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Yes, as long as you change the order of the gates without changing the qubits on which each gate acts. Proof: All phase gates are represented by diagonal unitary matrices. If $A$ has a diagonal matrix then controlled-$A$ also has a diagonal matrix. Therefore, all gates in your set of gates have diagonal matrices. Conclusion follows from the fact that ...


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Here's an intermediate result: it takes at least 5 T gates. The T count of the overlapping Toffoli construction has to be exactly equal to the T count of two Toffolis that overlap at exactly one control, and those two Toffolis can be used to produce a state known to require 5 T states to produce. This circuit with single-common-control Toffolis: Is ...


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I think that asking for an exact solution is pointless, because quantum computers don't have infinite precision. You are limited, for example, by accuracy of pulses that control the gates. To implement the idea of the mentioned answer, you can refer to this paper which introduces a general method for constructing an efficient and highly accurate quantum ...


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You're basically talking here about a quantum cellular automaton. I found a summary here, which I'm not particularly familiar with but looks good at first glance. The papers that I used in the dim and distant past when thinking about this are here and here. Two caveats: (i) they don't restrict themselves to binary. You could surely make an equivalence if you ...


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qsel is an esoteric programming language similar to Ook! or whitespace. All it's doing is requiring you to decompose the circuit into the gateset [CS, H] and then representing the circuit with a ridiculous format. This is possible because [CS, H] is universal and because anything and everything can be efficiently encoded into a binary system that uses two ...


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Entanglement As to how to create entangled states, the most easy way to do this is with the following circuit: qc = QuantumCircuit(4) qc.h(0) qc.cx(0, 1) qc.cx(1, 2) qc.cx(2, 3) This is an example for $n=4$, and you get the state $\frac{1}{\sqrt{2}}(|0\rangle^{\otimes 4} + |1\rangle^{\otimes 4})$; as confirmed by the statevector_simulator. svsim = Aer....


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The short answer to your first question is no, there is no "single standard" of representing circuits in terms of text/language. The closest to a "single standard" of representing circuits visually is the qiskit and cirq draw functions which produce very similar results that are basically standard in format . Due to the fact that no ...


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First, you need a "compression step" that maps a two-qubit observable like ZZ into a single qubit observable like IZ. That's what this does: That circuit maps ZZ on the left to Z_bottom on the right. You can then chain this step together in order to reduce an arbitrarily large ZZZ...Z product into a single Z observable, phase that Z observable, ...


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This is now possible. Please check https://quantum-computing.ibm.com/lab/docs/iql/manage/systems/midcircuit-measurement/


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