Quantum realization of the bilinear interpolation method for NEQR

Abstract

In recent years, quantum image processing is one of the most active fields in quantum computation and quantum information. Image scaling as a kind of image geometric transformation has been widely studied and applied in the classical image processing, however, the quantum version of which does not exist. This paper is concerned with the feasibility of the classical bilinear interpolation based on novel enhanced quantum image representation (NEQR). Firstly, the feasibility of the bilinear interpolation for NEQR is proven. Then the concrete quantum circuits of the bilinear interpolation including scaling up and scaling down for NEQR are given by using the multiply Control-Not operation, special adding one operation, the reverse parallel adder, parallel subtractor, multiplier and division operations. Finally, the complexity analysis of the quantum network circuit based on the basic quantum gates is deduced. Simulation result shows that the scaled-up image using bilinear interpolation is clearer and less distorted than nearest interpolation.

T-count Optimized Quantum Circuits for Bilinear Interpolation

“…Comparison of the T-count between the proposed quantum bilinear interpolation circuit for the scale down operation and the existing work in [5] is shown in Table II. The design in [5] has a T-count of order ≈ O(n 2 ). The proposed design's T-count is of order O(n 2 ).…”

“…We compute the T-count for the proposed work and the existing design by multiplying the T-count for each quantum functional block by the number of times it is used and then sum the result. Table I shows the number of functional blocks used by the design in [5]. Table II shows that the proposed quantum circuit for bilinear interpolation have an improvement ratio of ≈ 92.52% in terms of T-count when performing the scale down operation.…”

“…64 · n 2 − 12 · n − 8 ≈ 92.52% 1 is the design in [5] |10 · · · 01 • • |10 · · · 01 |0 Yn−1:0 The image is scaled up by a value n. The notation m + n − 1 : n means quantum register locations m + n − 1 through n for the output image position registers Y and X . The notation n − 1 : 0 means quantum register locations n−1 through 0 for the output image position registers Y and X .…”

“…Thus, researchers have proposed quantum image representations such as the Flexible Representation of Quantum Images (FRQI) [3] and the Novel Enhanced Quantum Representation (NEQR) [4]. Further, quantum circuits for image operations such as translation, geometric transformation and bilinear interpolation have also been developed [5] [6] [7]. If these quantum circuits are based on Clifford+T gates, they can be made fault tolerant with error correcting codes permitting reliable and scalable quantum computation [8] [9] [10] [11] [12].…”

“…The work in [5] also proposes a color information retrieval scheme based on quantum oracles operating as lookup tables. While an interesting design, the bilinear interpolation circuits in [5] suffers from significant T gate cost because the design is based on quantum arithmetic circuits that have high T-count. Further, the circuits suffer from added overhead due to extra quantum arithmetic operations which can be minimized.…”