Density matrix representation of hybrid tensor networks for noisy quantum devices
arXiv:2309.15761 · doi:10.22331/q-2025-08-07-1823
Abstract
The hybrid tensor network (HTN) method is a general framework allowing for the construction of an effective wavefunction with the combination of classical tensors and quantum tensors, i.e., amplitudes of quantum states. In particular, hybrid tree tensor networks (HTTNs) are very useful for simulating larger systems beyond the available size of the quantum hardware. However, while the realistic quantum states in NISQ hardware are highly likely to be noisy, this framework is formulated for pure states. In this work, as well as discussing the relevant methods, i.e., Deep VQE and entanglement forging under the framework of HTTNs, we investigate the noisy HTN states by introducing the expansion operator for providing the description of the expansion of the size of simulated quantum systems and the noise propagation. This framework enables the general tree HTN states to be explicitly represented and their physicality to be discussed. We also show that the expectation value of a measured observable exponentially vanishes with the number of contracted quantum tensors. Our work will lead to providing the noise-resilient construction of HTN states.
38 pages, 16 figures, published version
References in corpus (41)
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- A variational eigenvalue solver on a quantum processor
- The density-matrix renormalization group in the age of matrix product states
- Variational Quantum Algorithms
- Dynamical Decoupling of Open Quantum Systems
- Quantum computational chemistry
- Quantum Circuit Learning
- Quantum Chemistry in the Age of Quantum Computing
- Error mitigation for short-depth quantum circuits
- Entanglement renormalization
- The Variational Quantum Eigensolver: a review of methods and best practices
- Quantum Error Correction for Beginners
- Quantum Error Mitigation
- Classical simulation of quantum many-body systems with a tree tensor network
- Practical Quantum Error Mitigation for Near-Future Applications
- Hybrid quantum-classical algorithms and quantum error mitigation
- Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
- Quantum autoencoders for efficient compression of quantum data
- Trading classical and quantum computational resources
- Simulating Large Quantum Circuits on a Small Quantum Computer
- Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources
- Doubling the size of quantum simulators by entanglement forging
- Mitigating depolarizing noise on quantum computers with noise-estimation circuits
- Fundamental limits of quantum error mitigation
- Variational spin-squeezing algorithms on programmable quantum sensors
- Quantum error mitigation as a universal error-minimization technique: applications from NISQ to FTQC eras
- Decoding quantum errors with subspace expansions
- Circuit knitting with classical communication
- Simple Mitigation of Global Depolarizing Errors in Quantum Simulations
- Variational-State Quantum Metrology
- Constructing a virtual two-qubit gate by sampling single-qubit operations
- Quantum simulation with hybrid tensor networks
- Generalized quantum subspace expansion
- Universal Sampling Lower Bounds for Quantum Error Mitigation
- Universal cost bound of quantum error mitigation based on quantum estimation theory
- Error statistics and scalability of quantum error mitigation formulas
- Doubly optimal parallel wire cutting without ancilla qubits
- Quantum computing quantum Monte Carlo with hybrid tensor network for electronic structure calculations
- Hybrid Tree Tensor Networks for quantum simulation
- Quantum algorithm for calculation of transition amplitudes in hybrid tensor networks
- Constructing Local Bases for a Deep Variational Quantum Eigensolver for Molecular Systems