4
votes
Is APPROX-QCIRCUIT-PROB a BQP-complete problem?
In BQP-Complete Problems by Zhang (2012)
Like many [...] "semantic" complexity classes, BQP is not known to contain complete problems.What people usually study for completeness, in such a ...
- 9,132
3
votes
Is APPROX-QCIRCUIT-PROB a BQP-complete problem?
Just to further @Egretta.Thula's answer, a portion of the Wikipedia article on the APPROX-QCIRCUIT-PROB mentions $\alpha$ and $\beta$ and stated:
Note that the problem does not specify the behavior ...
- 10.7k
3
votes
Accepted
Quantum compilation algorithm with respect to other Shatten $p$-norm
Yes, you get the same behavior. This is because all norms on finite dimensional spaces are equivalent. That means that for every $p$ there exist constants $c_p, d_p > 0$ such that
$$
d_p \|X\|_p \...
- 5,355
2
votes
Accepted
Bounding operator norm by total variation distance
No you cannot, here's a counterexample.
Let $U=I$ be the identity matrix and let $S = \sum_{i} (-1)^{\delta_{0,i}} |i\rangle \langle i|$ where $\delta_{i,j}$ is the Kronecker delta. That is, $S$ is ...
- 5,355
2
votes
Accepted
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 ...
- 33.3k
1
vote
Accepted
Calculation of Trotter-Suzuki error bound
There are two aspects of your question that I will address separately: the computational and analytical. I believe the underlying issue is the same, but I will nonetheless address them separately.
...
- 595
Only top scored, non community-wiki answers of a minimum length are eligible