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3 votes

general way to decompose a CZ gate on $n$-qubit system

You can meet in the middle, use CXSWAPs instead of full swaps, and pipeline the CXSWAPs, to reduce the depth from $6n \pm O(1)$ to $n \pm O(1)$.
Craig Gidney's user avatar
  • 38.8k
3 votes
Accepted

How to apply the QAOA in such a QUBO problem?

This problem is known as the Currency Arbitrage Problem. This white paper shows how to formulate it as a QUBO. The white paper is talking about solving the problem using a quantum annealer. Of course, ...
Egretta.Thula's user avatar
2 votes
Accepted

Single bit teleportation for Hadamard gate

Here's a construction that does it with a one qubit state, by using a CY gate and an MX gate. This works because Hadamard is, up to Pauli gates, equivalent to a 90 degree rotation around the Y axis.
Craig Gidney's user avatar
  • 38.8k
2 votes
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General number of classical bits: recycles qubits

You can use the unpacking operator: qc = QuantumCircuit(m, w, *[cl_reg[i] for i in range(M)])
Tristan Nemoz's user avatar
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1 vote

State and observable decomposition into a sequence of native/universal gates

By a simple counting argument (see e.g Nielsen & Chuang Sec. 4.5.4), we know that almost all unitaries (or quantum states) have exponential circuit complexity. This should not come as a surprise, ...
Markus Heinrich's user avatar
1 vote

What is a "barrier" in Qiskit circuits?

"The barrier function creates a visual separation making the circuit diagram more readable, and it also prevents Qiskit from performing various simplifications and optimizations across barriers ...
Atharva Gambhir's user avatar
1 vote
Accepted

An equivalent classical circuit for Hadamard gate

No. A classical Hadamard gate has to act like a coin flip gate on a computational basis state, but must act like the identity when squared. That is, it needs to “remember” whether the input was $0$ or ...
Mark Spinelli's user avatar

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