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Finite subgroup of $U(4)$ containing a non-Clifford gate and all local Cliffords

No. There is no way to add a non Clifford gate to the local Clifford group $ Cl_1^{\otimes 2} $ and get a finite group. Definitions: A subgroup $ G $ of $ GL_n(\mathbb{C}) $ is reducible if we can ...
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How does CircuitQNN in qiskit machine learning calculate output probabiltiies?

what do sparse-integer probabilities and dense-integer probabilities correspond to? if I didn't understand your question wrong. It is just dense matrices and sparse matrices that we know in machine ...
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Finite subgroup of $U(4)$ containing a non-Clifford gate and all local Cliffords

This partial answer places additional restrictions on $U$. Constructing unitaries with infinite order By KAK decomposition, $U$ can be written as $$ U=(A_1\otimes A_0)e^{i\alpha X\otimes X + i\beta Y\...
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Gradient descent for a quantum-classical hybrid neural network

I understand it is tricky to do HNN with qiskit because of the lack of examples and explanations in the qiskit textbook. I recommend applying CircuitQNN will be ...
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Finite subgroup of $U(4)$ containing a non-Clifford gate and all local Cliffords

Here's an example for the real Pauli and Clifford groups : $$P_1=<X_1,Z_1>; |P_1|=8;$$ $$P_2=<X_1,Z_1,X_2,Z_2>; |P_2|=32;$$ $$C_1=<X_1,Z_1,H_1>; |C_1|=16;$$ $$C_1^{\otimes 2}=<X_1,...
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type object 'Circuit' has no attribute 'from_ops'

from_ops was deprecated a long time ago. You can just call cirq.Circuit(*ops) like ...
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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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  • 551
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How to decompose a multi qubit Clifford unitary into a sequence of clifford gates

There is only one method (the KAK decomposition) that is provably minimal in the number of 2-qubit gates, and it's for 2 qubit unitaries. I've found these 2 papers useful on that topic: paper 1 See ...
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Clifford circuit approximation to a random Clifford circuit

Clifford operations are discrete. They can't approximate arbitrary states. The state may not be close to a state reachable by Clifford operations. There are $O(L^2)$ distinct $L$-qubit states ...
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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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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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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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How to actually send Qiskit code to the que to be ran on an IBM Quantum Computer?

1. Load your account and select provider The Qiskit IBMQ account object is the local reference for accessing your IBM Quantum account, and all of the providers, ...
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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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When perform tomography, do I get back to the classical information $\alpha_1,\alpha_2,\beta_1,\beta_2$ that I embedded in qubit?

Short answer: If you perform state tomography you will recover ALL the information within the state to within the precision/number of times you repeated the measurement (except for an overall global ...
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