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What's an use case of the inner product between two qubits in a quantum algorithm?

$\newcommand{\q}[2]{\langle #1 | #2 \rangle}$ I know from linear algebra that the inner product of two vectors is 0 if the vectors are orthogonal. I also know the inner product is positive if the vectors more or less point in the same direction and…
R. Chopin
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Problem about qutrit teleportation protocol

I'm working through Scott Aaronson's Quantum Information Science problem sets, and I'm having trouble with a specific problem in ps5 (PDF). Specifically the following problem: A “qutrit” has the form $a|0\rangle+b|1\rangle+c|2\rangle$, where…
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How would one implement a quantum equivalent of a while loop in IBM QISkit?

I'm writing a simple multiplication algorithm that uses the Quantum Fourier Transform to repetitively add a number (the multiplicand) to itself and decrements another number (the multiplier). The repeated addition process is to be stopped once the…
6
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3 answers

How do we physically initialize qubits in a Quantum register?

In quantum algorithms we need to initialize the qubits at the start of our algorithm in some quantum register. Suppose that if we are working with a four qubit quantum register we can initialize the register into values such as $|0000\rangle$ or…
K Sarkar
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6
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2 answers

Randomness from deterministic machine

It is known that in a classical computer we can't generate a purely random number by deterministic process. I am taking a course in Quantum Computing, recently I learnt that using state we can generate a deterministic process which will produce…
tarit goswami
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6
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1 answer

Do we need multiple syndrome extraction rounds after each transversal gate?

This question is related to The reason of repeated syndrome measurement for surface codes. You can imagine either surface codes or color codes. For performing a logical gate, a standard way is that we perform a gate gadget (e.g. transversal gate),…
david
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Qiskit Quantum Composer Swap-Gate doesn't seem to be working properly

I have been experimenting with the swap-gate in Qiskit's Quantum-Composer and I'am confused: Initialized two qubits with 0, a not-gate on q[0] results in the state 01: I expect a subsequent swap-gate to result in state 10, but it leaves the state…
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Decompose a positive operator in Pauli basis

Define $\mathcal{P}_n$ to be the set of all $n$-qubit Pauli strings with phase $+1$. Then any Hermitian operator $H$ can be decomposed into linear combination of these Pauli strings. That is, $$ H=d^{-1}\sum_{P\in\mathcal{P}_n}{\rm tr}(PH)P $$ where…
cos
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6
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How scalable are quantum computers when measurement operations are considered?

From a high-level point of view, given a quantum program, typically the last few operations are measurements. In most cases, in order to extract a useful answer, it is necessary to run multiple times to reach a point where it is possible to…
6
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2 answers

Symmetry in Conditional Phase Shift Gates and Realizing CNOT through HCZH

Why are conditional phase shift gates, such as CZ, symmetrical? Why do both the control and target qubit pick up a phase? Furthermore, assuming that they are symmetrical, when using a CNOT gate as an H gate on the target qubit, a CZ gate, and…
Eric Li
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Smallest distance-2 codes with non-trivial logical transversal $T$ gates

It has been shown that the $[[15, 1, 3]]$ code is the smallest distance-3 code with logical transversal $T$ gates (See arXiv:2210.14066). I say a code admits logical transversal $T$ gates if 1. The transversal physical $T^{\otimes n}$ is a logical…
Yunzhe
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How many logical qubits are needed for RSA breaking?

I'm a graduate student in physics, and I’m looking for academic papers that estimate the number of logical qubits required for real-world quantum computing applications, particularly: Breaking RSA cryptography I want to cite reliable sources in my…
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Classical XOR gate in Quantum Circuit

Can we use classical XOR gate in a quantum circuit? Or are there any alternatives for XOR gate?
Govind
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Photon Entanglement using SPDC

Are there any good references where from I can learn about photon entanglement using spontaneous parametric down-conversion (SPDC)?
Govind
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6
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Trace of projected Gaussian operator product: puzzling difference between projection onto filled or empty fermionic mode

This question was motivated by a Mathoverflow posting. I am comparing two traces of fermionic creation/annihilation operators $a_n,a_n^\dagger$ ($n=1,2,\ldots N$): $$T_{\rm empty}= \operatorname{tr}\bigl(a_1 a_1^\dagger e^{a^\dagger X_1 a}a_1…