Variational LOCC-assisted quantum circuits for long-range entangled states
arXiv:2409.07281 · doi:10.1103/PhysRevLett.134.170601
Abstract
Long-range entanglement is an important quantum resource, particularly for topological orders and quantum error correction. In reality, preparing long-range entangled states requires a deep unitary circuit, which poses significant experimental challenges. A promising avenue is offered by replacing some quantum resources with local operations and classical communication (LOCC). With these classical components, one can communicate outcomes of midcircuit measurements in distant subsystems, substantially reducing circuit depth in many important cases. However, to prepare general long-range entangled states, finding LOCC-assisted circuits of a short depth remains an open question. Here, to address this challenge, we propose a quantum-classical hybrid algorithm to find optimal LOCC protocols for preparing ground states of given Hamiltonians. In our algorithm, we introduce an efficient way to estimate parameter gradients and use such gradients for variational optimization. Theoretically, we establish the conditions for the absence of barren plateaus, ensuring trainability at a large system size. Numerically, the algorithm accurately solves the ground state of long-range entangled models, such as the perturbed Greenberger-Horne-Zeilinger state and surface code. Our results demonstrate the advantage of our method over conventional unitary variational circuits: the practical advantage in the accuracy of estimated ground-state energy and the theoretical advantage in creating long-range entanglement.
23 pages, 16 figures, and 5 tables
References in corpus (36)
- A variational eigenvalue solver on a quantum processor
- Variational Quantum Algorithms
- Surface codes: Towards practical large-scale quantum computation
- Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
- Barren plateaus in quantum neural network training landscapes
- Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
- Scalable Quantum Simulation of Molecular Energies
- Hartree-Fock on a superconducting qubit quantum computer
- A Race Track Trapped-Ion Quantum Processor
- Low-distance Surface Codes under Realistic Quantum Noise
- Long-range quantum entanglement in noisy cluster states
- Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
- Differentiable Quantum Architecture Search
- Measurement as a shortcut to long-range entangled quantum matter
- TensorCircuit: a Quantum Software Framework for the NISQ Era
- Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
- Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
- Quantum Circuits assisted by LOCC: Transformations and Phases of Matter
- Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements
- Long-range entanglement from measuring symmetry-protected topological phases
- Preparation of matrix product states with log-depth quantum circuits
- Shortest Route to Non-Abelian Topological Order on a Quantum Processor
- Quantum simulation with hybrid tensor networks
- A measurement-based variational quantum eigensolver
- Topological Order from Measurements and Feed-Forward on a Trapped Ion Quantum Computer
- Experimental quantum computational chemistry with optimised unitary coupled cluster ansatz
- Constant-depth preparation of matrix product states with adaptive quantum circuits
- Relative Entropy Convergence for Depolarizing Channels
- Absence of barren plateaus in finite local-depth circuits with long-range entanglement
- Approximating many-body quantum states with quantum circuits and measurements
- State preparation by shallow circuits using feed forward
- A constructive algorithm for the Cartan decomposition of SU(2^N)
- Symmetry-enriched topological order from partially gauging symmetry-protected topologically ordered states assisted by measurements
- Complexity and order in approximate quantum error-correcting codes
- Tensor-network-assisted variational quantum algorithm
- Phases of Matrix Product States with Symmetric Quantum Circuits and Symmetric Measurements with Feedforward