Quantum Computing Stack Exchange Community Digest

Top new questions this week:

closeness between two unitaries on the bloch sphere

The fidelity between two (single-qubit) quantum states can be easily translated into the euclidean distance between the two states on the Bloch sphere (hilbert-schidmit distance). I'm curious if this ...

mathematics unitarity bloch-sphere linear-algebra  
user avatar asked by Hailey Han Score of 4
user avatar answered by Jonathan Trousdale Score of 2

Grover / amplitude amplification with exponentially high success probability

All the references on Grover / Amplitude Amplification (AA) (Mike&Ike, wiki, Lin Lin lecture notes, etc.) give a recipe for preparing the desired state (or amplifying the state) with probability $\...

grovers-algorithm amplitude-amplification  
user avatar asked by mavzolej Score of 4

How do I solve or start solving Preskill problem 2.1, concerned with the fidelity of measurement?

In Preskill's lecture notes on quantum information, problem 2.1 is concerned with the fidelity of measurement. Specifically, it defines the relative angle between two states as the inverse cosine of ...

textbook-and-exercises information-theory  
user avatar asked by requiemman Score of 4

How do I find the reduced density matrix of a system where two people share one qubit and have one qubit of their own?

I have the following problem and have attempted to find a solution to it, but to no avail. Alice and Bob have one qubit each, say $|\psi\rangle$ with Alice and $|\phi\rangle$ with Bob. They also share ...

textbook-and-exercises density-matrix  
user avatar asked by requiemman Score of 4
user avatar answered by Danylo Y Score of 3

Efficient way to calculate trace of product of Pauli string and matrix?

Basically the title, but more formally: is there a way to efficiently calculate the trace of the product of a Pauli string $P$ and a $2^n \times 2^n$ matrix $M$? That is, is there a way to calculate ...

pauli-gates trace pauli-group  
user avatar asked by Physics Penguin Score of 4
user avatar answered by Danylo Y Score of 2

What is the initial state in the second register in Shor's algorithm?

Following up on this question, can someone help me clear up the notation we're using for states in Shor's algorithm? It's very unclear what the sentence "where the second register is $|1\rangle$ ...

algorithm shors-algorithm  
user avatar asked by Jackson Walters Score of 3
user avatar answered by glS Score of 3

Proof of the 4.11 exercise in the Nielsen & Chuang book

In question 4.11 in Nielsen and Chuang's book, it states that there is a formula to describe any unitary matrix $U$ with two vectors $\vec{n}$ and $\vec{m}$ in the following way: $$U=\exp(i \alpha) ...

quantum-state nielsen-and-chuang  
user avatar asked by Matodo Score of 3
user avatar answered by DaftWullie Score of 2

Greatest hits from previous weeks:

How do I add 1+1 using a quantum computer?

This can be seen as the software complement to How does a quantum computer do basic math at the hardware level? The question was asked by a member of the audience at the 4th network of the Spanish ...

quantum-gate circuit-construction physical-realization  
user avatar asked by agaitaarino Score of 46
user avatar answered by Mithrandir24601 Score of 30

How can I implement an n-bit Toffoli gate?

I want to create a Toffoli gate controlled by n qubits, and implement it in QISKit. Can this be done? If so, how?

quantum-gate programming qiskit  
user avatar asked by Ali Javadi Score of 28
user avatar answered by Ali Javadi Score of 25

What is the "surface code" in the context of quantum error correction?

I am studying Quantum Computing and Information, and have come across the term "surface code", but I can't find a brief explanation of what it is and how it works. Hopefully you guys can ...

error-correction terminology surface-code  
user avatar asked by Ivanovitch Score of 41
user avatar answered by James Wootton Score of 29

How does the vectorization map relate to the Choi and Kraus representations of a channel?

I know that the Choi operator is a useful tool to construct the Kraus representation of a given map, and that the vectorization map plays an important role in such construction. How exactly does the ...

quantum-operation kraus-representation  
user avatar asked by Tobias Fritzn Score of 13
user avatar answered by John Watrous Score of 22

Is there proof that the D-wave (one) is a quantum computer and is effective?

I'm admittedly a novice in this field, but I have read that, while the D-wave (one) is an interesting device, there is some skepticism regarding it being 1) useful and 2) actually a 'quantum computer'....

performance annealing d-wave classical-computing experiment  
user avatar asked by Discrete lizard Score of 48

How does bra-ket notation work?

Quantum algorithms frequently use bra-ket notation in their description. What do all of these brackets and vertical lines mean? For example: $|ψ⟩=α|0⟩+β|1⟩$ While this is arguably a question about ...

user avatar asked by Ella Rose Score of 45
user avatar answered by Sir Cornflakes Score of 28

How do I apply the Hadamard gate to one qubit in a two-qubit pure state?

So in lectures I see lots of these: And somehow I intuitively understand it (at least for the 1 qubit case), but I don't understand the math – especially for 2 qubits.

mathematics hadamard  
user avatar asked by John T Score of 3

Can you answer these questions?

4 qubit QFT decomposition in the qiskit textbook

I am reading about the quantum Fourier transform (QFT) in the qiskit textbook, but got stuck at the last part of it which shows a decomposed version of the 4 qubit QFT circuit. It seems that the ...

qiskit quantum-circuit quantum-fourier-transform  
user avatar asked by pilsungk Score of 3

How does Qiskit's oracle synthesizer work?

Qiskit provides a phase oracle method that takes a Boolean formula as input and returns a phase oracle circuit for that function as output. Their source code informed me that the synthesis uses the ...

qiskit oracles  
user avatar asked by 이희원 Score of 1

Superconducting charge qubit and Cooper pairs

In the superconducting charge qubit implementation of the qubit what I've understood is that we read a 1 if a Cooper pair has gone through the Josephson Junction into the "island" and we ...

user avatar asked by Omeglac Score of 1
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