Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

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1500 questions
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votes
3 answers

How can I see, without math, the action of a gate in matrix form?

Suppose we have the Fredkin gate with $$ F= \left( {\begin{array}{cc} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 &…
Bidon
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3 answers

How to prepare mixed states on a quantum computer?

I am a little bit confused by density matrix notation in quantum algorithms. While I am pretty confident with working with pure states, I never had the need to work with algorithm using density matrices. I am aware we can have/create a quantum…
Nicholas Sathripa
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3 answers

Unentangling a qubit from a system: can we convert $\alpha|000\rangle+\beta|111\rangle$ into $\alpha|00\rangle+\beta|11\rangle$?

Let's say I start with the following arbitrary qubits: $$ \color{red}{\vert Q_1 \rangle = \alpha_1 \vert 0 \rangle + \beta_1 \vert 1 \rangle}\\ \color{green}{\vert Q_2 \rangle = \alpha_2 \vert 0 \rangle + \beta_2 \vert 1…
M. Al Jumaily
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Changing one qubit causes changes in another independent qubit on ibmqx2 in IBM Q Experience

When I run this program on ibmqx2 (the backend matters) in IBM Q Experience, the results are interesting. Essentially, the program measures the error rate on $|q_0\rangle$ after fiddling with $|q_1\rangle$. OPENQASM 2.0; include "qelib1.inc"; gate…
balios
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What are the "nice" properties of the diamond norm and why is it used?

I have heard about the diamond norm, and from what I understood it is a "nice" tool to quantify quality of quantum gates in the NISQ era. I would like to know a little more before going in detail in the litterature. My question are the…
Marco Fellous-Asiani
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How to transform e.g., a 4 by 4 unitary matrix into a quantum circuit

I am new to Quantum Computing. I would really appreciate if some one could offer me some ideas, suggestions and/or useful references to solve the following problem about realizing an arbitrary operator by a quantum circuit. If I start with a general…
Marxmas
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How to prepare Unitary Coupled Cluster ansatz for VQE in a circuit?

I have read the following paper by Dumitrescu et al. To make a Unitary Coupled Cluster (UCC) ansatz, one prepares with the following equation. $$ | \psi_{\rm{UCC}} \rangle = U(\theta)|\mathrm{HF}\rangle $$ Here, $U(\theta) = \exp[ T(\theta) -…
Ashy
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How to perform quantum state tomography on two qubits?

I would like to do a quantum tomography on two qubit states. Recently, I successfully did so for one qubit based on Nielsen-Chuang. They advise to use this formula for one qubit density operator estimation: \begin{equation} \rho =…
Martin Vesely
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Query on Reduced Graph States

Reduced graph states are characterized as follows (from page 46 of this paper): Let $A \subseteq V$ be a subset of vertices of a graph $G = (V,E)$ and $B = V\setminus A$ the complement of $A$ in $V$. The reduced state $\rho_{G}^{A}:=…
John Doe
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Is there a mistake in the VQE Ansatz in Cirq's tutorial?

I have been going through Cirq's VQE background tutorial and after examining the Ansatz it seems to me that the only layer that actually affects the final measurement is the rot_x_layer. The other layers simply act on the phases and therefore seem…
dncolomer
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8
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Better "In-Place" Amplification of QMA

$\def\braket#1#2{\langle#1|#2\rangle}\def\bra#1{\langle#1|}\def\ket#1{|#1\rangle}$ In MW05 the authors demonstrate so-called "in-place" amplitude amplification for QMA, exhibiting a method for Arthur to amplify his success probability without…
bean
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Prove that $\|p^{\otimes n} - q^{\otimes n}\| \leq n \|p-q\|$ for density operators $p,q$

I've been trying to figure this out for a while and I'm totally lost. My goal is to show that for two density operators $p$, $q$, that $$\|p^{\otimes n} - q^{\otimes n}\| \leq n \|p-q\|$$ So far I have constructed a weak inductive hypothesis over n…
Confused grad student
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8
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1 answer

How to factor Ising YY coupling gate into product of basic gates?

Let us consider Pauli YY coupling gate of the following form $$ YY_\phi= \left(\begin{matrix} \cos(\phi) & 0 & 0 & i \sin(\phi) \\ 0 & \cos(\phi) & -i \sin(\phi) & 0 \\ 0 & -i \sin(\phi) & \cos(\phi) & 0 \\ i \sin(\phi) & 0 & 0 &…
Marek
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8
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Is quantum complexity basis-invariant?

Quantum computing refers (occasionally implicitly) to a "computational basis". Some texts posit that such a basis may arise from a physically "natural" choice. Both mathematics and physics require meaningful notions to be invariant under a change of…
Martin Ziegler
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3 answers

How to prove that antipodal points on the Bloch sphere are orthogonal?

I started by assuming two antipodal states \begin{align*} |(\theta,\psi)\rangle &= \cos\dfrac{\theta}{2}|0\rangle + \sin\dfrac{\theta}{2}e^{i\psi}|1\rangle\\ |(\theta+\pi,\psi+\pi)\rangle&= \cos\dfrac{\theta+\pi}{2}|0\rangle +…
apen
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