QuantumComputingBench · graph-grounded exercise book
Reason from a target amplitude family to normalization, structural representations and a preparation construction. Inspect sparse and zero boundaries before transferring an argument to a circuit interface.
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.
In the low-wire-first recursive loader for a finite real amplitude table, each binary split of a sibling pair of real amplitudes (a, b) is realised by a single uniformly-controlled real Y-rotation. The rotation angle is …
local source supported
A sequential bond-dimension construction prepares a state one output bit at a time: each stage acts on a freshly introduced bit set to zero together with the current bond register, appending the new bit at the highest wi…
local source supported
A finite real tensor train with scalar (dimension-one) left and right boundaries defines its amplitudes by full contraction over all cores. Suppose the only hypothesis is that the sum of squared contracted amplitudes equ…
local source supported
A normalized finite real tensor train with a scalar terminal bond is right-canonicalized from the terminal end inward, absorbing each residual matrix into the preceding core. After this process, where does the total squa…
local source supported
For a finite real amplitude table f on n+1 wires, define its low-wire marginal by taking, at each prefix word b, the Euclidean length of the sibling pair (f at b-with-last-bit-0, f at b-with-last-bit-1). Prove that the t…
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Let f be a finite real amplitude table whose total squared Euclidean norm S = sum_b f(b)^2 is strictly positive. Prove that dividing every entry by sqrt(S) yields an exactly normalized state, i.e. sum_b (f(b)/sqrt(S))^2 …
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In the sequential bond construction, a complete state after n emitted bits is produced by applying stage matrices in order, starting from an explicit bond boundary vector. Assume for each stage index t and each clean inp…
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In the sequential bond construction, suppose every stage matrix is a full unitary on the fresh-bit-and-bond register and the run starts from a single bond basis label (one bond coordinate equal to one, the rest zero). Pr…
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A real tensor-train core carries orthonormal rows (its row-canonical condition). Show that embedding such a core into a complex matrix with the physical bit and new bond as output rows and the old bond as input columns y…
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In the sequential bond construction with a padded physical bond register larger than the active bond, a tempting simplification is to demand that the terminal cleanup stage send EVERY padded input column (not just the ac…
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In the sequential bond construction with rank changes inside a fixed padded register, a reader claims: 'If the completion columns of the stages (the inputs for inactive, zero-padded bond labels) are chosen differently, t…
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