Variational quantum support vector machine based on $$\Gamma $$ matrix expansion and variational universal-quantum-state generator

Abstract

We analyze a binary classification problem by using a support vector machine based on variational quantum-circuit model. We propose to solve a linear equation of the support vector machine by using a $$\Gamma $$ Γ matrix expansion. In addition, it is shown that an arbitrary quantum state is prepared by optimizing a universal quantum circuit representing an arbitrary $$U(2^N)$$ U ( 2 N ) based on the steepest descent method. It may be a quantum generalization of Field-Programmable-Gate Array (FPGA).

Preparing a Fast Pauli Decomposition for Variational Quantum Solving Linear Equations

“…It is generally accepted that a matrix can be decomposed into the following form where Γ i is tensor products of Pauli operators and can be expressed as ⊗ n i=1 𝜎 i 𝛼 . Algebraically, the coefficients are calculated as follows [43,44]…”

“…In quantum machine learning, we usually should deal with arbitrary random matrices, such as quantum support vector machine and [43] quantum singular value decomposition. [20] Our method applies to these situations as well.…”

Linear, Bidirectional and Circular Controlled Quantum Teleportation and Quantum State Sharing using a Seven Qubit Genuinely Entangled State

“…While the quantum support vector machine paradigm defined using Grover's algorithm gives a quadratic speedup, the implementation using the least squares approach provides an exponential speedup over classical algorithms (64). In recent years, we have had quantum support vector machine implementations with the Newton method, amplitude estimation, gradient descent and using quantum annealers as well as variational quantum-circuitry (128)(129)(130)(131)(132). neighbour methods is that the likelihood of two data-points that are proximal being of the same type is high (133).…”