Entangled Cloning of Stabilizer Codes and Free Fermions
arXiv:1608.04740 · doi:10.1103/PhysRevB.94.161112
Abstract
Though the no-cloning theorem [1] prohibits exact replication of arbitrary quantum states, there are many instances in quantum information processing and entanglement measurement in which a weaker form of cloning may be useful. Here, I provide a construction for generating an "entangled clone" for a particular but rather expansive and rich class of states. Given a stabilizer code or free fermion Hamiltonian, this construction generates an exact entangled clone of the original ground state, in the sense that the entanglement between the original and the exact copy can be tuned to be arbitrarily small but finite, or large, and the relation between the original and the copy can also be modified to some extent. For example, this work focuses on generating time-reversed copies of stabilizer codes and particle-hole transformed ground states of free fermion systems, although untransformed clones can also be generated. The protocol leverages entanglement to simulate a transformed copy of the Hamiltonian without having to physically implement it and can potentially be realized in superconducting qubits or ultracold atomic systems.
arXiv commentPublished version, with more generalizations of the result included. 5 pages, 1 figure
References in corpus (21)
- Topological Insulators
- Anyons in an exactly solved model and beyond
- Surface codes: Towards practical large-scale quantum computation
- Persistent entanglement in arrays of interacting particles
- Topological quantum memory
- String-net condensation: A physical mechanism for topological phases
- Quantum Error Correction for Quantum Memories
- Measuring entanglement entropy through the interference of quantum many-body twins
- Local stabilizer codes in three dimensions without string logical operators
- Topological Quantum Matter with Ultracold Gases in Optical Lattices
- Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
- Measuring entanglement growth in quench dynamics of bosons in an optical lattice
- Experimental Quantum Computations on a Topologically Encoded Qubit
- A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
- Digital quantum simulation of fermionic models with a superconducting circuit
- Analytic and numerical demonstration of quantum self-correction in the 3D Cubic Code
- State-Dependent Bulk-Boundary Maps and Black Hole Complementarity
- Measuring entanglement entropy of a generic many-body system with a quantum switch
- Majorana Fermion Surface Code for Universal Quantum Computation
- Bulk Topological Proximity Effect
- Universal two-qubit interactions, measurement and cooling for quantum simulation and computing