Related papers: Efficient Approximation of Quantum Channel Fidelit…
Coherent superposition is a key feature of quantum mechanics that underlies the advantage of quantum technologies over their classical counterparts. Recently, coherence has been recast as a resource theory in an attempt to identify and…
This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…
We analyze the physics of optimal protocols to prepare a target state with high fidelity in a symmetrically coupled two-qubit system. By varying the protocol duration, we find a discontinuous phase transition, which is characterized by a…
We study the properties of error correcting codes for noise models in the presence of asymmetries and/or correlations by means of the entanglement fidelity and the code entropy. First, we consider a dephasing Markovian memory channel and…
The accuracies of modern quantum logic clocks have surpassed those of standard atomic fountain clocks. These clocks also provide a greater degree of control, because before and after clock queries, we are able to apply chosen unitary…
Semidefinite relaxations are widely used to compute upper bounds on the objective of optimization problems involving noncommutative polynomials. Such optimization problems are prevalent in quantum information. We present an algorithm able…
Quantum error correction is a critical component for scaling up quantum computing. Given a quantum code, an optimal decoder maps the measured code violations to the most likely error that occurred, but its cost scales exponentially with the…
As the title indicates, this chapter presents a brief, self-contained introduction to five fundamental problems in Quantum Information Science (QIS) that are especially well-suited to be formulated as Semi-definite Programs (SDP). We have…
Neural networks are central to many emerging technologies, but verifying their correctness remains a major challenge. It is known that network outputs can be sensitive and fragile to even small input perturbations, thereby increasing the…
We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the…
We provide new results for computing and comparing the quantum gate fidelity of quantum channels via their Choi matrices. We extend recent work that showed there exist non-dual pairs of quantum channels with equal gate fidelity by providing…
Tremendous efforts have been paid for realization of fault-tolerant quantum computation so far. However, preexisting fault-tolerant schemes assume that a lot of qubits live together in a single quantum system, which is incompatible with…
We consider quantum-information division, which is characterized by a channel whose outputs have no correlation and are not completely randomized. We show that the quantum-information division is possible in a probabilistic manner by…
The surface code is one the most promising alternatives for implementing fault-tolerant, large-scale quantum information processing. Its high threshold for single-qubit errors under stochastic noise is one of its most attrative features. We…
The quantum capacity captures the value of a quantum channel for transmitting quantum information, establishing the fundamental limits on quantum communication. In spite of its central role in quantum information theory, the quantum…
Semidefinite Programming (SDP) provides tight lower bounds for Optimal Power Flow problems. However, solving large-scale SDP problems requires exploiting sparsity. In this paper, we experiment several clique decomposition algorithms that…
There is an increasing interest in quantum algorithms for optimization problems. Within convex optimization, interior-point methods and other recently proposed quantum algorithms are non-trivial to implement on noisy quantum devices. Here,…
It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show…
The goal of quantum channel discrimination and estimation is to determine the identity of an unknown channel from a discrete or continuous set, respectively. The query complexity of these tasks is equal to the minimum number of times one…
The efficiency of parameter estimation of quantum channels is studied in this paper. We introduce the concept of programmable parameters to the theory of estimation. It is found that programmable parameters obey the standard quantum limit…