## 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

### 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

### 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

### 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

### 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 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

### 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
 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

### 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

### 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

### 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

### 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

### 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

### 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

## Can you answer these questions?

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