The starting point of my thesis work was the study of optimization algorithms based on cavity method. These algorithms have been developed to a high degree of complexity in the last decade and they are also known as message passing algorithms (MPAs). My work has started by a question posed by my supervisor: what links can be found between those different approaches to the same problems? The starting aim of the PhD project was to explore the new ideas and algorithms that could result from a cross-fertilization between different approaches. During the first years we made a long and accurate comparison between different algorithms on a specific COP: the prize collecting Steiner tree problem. Looking to MPAs as an evolution of probability distributions of discrete variables led me to find some possible links with many body quantum physics, where typically we deal with probability amplitudes over discrete variables. In the recent years several results have appeared concerning the extension of the cavity method and message passing technics to quantum context. In 2012 Ramezanpour proposed a method, the variational quantum cavity method (VQCM), for finding approximate ground state wave functions based on a new messages passing algorithm used in stochastic optimization. Ramezanpour and I have extended this approach to find low excited states. In the last year of my Ph.D. I simplify the VQCM using imaginary time evolution operator. Moreover I extend this approach to find finite temperature density matri

Indaco Biazzo

The focus of this research activity is to work on pragmatic information reconciliation applied to QKD schemes based on single photon or weak pulse laser (WPL) sources, so as to use feed-forward techniques which minimize the interaction between transmitter and receiver. The core ideas of the thesis are employing Forward Error Correction (FEC) coding as opposed to two-way communication for information reconciliation in QKD schemes, exploiting all the available information for data processing at the receiver including information available from the quantum channel, since optimized use of this information can lead to significant performance improvement, and providing a security versus secret-key rate trade-off to the end-user within the context of QKD systems. Moreover, as shown by accurate experimental studies, the communication channel used for quantum key exchange is not able to reach high levels of reliability (the Quantum Bit Error Rate -QBER may have a high value), both because of the inherent characteristics of the system, and of the presence of a possible attacker. In order to obtain acceptable residual error rates, it is necessary to use a parallel classical and public channel, characterized by high transmission rates and low error rates, on which to transmit only the redundancy bits of systematic channel codes with performance possibly close to the capacity limit. Furthermore, since the more redundancy is added by the channel code, the more the corresponding information can be used to decipher the private message itself, it becomes necessary to design high-rate codes obtained by puncturing a low-rate mother code, possibly achieving a redundancy such that elements of the secret message cannot be uniquely determined from the redundancy itself, so for that purpose we designed high rate LDPC codes. Using high rate codes increases the security with trade-off to performance. Other low photon number applications have also been considered, such as weak-laser pulses (WLP) communication. For that purpose, a low-complexity photon-counting receiver has been considered which may be employed in long-distance amplification-free classical optical communication schemes, and which is typically modeled as an equivalent Binary Symmetric Channel (BSC). We have developed a time varying Binary Input-Multiple Output (BIMO) channel model for this low-complexity photon-counting receiver, and analyzed its performance in presence of soft-metric based capacity approaching iteratively decoded error correcting codes, such as soft-metric based Low Density Parity Check (LDPC) codes and polar codes. We show that the classical channel capacity of the suggested BIMO model is higher than the capacity of the BSC model, and that the use of the BIMO model allows to feed the channel decoder with soft information, in the form of Log-Likelihood Ratios (LLRs), achieving a significant reduction in Bit Error Rate (BER) and Frame Error Rate (FER) with respect to classical hard-metric-based schemes which should be used in conjunction with a BSC channel mode

Inam Bari*

PORTO Publications Open Repository TOrino

Soft Decoding Techniques for Quantum Key Distribution (QKD) and Weak Energy Optical Communication

The starting point of my thesis work was the study of optimization algorithms based on cavity method. These algorithms have been developed to a high degree of complexity in the last decade and they are also known as message passing algorithms (MPAs).
My work has started by a question posed by my supervisor: what links can be found between those different approaches to the same problems? The starting aim of the PhD project was to explore the new ideas and algorithms that could result from a cross-fertilization between different approaches. During the first years we made a long and accurate comparison between different algorithms on a specific COP: the prize collecting Steiner tree problem. 
Looking to MPAs as an evolution of probability distributions of discrete variables led me to find some possible links with many body quantum physics, where typically we deal with probability amplitudes over discrete variables. In the recent years several results have appeared concerning the extension of the cavity method and message passing technics to quantum context. In 2012 Ramezanpour proposed a method, the variational quantum cavity method (VQCM), for finding approximate ground state wave functions based on a new messages passing algorithm used in stochastic optimization. Ramezanpour and I have extended this approach to find low excited states. 
In the last year of my Ph.D. I simplify the VQCM using imaginary time evolution operator. Moreover I extend this approach to find finite temperature density matrix

BIAZZO, INDACO

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

English

Cavity algorithms under global
constraints: classical and quantum problems

Cavity algorithms under global constraints: classical and quantum problems

The focus of this research activity is to work on pragmatic information reconciliation applied to QKD schemes based on single photon or weak pulse laser (WPL) sources, so as to use feed-forward techniques which minimize the interaction between transmitter and receiver.
The core ideas of the thesis are employing Forward Error Correction (FEC) coding as opposed to two-way communication for information reconciliation in QKD schemes, exploiting all the available information for data processing at the receiver including information available from the quantum channel, since optimized use of this information can lead to significant performance improvement, and providing a security versus secret-key rate trade-off to the end-user within the context of QKD systems.
Moreover, as shown by accurate experimental studies, the communication channel used for quantum key exchange is not able to reach high levels of reliability (the Quantum Bit Error Rate -QBER may have a high value), both because of the inherent characteristics of the system, and of the presence of a possible attacker. In order to obtain acceptable residual error rates, it is necessary to use a parallel classical and public channel, characterized by high transmission rates and low error rates, on which to transmit only the redundancy bits of systematic channel codes with performance possibly close to the capacity limit.
Furthermore, since the more redundancy is added by the channel code, the more the corresponding information can be used to decipher the private message itself, it becomes necessary to design high-rate codes obtained by puncturing a low-rate mother code, possibly achieving a redundancy such that elements of the secret message cannot be uniquely determined from the redundancy itself, so for that purpose we designed high rate LDPC codes. Using high rate codes increases the security with trade-off to performance.
Other low photon number applications have also been considered, such as weak-laser pulses (WLP) communication. For that purpose, a low-complexity photon-counting receiver has been considered which may be employed in long-distance amplification-free classical optical communication schemes, and which is typically modeled as an equivalent Binary Symmetric Channel (BSC). We have developed a time varying Binary Input-Multiple Output (BIMO) channel model for this low-complexity photon-counting receiver, and analyzed its performance in presence of soft-metric based capacity approaching iteratively decoded error correcting codes, such as soft-metric based Low Density Parity Check (LDPC) codes and polar codes. We show that the classical channel capacity of the suggested BIMO model is higher than the capacity of the BSC model, and that the use of the BIMO model allows to feed the channel decoder with soft information, in the form of Log-Likelihood Ratios (LLRs), achieving a significant reduction in Bit Error Rate (BER) and Frame Error Rate (FER) with respect to classical hard-metric-based schemes which should be used in conjunction with a BSC channel model

BARI, INAM

"Soft Decoding Techniques for Quantum Key Distribution (QKD) and Weak Energy Optical Communication"

https://iris.polito.it/retrieve/handle/11583/2531893/61961/Thesis_PhD_InamBari.pdf

Cavity algorithms under global constraints: classical and quantum problems

Abstract

Similar works

Full text

Available Versions

PORTO Publications Open Repository TOrino

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

PORTO Publications Open Repository TOrino

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)