etc from scratch with classical logic gate, I never deal with such binary direction because classical bit doesn't ...
1 vote
1k views

### How do two qubit states differing by a global phase relate to each other?

I have looked at the following: What is the difference between a relative phase and a global phase? In particular, what is a phase? Global and relative phases of kets in QM Global phases and ...
6k views

### What are magic states?

I wonder what are magic states, and a magic state gadget. While I'm reading a paper, these terms frequently appear.
11k views

### How to input 2 qubits in 2 Hadamard gates?

Let's say we have a circuit with $2$ Hadamard gates: Let's take the $|00\rangle$ state as input. The vector representation of $|00\rangle$ state is $[1 \ 0 \ 0 \ 0]$, but this is the representation ...
800 views

### How to compactly represent multiple qubit states?

Since access to quantum devices capable of quantum computing is still extremely limited, it is of interest to simulate quantum computations on a classical computer. Representing the state of $n$ ...
766 views

### Is acting with a positive map on a state not part of a larger system allowed?

In the comments to a question I asked recently, there is a discussion between user1271772 and myself on positive operators. I know that for a positive trace-preserving operator $\Lambda$ (e.g. the ...
4k views

### How and why does swap test works?

I am having some trouble understanding why a SWAP test would work. I meant I read that and understood the concepts as follows: If the two input states are equal, the output register always results in ...
739 views

Consider an arbitrary $n$-qubit state $\lvert \psi \rangle$. How much do we understand about the probability distribution of the fidelity of $\lvert \psi \rangle$ with a tensor product $\lvert \alpha \... 9 votes 2 answers 4k views ### Measuring in standard basis meaning What does it mean to measure a qubit (or multiple qubits) in standard basis? 8 votes 1 answer 290 views ###$n$qubit vs. a$d=2^n$qudit states and measurements The pure states of a qudit inhabit the$\mathbb{CP}(d-1)$manifold. Is it true that the pure states of$n$qubits live on the$\mathbb{CP}(2^n-1)$manifold? If the answer to the first question is yes,... 6 votes 1 answer 325 views ### Does the circuit with qubit-wise CZ gates compute the inner product of two states? If not, is there another circuit that does? I've been searching for a quantum algorithm to compute the the inner product between two$n$-qubit quantum states, namely$\langle\phi|\psi\rangle$, which is in general a complex number. One can get$|...
How can I get a subspace of a quantum circuit? More precisely, I'm dealing with quantum circuit with data qubits ('q') and ancilla qubits ('anc'), such as $(q_0,q_1,...,q_n,anc_0,..anc_m)$. After some ...