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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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How to efficiently calculate the inverse of a Kronecker product?

This is a follow-up question to a previous question I had, where the correct answer was to use the Kronecker product. Given, for example, a vector representing two qubits $$\begin{bmatrix}0 \\ 1 \\ 0 \\ 0\end{bmatrix}$$ is there an algorithm to…
1ijk
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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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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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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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How to decompose a unitary transform into two-level unitary matrices?

I'm struggling to understand the process of how to decompose a unitary transform into two-level unitary matrices. I've been trying to understand the process as detailed in arXiv:1210.7366, but I don't get where those 2x2 matrices in the individual…
Yuerno
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Access results from an experiment without having to run the script again

I have ran an experiment in one of the IBM processors and the work has finished. However, I can not obtain the data as histograms or counts in the qiskit notebook because the experiment was concluded while I was logged off and therefore now I would…
Henao
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What design considerations set the frequency bounds for superconducting qubits?

Superconducting qubits generally have frequencies within the range of 4 - 8 GHz. What design considerations give the upper and lower bounds for what is a feasible design. I.e, why can't they be higher or lower in frequency?
psitae
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Can the Kraus decomposition always be chosen to be a statistical mixture of unitary evolutions?

If $\mathcal{E}$ is a CPTP map between hermitian operators on two Hilbert spaces, then we can find a set of operators $\{K_j\}_j$ such that $$\mathcal{E}(\rho)=\sum_j K_j\rho K_j^\dagger $$ in the same spirit as any density matrix $\rho$ can be…
user2723984
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How are arbitrary $2\times 2$ matrices decomposed in the Pauli basis?

I read in this article (Apendix III p.8) that for $A\in \mathcal{M}_2$, since the normalized Pauli matrices $\{I,X,Y,Z\}/\sqrt{2}$ form an orthogonal matrix basis. $$A=\frac{Tr(AI)I+Tr(AX)X+Tr(AY)Y+Tr(AZ)Z}{2} $$ I don't understand, where does the…
lufydad
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What is intuition for the trace distance between quantum states?

Given two mixed states $\rho$ and $\sigma$, the trace distance between the states is defined by $\sum_{i=1}^n |\lambda_i|$, where $\lambda_i$'s are eigenvalues of $\rho - \sigma$. I know the definition of eigenvalues, but I don't have intuition on…
satya
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Does the Choi-Jamiolkowski isomorphism really establish a connection between kinematics and dynamics?

I understand the mathematical construction of the Choi-Jamiolkowski isomorphism aka channel-state duality. It all makes sense formally, yet I still struggle to grasp its physical (or quantum-informational) meaning. Does the isomorphism between…
quantumorsch
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Calculating power of a quantum computer for RSA

As discussed in this question, the expected security of 1024-bit RSA is 80-bits: NIST SP 800-57 §5.6.1 p.62–64 specifies a correspondence between RSA modulus size $n$ and expected security strength $s$ in bits: Strength RSA modulus size 80 …
R1-
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$n$ 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, then how do the sets of measurements on $n$…
mavzolej
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