A method of performing a constant-time fractional quantum Fourier-Kravchuk transform, characterised in that input data sequence is encoded in quantum amplitudes of a d -level state, which is processed by a single quantum gate implementing an exchange interaction, and the result is read out by means of quantum detectors located downstream the quantum gate, wherein the single quantum gate fulfils all the following prerequisites: • the interaction of two independent modes a and b in the quantum gate is governed by the following Hamiltonian H = H 0 + H I, wherein H 0 is the free quantum oscillator energy and H I -the interaction Hamiltonian H 0 = ħ 2 a † a + b † b, H I = iħ 2 ga † b − g * ab †, where g corresponds to the exchange interaction strength and g* is its complex conjugate, • the evolution operator generated by the Hamiltonian H is the following U = exp − iθH / ħ, where θ is an evolution parameter, • the quantum input state | Ψ 〉 = ∑ l = 0 S x l | l, S − l 〉 encodes the sequence to be transformed (x 0,x 1,...,x S); wherein the exchange interaction followed by particle-counting detection implements the α-fractional QKT transform of the input probability amplitudes x 0, x 1,..., x S → X 0 2, X 1 2,..., X S 2 where α = 2 g θ π and | X k | 2 are particle number statistics measured downstream the quantum gate for k = 0,..., S which correspond to X k = ∑ l = 0 S e − i πa 2 S 2 e i π 2 l − k φ k p l − Sp, S ⋅ x l, k = 0,..., S where p = sin 2 πα 4, • the quantum gate is implemented by a beam splitter and the input data are encoded as superposition of multiphoton Fock states that interfere on the beam splitter with the beam splitting ratio r, and the result is read from the system by means of photon counting detectors, wherein g = -i (| g | = 1); whereby the α-fractional QKT transform is performed where the fractionality is expressed by the formula α = 2 π arcsin r. • the interaction of two independent modes a and b in the quantum gate is governed by the following Hamiltonian H = H 0 + H I, wherein H 0 is the free quantum oscillator energy and H I -the interaction Hamiltonian H 0 = ħ 2 a † a + b † b, H I = iħ 2 ga † b − g * ab †, where g corresponds to the exchange interaction strength and g* is its complex conjugate, H 0 is the free quantum oscillator energy and H I -the interaction Hamiltonian H 0 = ħ 2 a † a + b † b, H I = iħ 2 ga † b − g * ab †, g corresponds to the exchange interaction strength and g* is its complex conjugate, • the evolution operator generated by the Hamiltonian H is the following U = exp − iθH / ħ, where θ is an evolution parameter, • the quantum input state | Ψ 〉 = ∑ l = 0 S x l | l, S − l 〉 encodes the sequence to be transformed (x 0,x 1,...,x S); wherein the exchange interaction followed by particle-counting detection implements the α-fractional QKT transform of the input probability amplitudes x 0, x 1,..., x S → X 0 2, X 1 2,..., X S 2 where α = 2 g θ π and | X k | 2 are particle number statistics measured downstream the quantum gate for k = 0,..., S which correspond to X k = ∑ l = 0 S e − i πa 2 S 2 e i π 2 l − k φ k p l − Sp, S ⋅ x l, k = 0,..., S where p = sin 2 πα 4, wherein the exchange interaction followed by particle-counting detection implements the α-fractional QKT transform of the input probability amplitudes x 0, x 1,..., x S → X 0 2, X 1 2,..., X S 2 where α = 2 g θ π and | X k | 2 are particle number statistics measured downstream the quantum gate for k = 0,..., S which correspond to X k = ∑ l = 0 S e − i πa 2 S 2 e i π 2 l − k φ k p l − Sp, S ⋅ x l, k = 0,..., S where p = sin 2 πα 4, • the quantum gate is implemented by a beam splitter and the input data are encoded as superposition of multiphoton Fock states that interfere on the beam splitter with the beam splitting ratio r, and the result is read from the system by means of photon counting detectors, wherein g = -i (| g | = 1); whereby the α-fractional QKT transform is performed where the fractionality is expressed by the formula α = 2 π arcsin r.