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Questions tagged [block-encoding]

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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, ...
SescoMath's user avatar
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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}|...
SescoMath's user avatar
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1 vote
1 answer
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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)...
Enigma's user avatar
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3 votes
1 answer
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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 $U$, ...
Loic Stoic's user avatar
3 votes
1 answer
219 views

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:...
mavzolej's user avatar
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2 votes
2 answers
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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 ...
wavosa's user avatar
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