Automated detection of symmetry-protected subspaces in quantum simulations
arXiv:2302.08586 · doi:10.1103/PhysRevResearch.5.033082
Abstract
The analysis of symmetry in quantum systems is of utmost theoretical importance, useful in a variety of applications and experimental settings, and is difficult to accomplish in general. Symmetries imply conservation laws, which partition Hilbert space into invariant subspaces of the time-evolution operator, each of which is demarcated according to its conserved quantity. We show that, starting from a chosen basis, any invariant, symmetry-protected subspaces which are diagonal in that basis are discoverable using transitive closure on graphs representing state-to-state transitions under -local unitary operations. Importantly, the discovery of these subspaces relies neither upon the explicit identification of a symmetry operator or its eigenvalues nor upon the construction of matrices of the full Hilbert space dimension. We introduce two classical algorithms, which efficiently compute and elucidate features of these subspaces. The first algorithm explores the entire symmetry-protected subspace of an initial state in time complexity linear to the size of the subspace by closing local basis state-to-basis state transitions. The second algorithm determines, with bounded error, if a given measurement outcome of a dynamically-generated state is within the symmetry-protected subspace of the state in which the dynamical system is initialized. We demonstrate the applicability of these algorithms by performing post-selection on data generated from emulated noisy quantum simulations of three different dynamical systems: the Heisenberg-XXX model and the and quantum cellular automata. Due to their efficient computability and indifference to identifying the underlying symmetry, these algorithms lend themselves to the post-selection of quantum computer data, optimized classical simulation of quantum systems, and the discovery of previously hidden symmetries in quantum mechanical systems.
arXiv comment23 pages, 7 figures, 4 appendices
References in corpus (29)
- Surface codes: Towards practical large-scale quantum computation
- Quantum Chemistry in the Age of Quantum Computing
- Floquet Time Crystals
- Invariant Variation Problems
- Hartree-Fock on a superconducting qubit quantum computer
- Hybrid quantum-classical algorithms and quantum error mitigation
- Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
- Low-cost error mitigation by symmetry verification
- Nature of the quantum phase transitions in the two-dimensional hardcore boson model
- Fundamental limits of quantum error mitigation
- Group-Invariant Quantum Machine Learning
- The Standard Model of Particle Physics
- Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges
- Error Mitigation by Symmetry Verification on a Variational Quantum Eigensolver
- Decoding quantum errors with subspace expansions
- Multi-exponential Error Extrapolation and Combining Error Mitigation Techniques for NISQ Applications
- Chaos and Complexity of quantum motion
- Restrictions on realizable unitary operations imposed by symmetry and locality
- Floquet higher-order topological insulators and superconductors with space-time symmetries
- Machine-learning hidden symmetries
- Non-Abelian eigenstate thermalization hypothesis
- Noncommuting conserved quantities in quantum many-body thermalization
- Non-Abelian symmetry can increase entanglement entropy
- Experimental observation of thermalization with noncommuting charges
- SymmetryGAN: Symmetry Discovery with Deep Learning
- Degenerated Liouvillians and Steady-State Reduced Density Matrices
- Small-world complex network generation on a digital quantum processor
- Floquet Supersymmetry
- Entanglement and complexity of interacting qubits subject to asymmetric noise