Approximate complex amplitude encoding algorithm and its application to data classification problems
arXiv:2211.13039 · doi:10.1103/PhysRevA.109.052423
Abstract
Quantum computing has a potential to accelerate the data processing efficiency, especially in machine learning, by exploiting special features such as the quantum interference. The major challenge in this application is that, in general, the task of loading a classical data vector into a quantum state requires an exponential number of quantum gates. The approximate amplitude encoding (AAE) method, which uses a variational means to approximately load a given real-valued data vector into the amplitude of a quantum state, was recently proposed as a general approach to this problem mainly for near-term devices. However, AAE cannot load a complex-valued data vector, which narrows its application range. In this work, we extend AAE so that it can handle a complex-valued data vector. The key idea is to employ the fidelity distance as a cost function for optimizing a parameterized quantum circuit, where the classical shadow technique is used to efficiently estimate the fidelity and its gradient. We apply this algorithm to realize the complex-valued-kernel binary classifier called the compact Hadamard classifier, and then give a numerical experiment showing that it enables classification of Iris dataset and credit card fraud detection.
13 pages, 8 figures
References in corpus (32)
- Quantum Machine Learning
- Quantum algorithm for solving linear systems of equations
- Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
- Barren plateaus in quantum neural network training landscapes
- Quantum support vector machine for big data classification
- Improved Simulation of Stabilizer Circuits
- Quantum principal component analysis
- Predicting Many Properties of a Quantum System from Very Few Measurements
- Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
- Quantum random access memory
- Quantum machine learning: a classical perspective
- An initialization strategy for addressing barren plateaus in parametrized quantum circuits
- Quantum Circuits for General Multiqubit Gates
- Quantum-assisted quantum compiling
- Quantum-state preparation with universal gate decompositions
- Differentiable Learning of Quantum Circuit Born Machine
- Implementing a distance-based classifier with a quantum interference circuit
- Noise Resilience of Variational Quantum Compiling
- Quantum circuits with uniformly controlled one-qubit gates
- The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine
- Large gradients via correlation in random parameterized quantum circuits
- Circuit-Based Quantum Random Access Memory for Classical Data
- Black-box quantum state preparation without arithmetic
- Approximate amplitude encoding in shallow parameterized quantum circuits and its application to financial market indicator
- Non-adiabatic molecular quantum dynamics with quantum computers
- The theory of the quantum kernel-based binary classifier
- Circuit-based quantum random access memory for classical data with continuous amplitudes
- Grid-based methods for chemistry simulations on a quantum computer
- Depth optimization of CZ, CNOT, and Clifford circuits
- Compact quantum kernel-based binary classifier
- CNOT circuits need little help to implement arbitrary Hadamard-free Clifford transformations they generate
- Generative model for learning quantum ensemble via optimal transport loss