Quantum Computing Stack Exchange Community Digest

Top new questions this week:

What is the difference between the "Fubini-Study distances" $\arccos|\langle\psi|\phi\rangle|$ and $\sqrt{1-|\langle\psi|\phi\rangle|}$?

I sometimes see the "Fubini-Study distance" between two (pure) states $|\psi\rangle,|\phi\rangle$ written as $$ d(\psi,\phi)_1=\arccos(|\langle\psi|\phi\rangle|), $$ for example in the Wikipedia page. ...

fidelity state-space-geometry  
asked by glS 5 votes
answered by Chris Ferrie 5 votes

Global phase and single qubit gate: does it actually matter for two (or more) qubit gates?

Consider the $X$ gate. Mathematically, we have $X=i e^{-i\frac{\pi}{2} X}$ But as global phase of unitaries don't matter because they will simply act a global phase to the wavefunction, we can ...

algorithm quantum-gate  
asked by StarBucK 5 votes
answered by Chris Ferrie 5 votes

Why is the size of the top register for Shor's algorithm chosen as it is?

Let $N$ be the number we're trying to factor. In Shor's algorithm, the top register then has $2 \lceil\log_2(N)\rceil+1$ qubits, while the bottom register (the ancilla qubits) has ...

shors-algorithm  
asked by David Cian 4 votes
answered by John Watrous 6 votes

Constructing a circuit for $C^1(U)$ for rotation operators with TWO single qubit gates and CNOT gate

This is the exercise 4.23 from Nielsen and Chuang, asking that if it is possible to construct $C^1(U)$ for $U=R_{x,y}(\theta)$ with TWO single qubit gates and CNOT gate. My answer is no, and I would ...

quantum-gate circuit-construction nielsen-and-chuang  
asked by fagd 3 votes
answered by DaftWullie 1 vote

Where are the physical gates in the Google processor?

Google's article Quantum supremacy using a programmable superconducting processor states that the processor "53 qubits, 1,113 single-qubit gates, 430 two-qubit gates, and a measurement on each qubit, ...

quantum-gate physical-realization google-sycamore  
asked by vy32 3 votes
answered by Mark S 4 votes

Quantum computing w.r.t. the many-worlds theory

Quantum algorithms are inherently probabilistic. Let's say I run Shor's factoring algorithm on some number. There's a chance that the output I observe is incorrect. Does the many-worlds theory suggest ...

algorithm shors-algorithm  
asked by TWal 2 votes
answered by czwang -1 votes

How will quantum computers access large amounts of storage?

I've seen many articles in the popular press saying that quantum computers will enable searching through huge amounts of data in an instant. But I can't figure out how the current architectures can do ...

quantum-gate physical-realization quantum-memory  
asked by vy32 2 votes
answered by Martin Vesely 1 vote

Greatest hits from previous weeks:

How to show a density matrix is in a pure/mixed state?

Say we have a single qubit with some density matrix, for example lets say we have the density matrix $\rho=\begin{pmatrix}3/4&1/2\\1/2&1/2\end{pmatrix}$. I would like to know what is the ...

quantum-state quantum-information mathematics density-matrix  
asked by bhapi 4 votes
answered by DaftWullie 8 votes

Understanding the oracle in Deutsch's algorithm

I am reading John Watrous' notes from his course CPSC 519 on quantum computing. In a pre-discussion before presenting Deutsch's algorithm to determine whether a function is constant or not, the author ...

algorithm deutsch-jozsa-algorithm  
asked by IntegrateThis 5 votes
answered by Mariia Mykhailova 8 votes

Can the Bloch sphere be generalized to two qubits?

The Bloch sphere is a nice visualization of single qubit states. Mathematically, it can be generalized to any number of qubits by means of a high-dimensional hypersphere. But such things are not easy ...

resource-request bloch-sphere state-space-geometry  
asked by James Wootton 16 votes
answered by Craig Gidney 13 votes

How to interpret a quantum circuit as a matrix?

If a circuit takes more than one qubit as its input and has quantum gates which take different numbers of qubits as their input, how would we interpret this circuit as a matrix? Here is a toy ...

quantum-gate matrix-representation  
asked by Archil Zhvania 15 votes
answered by heather 17 votes

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  
asked by Ali Javadi 17 votes
answered by Ali Javadi 19 votes

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 ...

notation  
asked by Ella Rose 30 votes
answered by jk - Reinstate Monica 19 votes

Quantum states are unit vectors... with respect to which norm?

The most general definition of a quantum state I found is (rephrasing the definition from Wikipedia) Quantum states are represented by a ray in a finite- or infinite-dimensional Hilbert space over ...

quantum-state notation unitarity mathematics  
asked by Nelimee 14 votes
answered by user1271772 5 votes

Can you answer these questions?

Quantum state discrimination and lower bound for conditional von Neumann entropy

Consider two quantum states $\rho_A$ and $\sigma_A$, and define the classical-quantum state over a classical binary system $B$ and $A$, $$\omega_{AB}^\epsilon :=\epsilon \vert 0 \rangle \langle 0 ...

quantum-information measurement entropy  
asked by Artemy 1 vote

Does the massive parallelization in Quantum computing imply parallelization of input (as opposed to Turing machine)?

Being a newbie in this field, I'm trying to understand what types of real-life workloads are suitable for migrating to Quantum computers. Intuitively, it seems to me that if a Quantum computer ingests ...

classical-computing performance quantum-parallelism quantum-turing-machine  
asked by Erez Buchnik 1 vote
answered by Martin Vesely 0 votes

Convexity of coherent information - erroneous argument!

Consider a state $\rho_{AB}$. Let it have purification $\psi_{A'AB}$. I am interested in the coherent information of this state which is given by $$I(A\rangle B)_\rho = S(B)_\rho - S(AB)_\rho$$ I ...

quantum-information entropy  
asked by user1936752 2 votes
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