Scaling of variational quantum circuit depth for condensed matter systems

Abstract

We benchmark the accuracy of a variational quantum eigensolver based on a finite-depth quantum circuit encoding ground state of local Hamiltonians. We show that in gapped phases, the accuracy improves exponentially with the depth of the circuit. When trying to encode the ground state of conformally invariant Hamiltonians, we observe two regimes. A finite-depth regime, where the accuracy improves slowly with the number of layers, and a finite-size regime where it improves again exponentially. The cross-over between the two regimes happens at a critical number of layers whose value increases linearly with the size of the system. We discuss the implication of these observations in the context of comparing different variational ansatz and their effectiveness in describing critical ground states.

arXiv comment11 + 4 pages, 5 figures

References in corpus (47)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Entanglement Entropy and Quantum Field Theory
• Quantum Simulation
• Area laws for the entanglement entropy - a review
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Barren plateaus in quantum neural network training landscapes
• Geometric and Renormalized Entropy in Conformal Field Theory
• Quantum Chemistry in the Age of Quantum Computing
• An Area Law for One Dimensional Quantum Systems
• On Geometric Entropy
• A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
• Quantum entanglement in condensed matter systems
• Matrix product states represent ground states faithfully
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Efficient variational quantum simulator incorporating active error minimisation
• Data re-uploading for a universal quantum classifier
• Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
• Quantum Computation as Geometry
• Variational ansatz-based quantum simulation of imaginary time evolution
• Quantum Algorithms for Quantum Field Theories
• Quantum autoencoders for efficient compression of quantum data
• Variational Quantum Computation of Excited States
• Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
• Quantum-assisted quantum compiling
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Scaling of entanglement support for Matrix Product States
• Quantum Metropolis Sampling
• Variational quantum algorithms for discovering Hamiltonian spectra
• The power of quantum systems on a line
• Variational Quantum State Diagonalization
• Many-body quantum chaos: Analytic connection to random matrix theory
• Quantum circuits for strongly correlated quantum systems
• Hamiltonian complexity
• Improved Techniques for Preparing Eigenstates of Fermionic Hamiltonians
• Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
• Matrix Product Unitaries: Structure, Symmetries, and Topological Invariants
• Using Quantum Computers for Quantum Simulation
• Efficient Discrete Approximations of Quantum Gates
• Variational Quantum Unsampling on a Quantum Photonic Processor
• Numerical Renormalization Group at Criticality
• Conformal Data from Finite Entanglement Scaling
• Variational Consistent Histories as a Hybrid Algorithm for Quantum Foundations
• Quantum circuit complexity of one-dimensional topological phases
• Bridging Perturbative Expansions with Tensor Networks
• The Quartic Oscillator: a Non-Perturbative Study by Continuous Unitary Transformations

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• Circuit Complexity through phase transitions: consequences in quantum state preparation
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• Implementing Jastrow--Gutzwiller operators on a quantum computer using the cascaded variational quantum eigensolver algorithm
• Universal imaginary-time critical dynamics on a quantum computer
• Unveiling quantum phase transitions from traps in variational quantum algorithms
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• Finite-depth scaling of infinite quantum circuits for quantum critical points
• Quantum Chaos in Random Ising Networks
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