4
votes
How is the computational power defined in Quatum Computing?
A simple answer to this question cannot be given as we have not discovered the "transistor" in quantum computing. Possible solutions or hardware implementations are:
Ion Traps
...
- 904
3
votes
Accepted
How would you write $ e^{i \frac{\pi}{4} \text{CNOT}}$ in ZX calculus?
Is there any simple method to write gates of the form $e^{i \frac{\pi}{4} \sigma_z^{(1)} \sigma_x^{(2)}}
$?
This graph should perform $\exp(i \theta \cdot (Z \otimes X))$:
There may be a factor of 2 ...
- 40.7k
3
votes
How to realize the index shift operation in quantum circuit?
All qubit rearrangements can be implemented with two layers of swap gates. In the case of a shift operation, swap qubit $k$ with qubit $n-k-1$ for each $k < n/2$ then swap qubit $k+1$ with qubit $n-...
- 40.7k
3
votes
How is the computational power defined in Quatum Computing?
You might want to take a look at the report from the Homeland Security R&D department, which gives a formula for estimating the power consumption of a quantum computer:
Energy consumed = runtime ×...
- 3,146
3
votes
Given a non-Clifford quantum circuit $U$, is it possible to construct a commuting Clifford circuit $C$?
Generically, no.
Consider the single-qubit unitary $U=HT$. We want to find a $C$ such that
$$
CUC^\dagger=U
$$
but since $C$ is Clifford, it transforms Paulis into Paulis. So, decompose $U$ in terms ...
- 60.7k
3
votes
Accepted
Is it possible to approximately compile Toffoli using H and CSWAP?
TL;DR: Nope. The triple tensor product of the $+1$ eigenstate of the Hadamard gate is a $+1$ eigenstate of every product of the controlled-SWAP gate and the Hadamard. This is not the case for Toffoli, ...
- 24.2k
2
votes
Is it possible to approximately compile Toffoli using H and CSWAP?
You can exactly implement a Toffoli using CSWAPs catalyzed by a singlet state:
The singlet state is the -1 eigenstate of the swap gate, and you can get phase kickback from a swap by using cswap, so ...
- 40.7k
2
votes
How to realize the index shift operation in quantum circuit?
CW because this is mostly cumulative with the other answers
As the other answers explain, a ladder of SWAP gates should suffice to perform such a circular shift operation. Many times it would not ...
2
votes
How to realize the index shift operation in quantum circuit?
I'll try to extend on @Jezer's answer. Although the obvious answer is the staircase product of SWAP operators $$S = \prod_{i=1}^{n-1} SWAP_{i,i+1},$$
it is most certainly more resource efficient to ...
- 482
1
vote
Finding a unitary transformation to swap the control bit
Unitaries $U$ are diagonalisable. That means there exists a unitary $V$ such that $VUV^\dagger=P$, where $P$ is a phase gate (diagonal matrix). This means that we can think of controlled-$U$ as the ...
- 60.7k
1
vote
How to realize the index shift operation in quantum circuit?
You could implement this with SWAP gates. Apply a SWAP on qubits 0 and 1, then on qubits 1 and 2, and so on, till you finally SWAP qubits n-1 and n.
If however, you're interested in designing ...
- 11
1
vote
Accepted
Coding a hamiltonian in qiskit
Qiskit's class SparsePauliOp can be used to define sparse $\text{N}$-qubit operators in Pauli basis representation. And in your case, it is better to utilize ...
- 11.5k
Only top scored, non community-wiki answers of a minimum length are eligible