Quantum Information Protocols with limited resources

• Applicant: Professor Dr. Juan Ignacio Cirac
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2019 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 414325145

• Final Report Year: 2023

Final Report Abstract

After many years of intensive research, it is now possible to control and manipulate tens of qubits with high precision. This has been achieved with trapped ions, cold atoms, superconductors, and photons, and it is very likely that other technologies will soon catch up. Even though a full-fledged quantum computer is still very far in time, it is expected that in the next few years quantum processors composed of up to hundred qubits will be available, and that one will be able to reliably perform more than thousand quantum gates without having to resort to error correction schemes. Under these conditions, can we take advantage of those small systems? And, what can we learn? This project aimed at: (i) developing applications and protocols which can be carried out with small quantum processors, and that outperform existing and planned classical devices; (ii) revisiting classical algorithms and methods inspired by quantum information processing to apply them to quantum devices and many-body systems; (iii) bridging the gap between abstract results and specific experimental setups. In the reporting period we have: Developed quantum algorithms for early quantum devices. First, we have proposed and analyzed one to solve quantum many-body problems at finite energies and temperature with a quantum advantage and also overcoming the sign problem which plagues classical methods. Second, developed quantum algorithms to power matrices, and analyzed the propagation of errors in NISQ devices for such kind of methods. Third, proposed quantum machine algorithms to solve classical problems by using the enhanced expressivity of quantum devices. Investigated how tensor-network machine learning methods can efficiently describe large images and text data sets. We have also analyzed various many-body states that can be created in experiments, and determined their entanglement properties based on symmetries. We have introduced and characterized a family of tensor network states that can be efficiently created in 2D systems and be used for quantum information purposes. We have also proposed a method of quantum certification and verification based on tensor network states and Pauli measurements. We have also investigated how to implement the ideas above with different physical platforms, like photons, ions and superconducting qubits. We have proposed some specific experiments, and determine how to assess their success. All this research has been done in close contact with the other members of BeyondC and some papers have been published with different collaborators. Unfortunately, we are not allowed to go to the second phase of BeyondC for legal reason. In any case, we will continue active collaborations and contact with the other consortia in the new project extension, which has been recently granted.

Publications

• Matrix Product States: Entanglement, Symmetries, and State Transformations. Physical Review Letters, 123(17).
  Sauerwein, David; Molnar, Andras; Cirac, J. Ignacio & Kraus, Barbara
  
• Algorithms for Quantum Simulation at Finite Energies. PRX Quantum, 2(2).
  Lu, Sirui; Bañuls, Mari Carmen & Cirac, J. Ignacio
  
• Convergence Guarantees for Discrete Mode Approximations to Non-Markovian Quantum Baths. Physical Review Letters, 127(25).
  Trivedi, Rahul; Malz, Daniel & Cirac, J. Ignacio
  
• Quantum algorithms for powering stable Hermitian matrices. Physical Review A, 103(6).
  González, Guillermo; Trivedi, Rahul & Cirac, J. Ignacio
  
• Adiabatic Spectroscopy and a Variational Quantum Adiabatic Algorithm. PRX Quantum, 3(2).
  Schiffer, Benjamin F.; Tura, Jordi & Cirac, J. Ignacio
  
• Enhancing Generative Models via Quantum Correlations. Physical Review X, 12(2).
  Gao, Xun; Anschuetz, Eric R.; Wang, Sheng-Tao; Cirac, J. Ignacio & Lukin, Mikhail D.
  
• Error Propagation in NISQ Devices for Solving Classical Optimization Problems. PRX Quantum, 3(4).
  González-García, Guillermo; Trivedi, Rahul & Cirac, J. Ignacio
  
• Preparation and verification of tensor network states. Physical Review Research, 4(2).
  Cruz, Esther; Baccari, Flavio; Tura, Jordi; Schuch, Norbert & Cirac, J. Ignacio
  
• Sequential Generation of Projected Entangled-Pair States. Physical Review Letters, 128(1).
  Wei, Zhi-Yuan; Malz, Daniel & Cirac, J. Ignacio
  
• Transitions in Computational Complexity of Continuous-Time Local Open Quantum Dynamics. Physical Review Letters, 129(26).
  Trivedi, Rahul & Cirac, J. Ignacio