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Rigorous security proof for Wiesner's quantum money

In his celebrated paper "Conjugate Coding" (written around 1970), Stephen Wiesner proposed a scheme for quantum money that is unconditionally impossible to counterfeit, assuming that the issuing bank has access to a giant table of random numbers and…
Didix
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Quantum memory assisting classical memory

Consider a classical computer, one making, say, a calculation involving a large amount of data. Would quantum memory allow it to store that information (in the short term) more efficiently, or better handle that quantity of data? My thought would be…
auden
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What can we learn from 'quantum bogosort'?

Recently, I've read about 'quantum bogosort' on some wiki. The basic idea is, that like bogosort, we just shuffle our array and hope it gets sorted 'by accident' and retry on failure. The difference is that now, we have 'magic quantum', so we can…
Discrete lizard
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How can I decompose a matrix in terms of Pauli matrices?

I need to see an example of how Hamiltonian, i.e. any Hermitian matrix, can be decomposed into a linear combination of Pauli matrices. I would prefer an option to do this in larger than 2 dimensions, if that is possible.
yishairasowsky
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What is the relationship between Choi and Chi matrix in Qiskit?

I'm struggling with the framework for quantum process tomography on Qiskit. The final step of such a framework is running fit method of ProcessTomographyFitter class. Documentation states that such function gives a Choi matrix as output.…
Daniele Cuomo
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Qiskit - Z expectation value from counts?

For a given state $|\psi\rangle$, how would I work out $\langle\psi|Z|\psi\rangle$ ? If I run a quantum circuit and get the counts dictionary on qiskit, I get observables in the Z basis. For n=1 qubits, the basis states returned are $|0\rangle$ &…
Zohim Chandani
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How many classical bits are needed to represent a qubit?

I have two question concerning information content of qubit. Question 1: How many classical bits are needed to represent a qubit: A qubit can be represented by a vector $q = \begin{pmatrix}\alpha \\\beta \end{pmatrix}, ~~ \alpha, \beta \in…
Martin Vesely
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Does the Quantum Fourier Transform (QFT) preserve entanglement?

It is well known that entanglement in a quantum state is not affected when you perform a combination of 1-qubit unitary transformations. I have seen that the QFT can be decomposed into product of 1-qubit unitary transformations (for example in…
Hùng Phạm
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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 consider implementing $X$ by $e^{-i\frac{\pi}{2} X}$,…
Marco Fellous-Asiani
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Travelling salesman problem on quantum computer

Recently a pre-print of article Efficient quantum algorithm for solving travelling salesman problem: An IBM quantum experience appeared. The authors use a phase estimation as a core for their algorithm. This part of the algorithm is used for a…
Martin Vesely
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Why does representation theory often arise in the context of quantum algorithms for the hidden subgroup problem?

I noticed that approaches for finding quantum algorithms the hidden subgroup problem for both Abelian groups ($(\Bbb Z_n\times \Bbb Z_n, +)$, $(\Bbb R, +)$, etc.) and non-Abelian finite groups like the dihedral group and symmetric group often use…
Sanchayan Dutta
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Entanglement-assisted hashing bound for asymmetric depolarizing channels

I reading the paper EXIT-Chart Aided Quantum Code Design Improves the Normalised Throughput of Realistic Quantum Devices, which proposes the use of QTCs in order to do quantum error correction for realistic quantum devices whose error model can be…
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Number of qubits to achieve quantum supremacy?

Google's Sycamore paper describes achieving quantum supremacy on a $53$-qubit quantum computer. The layout of Sycamore is $n=6\times 9=54$ nearest neighbors, with one qubit nonfunctional. They apply $m=20$ total cycles in their experiment; each…
Mark Spinelli
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Strong vs weak simulations and the polynomial hierarchy collapse

(Edited to make the argument and the question more precise) An argument for quantum computational "supremacy" (specifically in Bremner et al. and the Google paper) assumes that there exists a classical sampler that outputs a probability $q_x$, $x…
Ninnat Dangniam
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Oracle for welded tree walk

There is a famous paper by Childs, et al, in which it is shown that a quantum algorithm can find the name of the exit node for a certain graph in a way that is exponentially faster than any classical algorithm. This speedup assumes an oracle that…
James Wootton
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