Error- and Loss-Tolerances of Surface Codes with General Lattice Structures

We propose a family of surface codes with general lattice structures, where the error-tolerances against bit and phase errors can be controlled asymmetrically by changing the underlying lattice geometries. The surface codes on various lattices are found to be efficient in the sense that their threshold values universally approach the quantum Gilbert-Varshamov bound. We find that the error-tolerance of surface codes depends on the connectivity of underlying lattices; the error chains on a lattice of lower connectivity are easier to correct. On the other hand, the loss-tolerance of surface codes exhibits an opposite behavior; the logical information on a lattice of higher connectivity has more robustness against qubit loss. As a result, we come upon a fundamental trade-off between error- and loss-tolerances in the family of the surface codes with different lattice geometries.Comment: 5pages, 3 figure

Optimal cavity design for minimizing errors in cavity-QED-based atom-photon entangling gates with finite temporal duration

We investigate atom-photon entangling gates based on cavity quantum electrodynamics (QED) for a finite photon-pulse duration, where not only the photon loss but also the temporal mode-mismatch of the photon pulse becomes a severe source of error. We analytically derive relations between cavity parameters, including transmittance, length, and effective cross-sectional area of the cavity, that minimize both the photon loss probability and the error rate due to temporal mode-mismatch by taking it into account as state-dependent pulse delay. We also investigate the effects of pulse distortion using numerical simulations for the case of short pulse duration.Comment: 8 pages, 5 figure

Noise propagation in hybrid tensor networks

The hybrid tensor network (HTN) method is a general framework allowing for the construction of an effective wavefunction with the combination of classical tensors and quantum tensors, i.e., amplitudes of quantum states. In particular, hybrid tree tensor networks (HTTNs) are very useful for simulating larger systems beyond the available size of the quantum hardware. However, while the realistic quantum states in NISQ hardware are highly likely to be noisy, this framework is formulated for pure states. In this work, as well as discussing the relevant methods, i.e., Deep VQE and entanglement forging under the framework of HTTNs, we investigate the noisy HTN states by introducing the expansion operator for providing the description of the expansion of the size of simulated quantum systems and the noise propagation. This framework enables the general tree HTN states to be explicitly represented and their physicality to be discussed. We also show that the expectation value of a measured observable exponentially vanishes with the number of contracted quantum tensors. Our work will lead to providing the noise-resilient construction of HTN states.Comment: 20 pages, 8 figure