Quantum Computing Stack Exchange
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Prove the fidelity can be written in terms of Pauli expectation values as ${\rm tr}(\rho\sigma)=\sum_k \chi_\rho(k)\chi_\sigma(\rho)$

I am reading through "Direct Fidelity Estimation from Few Pauli Measurements" and it states that the measure of fidelity between a desired pure state $\rho$ and an arbitrary state $\sigma$ is $\mathrm{tr}(\rho\sigma)$. It then describes a…
Quantum Guy 123
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Postselection and hardness of estimating amplitudes

Let $A$ be a class of quantum circuits such that \begin{equation} \text{Post}A = \text{Post}BQP, \end{equation} where $\text{Post}$ indicates post-selection. Is only this amount of information sufficient to conclude that it is $\# P$ hard to…
BlackHat18
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Lower bounds on the number of measurements outcomes required for quantum state tomography

It seems that in order to reconstruct a quantum state, a large number of measurements is typically used. Are there any known theoretical lower bounds on the number of measurements required to reconstruct a state? Do we get different lower bounds if…
Haim
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Distinguishing $\frac{| 0 \rangle + e^{i\theta} |1 \rangle}{\sqrt{2}} $ from $| 0 \rangle/|1 \rangle$ with probability $1/2 + \epsilon$

I am given one copy of one of two quantum states - $\frac{| 0 \rangle + e^{i\theta} | 1 \rangle}{\sqrt{2}} $, for some unknown fixed $\theta$. One of $| 0 \rangle/|1 \rangle$ - don't know which one, but one of the two. I need to guess which one of…
nishkr
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How to visualize Hadamard gate as $X$-$Z$-$X$ decomposition?

In the book Quantum Computation and Quantum Information by Nielsen and Chuang, chapter 4, exercise 4.4 (pg. 175), the author has asked to express Hadamard gate as product of $R_x$, $R_z$ rotations and $e^{i\phi}$ for some angle $\phi$. I have found…
Trishant Sahu
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What is the largest linear system of equations solved using HHL experimentally?

Can someone tell what is the largest system of equations solved using HHL algorithm experimentally? I know the $8$ x $8$ system has been solved experimentally. Has someone gone beyond this to solve $16$ x $16$ or $32$ x $32$ or beyond? If yes please…
quankid
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If $\rho,\sigma$ are classical-quantum states, can the fidelity $F(\rho,\sigma)$ be expressed in terms of $F(\rho_i,\sigma_i)$?

Let $\rho = \sum_i \vert i\rangle\langle i\vert \otimes \rho_i$ and $\sigma = \sum_i\vert i\rangle\langle i\vert\otimes\sigma_i$ where we are using the same orthonormal basis indexed by $\vert i\rangle$ for both states. The quantum fidelity is…
Wut
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Is VQA quicker than classical machine learning?

Variational Quantum Algorithm (VQA) is a kind of quantum algorithm corresponding to classical machine learning. Unlike the square speed up of Grover's algorithm, the circuit in VQA does not seem to guarantee being faster than classical machine…
narip
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Why is a state Gaussian if and only if its covariance matrix satisfies $\boldsymbol\sigma+i\boldsymbol\Omega\ge0$?

Let $\rho$ be a Gaussian state, described by the $2N\times 2N$ covariance matrix $\newcommand{\bs}[1]{{\boldsymbol{#1}}}\bs\sigma$. Denote with $\bs\Omega$ the $N$-mode symplectic form associated with the space: $$\bs\Omega\equiv…
glS
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Use one_body_integrals to know which orbitals to freeze in ElectronicStructureProblem

In exercise 5 of the this year's IBM Quantum Challenge, you need to use the FreezeCoreTransformer (along two_qubit_reduction and z2symmetry_reduction) to reduce the number of qubits to 4 and achieve a cost of 3. I managed to figure out that the…
epelaez
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Can you make anyons in 3 dimensions using rings?

I heard that anyons can only be made in 2 dimensions because when you visualize the spacetime diagram of a 2-dimensional system with point particles, you can get braids, but if you do the same with a 3-dimensional system, you get only the un-braid…
MaudPieTheRocktorate
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Paper references on how quantum algorithms have an impact on cryptography?

Could you please help me in finding some research paper references on the impact of Quantum algorithms on symmetric and asymmetric cryptography ? Also, I request if I can get some references or notes demonstrating the impact on cryptography with…
Azhar Hossen
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Setting initial state in Qiskit unitary simulator

I'm getting started in IBM quantum lab for quantum computing. My task is to put quantum state $|0\rangle$ on the 1st qubit and state $|1\rangle$ on second one. I tried using this method to initialize it as: qc.initialize(0,0) qc.initialize(1,1) but…
Vedo
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Is it true that for a quantum algorithm to be efficient it must feature a highly entangled state at some point?

I'm wrapping my head around how and why quantum computers can provide advantage over classical. A basic and naive argument is that the dimension of the Hilbert space of $n$ qubits grows as $2^n$. However, without exponentially sized circuits of 1-…
Nikita Nemkov
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What are spin-coherent states?

Trying to understand the paper; https://arxiv.org/pdf/1702.02577.pdf and ran into "spin-coherent" states. I wonder those are.
John Parker
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