Quantum approximated cloning-assisted density matrix exponentiation
arXiv:2311.11751 · doi:10.1103/PhysRevResearch.7.013264
Abstract
Classical information loading is an essential task for many processing quantum algorithms, constituting a cornerstone in the field of quantum machine learning. In particular, the embedding techniques based on Hamiltonian simulation techniques enable the loading of matrices into quantum computers. A representative example of these methods is the Lloyd-Mohseni-Rebentrost protocol, which efficiently implements matrix exponentiation when multiple copies of a quantum state are available. However, this is a quite ideal set up, and in a realistic scenario, the copies are limited and the non-cloning theorem prevents from producing more exact copies in order to increase the accuracy of the protocol. Here, we propose a method to circumvent this limitation by introducing imperfect quantum copies, which significantly improve the performance of the LMR when the eigenvectors are known.
References in corpus (38)
- Quantum Machine Learning
- Quantum algorithm for solving linear systems of equations
- Quantum support vector machine for big data classification
- Quantum machine learning in feature Hilbert spaces
- Quantum principal component analysis
- Quantum Copying: Beyond the No-Cloning Theorem
- Hamiltonian Simulation by Qubitization
- Optimal Hamiltonian Simulation by Quantum Signal Processing
- Simulating Hamiltonian dynamics with a truncated Taylor series
- The effect of data encoding on the expressive power of variational quantum machine learning models
- Power of data in quantum machine learning
- Efficient quantum algorithms for simulating sparse Hamiltonians
- Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
- Quantum advantage in learning from experiments
- Quantum Data Fitting
- A Theory of Trotter Error
- Digitized adiabatic quantum computing with a superconducting circuit
- A random compiler for fast Hamiltonian simulation
- Preconditioned quantum linear system algorithm
- Prediction by linear regression on a quantum computer
- Quantum computational finance: Monte Carlo pricing of financial derivatives
- Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
- Quantum Discriminant Analysis for Dimensionality Reduction and Classification
- Efficient Quantum Circuits for Diagonal Unitaries Without Ancillas
- Hamiltonian Simulation with Optimal Sample Complexity
- Fixed Depth Hamiltonian Simulation via Cartan Decomposition
- Towards Pricing Financial Derivatives with an IBM Quantum Computer
- Bayesian Deep Learning on a Quantum Computer
- Distinguishability of generic quantum states
- First-Order Trotter Error from a Second-Order Perspective
- Efficient quantum amplitude encoding of polynomial functions
- Quantum algorithms for approximate function loading
- Biomimetic Cloning of Quantum Observables
- Quantum Capsule Networks
- A quantum hamiltonian simulation benchmark
- Unified Universal Quantum Cloning Machine and Fidelities
- Digital-analog co-design of the Harrow-Hassidim-Lloyd algorithm
- Accelerating Quantum Algorithms with Precomputation