  Singular value thresholding (SVT) operation is a fundamental core module in
many mathematical models in computer vision and machine learning, particularly
for many nuclear norm minimizing-based problems. We presented a quantum SVT
(QSVT) algorithm which was used as a subroutine to address an image
classification problem. This algorithm runs in
$O\left[\log\left(pq\right)\right]$, an exponential speed improvement over the
classical algorithm which runs in $O\left[poly\left(pq\right)\right]$. In this
study, we investigate this algorithm and design a scalable quantum circuit for
QSVT. In the circuit design, we introduce an adjustable parameter $\alpha$ to
ensure the high probability of obtaining the final result and the high fidelity
of actual and ideal final states. We also show that the value of $\alpha$ can
be computed ahead of implementing the quantum circuit when the inputs of the
QSVT algorithm, i.e. matrix ${\bf{A}}$ and constant $\tau$, are given. In
addition, we propose a small-scale quantum circuit for QSVT. We numerically
simulate and demonstrate the performance of this circuit, verifying its
capability to solve the intended SVT. The quantum circuit for QSVT implies a
tempting possibility for experimental realization on a quantum computer.
