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3 votes

What are the best-known lower bounds on the number of measurements required for quantum state tomography?

This preprint is just submitted a few days ago: An Improved Sample Complexity Lower Bound for Quantum State Tomography by Henry Yuen. It shows that $\Omega(rd/\epsilon)$ copies of an unknown rank-$r$, ...
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Why Quantum Computing can help in Portfolio Optimization?

It depends on algorithm you use for the optimization. In certain cases, you can use HHL algorithm because the optimization is converted to solution of a linear system. In this case the can obtain up ...
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How to deterministically add two integers on a quantum computer

There are quite a few ways to make an adder on QC. I recommend watching Circuit Sessions with Ali Javadi, demo notebook from the talk so, a simple explanation, what makes a quantum computer faster ...
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  • 423
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What is the shortest-circuit-depth quantum-benchmarking algorithm?

it depends what you want to benchmark. I believe the shortest-circuit benchmarking is Measuring Gate Fidelities. take a look at https://metriq.info for Community-...
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  • 423
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Clarification about QTF proof regarding equality of QFT application and circuit application

I suppose there are two sources of confusion here -- one is the reversed order of the qubits between the circuit and the unitary, and the other is the use of $x$. In terms of qubit ordering, I think ...
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1 vote
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Definitions of a quantum circuit's depth and connectivity

I would like to give explicit definitions of the circuit depth and connectivity. I assume that the meaning of terms like vector state, quantum circuit, wires, and 1- and 2-qubit gates is understood. I'...
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  • 196
4 votes

Definitions of a quantum circuit's depth and connectivity

The traditional definitions of classical Boolean circuits work perfectly well here: https://en.wikipedia.org/wiki/Boolean_circuit. This is the definition that gives you Niel de Beaudrap's definition. ...
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2 votes

Definitions of a quantum circuit's depth and connectivity

Let me try to provide a more precise definition of connectivity in a quantum circuit. Every quantum circuit defines a graph (network), with vertices (nodes) given by qubits. There is an edge $q_1 q_2$ ...
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  • 332
1 vote

Is it possible to implement an in-place multiplication quantum circuit?

Generally, any classical computation can be turned into a reversible computation using enough ancilla bits. This is also true for the quantum case. Specifically, the $AND$ gate can be built using the $...
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