Quantum Algorithms for State Preparation and Data Classification based on Stabilizer Codes

Abstract

Quantum error correction (QEC) is a way to protect quantum information against noise. It consists of encoding input information into entangled quantum states known as the code space. Furthermore, to classify if the encoded information is corrupted or intact, a step known as syndrome detection is performed. For stabilizer codes, this step consists of measuring a set of stabilizer operators. In this paper, inspired by the QEC approach, and specifically stabilizer codes, we propose a prototype quantum circuit model for classification of classical data. The core quantum circuit can be considered as a \emph{quantum perceptron} where the classification is based on syndrome detection. In this proposal, a quantum perceptron is realized by one stabilizer as part of a stabilizer code, while a quantum neural network (QNN) layer is realized by a stabilizer code which consists of many stabilizers. The concatenation of stabilizer codes results in complex QNNs. The QNN is trained by performing measurements and optimization of a set of parameterized stabilizers. We demonstrate the concept numerically. In this paper we also consider the first challenge to most applications of quantum computers, including data classification, which is to load data into the memory of the quantum computer. This loading amounts to representing the data as a quantum state, i.e., quantum state preparation. An exact amplitude encoding algorithm requires a circuit of exponential depth. We introduce an alternative recursive algorithm which approximates amplitude encoding with only a polynomial number of elementary gates. We name it recursive approximate-scheme algorithm (RASA).

References in corpus (28)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Elementary gates for quantum computation
• Barren plateaus in quantum neural network training landscapes
• Quantum machine learning in feature Hilbert spaces
• Quantum Circuit Learning
• Quantum Error Correction for Quantum Memories
• Quantum random access memory
• Synthesis of Quantum Logic Circuits
• The quest for a Quantum Neural Network
• Continuous-variable quantum neural networks
• Quantum state discrimination and its applications
• Quantum generalisation of feedforward neural networks
• An Artificial Neuron Implemented on an Actual Quantum Processor
• Quantum Hopfield neural network
• Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications
• Simulating a perceptron on a quantum computer
• Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates
• Probabilistic Quantum Memories
• Emergent irreversibility and entanglement spectrum statistics
• Adaptive Variational Quantum Imaginary Time Evolution Approach for Ground State Preparation
• Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits
• Quantum algorithms for approximate function loading
• Interpretable Quantum Advantage in Neural Sequence Learning
• Quantum time dynamics of 1D-Heisenberg models employing the Yang-Baxter equation for circuit compression
• An Alternative Approach to Quantum Imaginary Time Evolution
• Projection algorithm for state preparation on quantum computers
• An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation
• Quantum simulations of Fermionic Hamiltonians with efficient encoding and ansatz schemes