Algebraic structure of path-independent quantum control

@article{Ma2022AlgebraicSO,
  title={Algebraic structure of path-independent quantum control},
  author={Wen-Long Ma and Shu-Shen Li and Liang Jiang},
  journal={Physical Review Research},
  year={2022}
}
Path-independent (PI) quantum control has recently been proposed to integrate quantum error correction and quantum control [Phys. Rev. Lett. 125 , 110503 (2020)], achieving fault-tolerant quantum gates against ancilla errors. Here we reveal the underlying algebraic structure of PI quantum control. The PI Hamiltonians and propagators turn out to lie in an algebra isomorphic to the ordinary matrix algebra, which we call the PI matrix algebra. The PI matrix algebra, defined on the Hilbert space of… 

Figures and Tables from this paper

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
Quantum optimal control, a toolbox for devising and implementing the shapes of external fields that accomplish given tasks in the operation of a quantum device in the best way possible, has evolved
Encoding Qubits in Multimode Grid States
TLDR
This work proposes to encode logical qubits in grid states of an ensemble of harmonic oscillator modes, and demonstrates numerically that multimode grid codes have, compared to their singlemode counterpart, increased robustness against propagation of errors from ancillas used for error correction.

References

SHOWING 1-10 OF 38 REFERENCES
Path-Independent Quantum Gates with Noisy Ancilla.
TLDR
The path independence criterion for fault-tolerant quantum gates against ancilla errors is introduced, and a path-independent gate is provided for superconducting circuits with a hardware-efficient design.
Noise-resilient quantum evolution steered by dynamical decoupling
TLDR
This work designs and implements a self-protected controlled-NOT gate on the electron spin of a nitrogen-vacancy centre and a nearby carbon-13 nuclear spin in diamond at room temperature by employing an engineered dynamical decoupling control on the electrons.
Robustness of Decoherence-Free Subspaces for Quantum Computation
It was shown recently [D.A. Lidar et al., Phys. Rev. Lett. 81, 2594 (1998)] that within the framework of the semigroup Markovian master equation, decoherence-free (DF) subspaces exist which are
A Theory of Quantum Error-Correcting Codes
TLDR
A general theory of quantum error correction based on encoding states into larger Hilbert spaces subject to known interactions is developed and necessary and sufficient conditions for the perfect recovery of an encoded state after its degradation by an interaction are obtained.
Quantum error correction in a solid-state hybrid spin register
TLDR
It is demonstrated that joint initialization, projective readout and fast local and non-local gate operations can all be achieved in diamond spin systems, even under ambient conditions, paving the way to large-scale quantum computation.
Error-transparent operations on a logical qubit protected by quantum error correction
TLDR
It is verified that the ET gates outperform the non-ET gates with a substantial improvement of the gate fidelity after an occurrence of the single-photon-loss error, paving the way towards fault-tolerant quantum computation.
Extending the lifetime of a quantum bit with error correction in superconducting circuits
TLDR
A QEC system that reaches the break-even point by suppressing the natural errors due to energy loss for a qubit logically encoded in superpositions of Schrödinger-cat states of a superconducting resonator is demonstrated.
Dynamical Decoupling of Open Quantum Systems
We propose a novel dynamical method for beating decoherence and dissipation in open quantum systems. We demonstrate the possibility of filtering out the effects of unwanted (not necessarily known)
NMR techniques for quantum control and computation
Fifty years of developments in nuclear magnetic resonance (NMR) have resulted in an unrivaled degree of control of the dynamics of coupled two-level quantum systems. This coherent control of nuclear
Cavity State Manipulation Using Photon-Number Selective Phase Gates.
TLDR
This work introduces the selective number-dependent arbitrary phase (snap) gate, which imparts a different phase to each Fock-state component using an off-resonantly coupled qubit, and creates a one-photon Fock state with high fidelity.
...
...