Questions tagged [block-encoding]
6 questions
3
votes
1 answer
Avoiding garbage amplitudes in block-encoding
Block-encoding is a technique to embed non-unitary operations in quantum circuits. Let's restrict it to just Hermitian operations.
Suppose $H$ is some operation. To encode it into a quantum gate $U$, the following method is used:
$$
U =…
Loic Stoic
- 433
- 2
- 10
3
votes
2 answers
Block encoding of a diagonal matrix with equidistant eigenvalues
What would be the simplest way to construct a block encoding circuit $U_A$ for a $2^n\times 2^n$ matrix $A$ proportional to $\operatorname{diag}(0,1,2,\ldots,2^n-1)$?
A couple of options I can imagine:
Use quantum adder $|x, y\rangle\mapsto|x,…
mavzolej
- 2,271
- 9
- 18
3
votes
2 answers
Time complexity of block-encoded matrices
A lot of modern quantum computation has this idea of "block-encoding" matrices; loosely, this is encoding a non-unitary matrix into the top left corner of a larger unitary matrix. This technique is referenced a lot, but I don't see how it can be…
wavosa
- 439
- 2
- 7
2
votes
1 answer
Constructing a block unitary from non-unitary matrices
Background:
I have a function $f(s_i, s_f, x)$ where $s_i \in \{0,1,2,3\}; \quad x,s_f \in \{0,1\}$ which is defined as:
$$
f(s_i, s_f, x) =
\begin{cases}
1, & \text{if } (s_i, s_f, x) \in\{(0,0,0),(1,0,1),(2,1,1),(3,1,0)\}\\
0, &…
Enigma
- 55
- 4
1
vote
1 answer
Verifying block encoding by computing inner products
Assume that we know each matrix element $A_{ij}$ of a $n$-qubit matrix $A$, and we are given an $(n+m)$-qubit unitary $U_A$ that we would like to verify is a $(1,m)$-block encoding of $A$. To do this, we need to check that
$$\langle 0^m, i | U_A…
Sergio Escobar
- 811
- 4
- 9
0
votes
0 answers
Constructing amplitude oracle for complex-valued matrix
Let $a, b \in \mathbb R$ such that $\vert a + ib \vert < 1$. Does there exists a generic $2$-qubit unitary such that $$(a |0\rangle + \sqrt{1 - a^2}| 1 \rangle) \otimes (b|0\rangle + \sqrt{1 - b^2}|1\rangle) \xrightarrow{U} ((a + ib)|0\rangle +…
Sergio Escobar
- 811
- 4
- 9