Quantum classifier with tailored quantum kernel

Abstract

Kernel methods have a wide spectrum of applications in machine learning. Recently, a link between quantum computing and kernel theory has been formally established, opening up opportunities for quantum techniques to enhance various existing machine-learning methods. We present a distance-based quantum classifier whose kernel is based on the quantum state fidelity between training and test data. The quantum kernel can be tailored systematically with a quantum circuit to raise the kernel to an arbitrary power and to assign arbitrary weights to each training data. Given a specific input state, our protocol calculates the weighted power sum of fidelities of quantum data in quantum parallel via a swap-test circuit followed by two single-qubit measurements, requiring only a constant number of repetitions regardless of the number of data. We also show that our classifier is equivalent to measuring the expectation value of a Helstrom operator, from which the well-known optimal quantum state discrimination can be derived. We demonstrate the performance of our classifier via classical simulations with a realistic noise model and proof-of-principle experiments using the IBM quantum cloud platform.

Comparison of quantum-walk implementations on noisy intermediate-scale quantum computers

“…For the implementation we make use of IBMQ's Qiskit development kit [29,30] in order to simulate and execute the quantum circuits. Currently, there is a lot of interest in running quantum applications on NISQ systems [31][32][33][34][35]. On the other hand, there are very few studies of quantum walks on hardware, with an early notable work by [36] representing the first implementation of a discrete coined quantum walk implemented on a quantuminformation processor.…”

Quantum Error Mitigation With Artificial Neural Network

“…The noise model is described in detail in Ref. [41]. For simulations with the IBM Q noise model, the error mitigation performance was tested with and without the measurement error mitigation technique described in Sec.…”

Solving nonlinear differential equations with differentiable quantum circuits

“…For prototypical linear algebra tasks, quantum computers can be used as exponential accelerators for solving linear system of equations (LSE), as offered by the HHL algorithm [9] and other quantum LSE approaches with improved scaling [10][11][12][13][14]. These developments, among others, have led to the nascent field of quantum machine learning [15][16][17][18][19][20][21][22][23][24]. Quantum LSE solvers can be applied to linear differential equations that are rewritten as systems of algebraic equations using a finite differencing scheme (Euler's method).…”