  The Painlev\'e equations can be written as Hamiltonian systems with affine
Weyl group symmetries. A canonical quantization of the Painlev\'e equations
preserving the affine Weyl group symmetries has been studied. While, the
Painlev\'e equations are isomonodromic equations for certain second-order
linear differential equations. In this paper, we introduce a canonical
quantization of Lax equations for the Painlev\'e equations and construct
symmetries of the quantum Lax equations. We also show that our quantum Lax
equations are derived from Virasoro conformal field theory.
