QuantumComputingBench · graph-grounded exercise book
Track the represented operator, its normalizer and the accepted subspace. Keep preparation, SELECT, unprepare, workspace cleanup and resource tiers visible when composing constructions.
Back to Block Encoding and oracle composition
These links open the shared core's formal companion panel. Each card distinguishes admitted fixed-reference views from pending formalization. Preserve the exact core contract and split; a formal view is not another core.
Let U be a unitary on n system qubits and a auxiliary qubits. For a strictly positive real alpha, define B=(<0^a| tensor I)U(|0^a> tensor I). State what it means for U to encode a system operator A exactly or with induce…
local source supported
A circuit acts on a signal register S, a workspace W and a data register D, starting S,W at zero. The signal value0 is called success. Explain the additional mathematical promise needed to call W clean on every successfu…
nl bridge from inspected source
Keep total dimension2, the single system index embedded at total index0, and real orthogonal matrices. The inherited explicit assumption is 0<x<1. The historical question instead wrote 0<|x|<1: identify this range discre…
nl bridge from inspected source
On finite complex registers ordered coefficient × (selector × system), let P be a unitary PREPARE on the selector, let R_{s,x} be unitary coefficient-register blocks controlled by selector s and system basis label x, and…
local source supported
For the logical unprepare-select-amplitude-prepare LCU matrix on registers coefficient x (selector x system), derive the exact clean projected entry between clean input (clean coefficient, clean selector, systemColumn) a…
local source supported
Consider the 2x2 scalar dilation whose top-left clean entry is x, whose two off-diagonal entries are both y, and whose bottom-right entry is -x. Treat the single top-left entry as the one-dimensional clean block encoding…
local source supported
Retain rational square matrices A indexed by Fin n and a column support function c:Fin n→Fin n, with amp(j)=A(c(j),j) and reconstruction R_c(A)(i,j)=amp(j) if i=c(j), else0. The inherited convention describes support at …
local source supported
Suppose unitaries U and V have clean blocks A and B on the same data space. Explain why applying V then U with DISJOINT auxiliary registers initialized at zero yields clean block AB. Show concretely why simply reusing a …
nl bridge from inspected source
In an LCU-style assembly of a Hermitian piece, each selected term contributes a scaled controlled-phase source whose upper block carries the intended operator and whose lower-right filler block is normalizer times a phas…
local source supported
Keep the rational finite-square backend and a self-map p:Fin n→Fin n; permMatrix p has entry1 exactly when row=p(column). The historical question demands that bijectivity, not merely injectivity, is needed for the row Gr…
local source supported