This work motivates and applies operational methodology to simulation of quantum statistics of separable qubit X states. Three operational algorithms for evaluating separability probability distributions are put forward. Building on previous findings, the volume function characterizing the separability distribution is determined via quantum measurements of multi-qubit observables. Three measuring states, one for each algorithm are generated via (i) a multi-qubit channel map, (ii) a unitary operator generated by a Hamiltonian describing a non-uniform hypergraph configuration of interactions among 12 qubits, and (iii) a quantum walk CP map in a extended state space. Higher order CZ gates are the only tools of the algorithms hence the work associates itself computationally with the Instantaneous Quantum Polynomial-time Circuits (IQP), while wrt possible implementation the work relates to the Lechner-Hauke-Zoller (LHZ) architecture of higher order coupling. Finally some uncertainty aspects of the quantum measurement observables are discussed together with possible extensions to non-qubit separable bipartite systems.
This work motivates and applies operational methodology to simulation of quantum statistics of separable qubit X states. Three operational algorithms for evaluating separability probability distributions are put forward. Building on previous findings, the volume function characterizing the separability distribution is determined via quantum measurements of multi-qubit observables. Three measuring states, one for each algorithm are generated via (i) a multi-qubit channel map, (ii) a unitary operator generated by a Hamiltonian describing a non-uniform hypergraph configuration of interactions among 12 qubits, and (iii) a quantum walk CP map in a extended state space. Higher order CZ gates are the only tools of the algorithms hence the work associates itself computationally with the Instantaneous Quantum Polynomial-time Circuits (IQP), while wrt possible implementation the work relates to the Lechner-Hauke-Zoller (LHZ) architecture of higher order coupling. Finally some uncertainty aspects of the quantum measurement observables are discussed together with possible extensions to non-qubit separable bipartite systems.
The rapid advance of quantum information technology requires precise control and manipulation of quantum systems and of their properties; in particular, it is essential to certify that quantum processors truly work quantum mechanically, in order to validate experiments and their results. The problem of certification of quantum states and devices is a demanding one, thus many attempts have been put forward to find ways of efficiently test their basic functionalities, such as their entanglement properties. The main problems addressed in this thesis concern indeed finding optimal strategies for the estimation and characterization of quantum states and channels, with a special focus on entanglement correlations. In our first work we considered the certification of entanglement across a given partition of a multi-qubit system, when only partial information about the corresponding quantum state is available; we tackled the problem of finding the best measurement strategy introducing the statistics of lengths of measurement sequences, choosing multi-qubit Pauli-measurements as observables. Using a sample of random unknown states, we were able to identify the (on average) shortest, i.e. most efficient, measurement sequence to detect entanglement. The investigation was carried out with an algorithm based on the truncated moment sequences (tms) problem, which provides necessary and sufficient conditions for entanglement or separability of a quantum state of a finite dimensional system. This study results in a very efficient strategy especially for symmetric states, for which only a tiny fraction (10−6) of randomly chosen entangled states are undetected for systems with 6 qubits or more. We continued in our second work with the problem of separability of quantum channels to answer the question whether a given quantum device is able to create entanglement or not. The Choi matrix representation, provided by the Choi–Jamiołkowski isomorphism, casts the problem in terms of systems and ancillas, giving different classes of separability depending on the cut considered between them. Once again, the tms framework turned out to be well suited for this study, giving a unifying approach for the different separability problems; a solution is found in terms of the tms associated to the coordinates of the Choi state, in a fixed basis, and semidefinite programming is used to get a separability certificate. We explored examples of families of 2-qubit and single-qutrit channels, for which our algorithm can give an answer in cases where other criteria remain inconclusive. In a further work we shifted our attention to a different direction, highlighting a connection between the fields of quantum information, Bose-Einstein condensation (BEC) and analogue gravity, thus showing the relevance of quantum information notions in a broader context. We studied the entanglement properties of a BEC analogue of a black hole, which is described by a three-mode Gaussian state; we investigated bipartite and tripartite entanglement measures based on the covariance matrix description, both at zero and finite temperature, providing the best experimental configuration for entanglement detection. In a final stage of this thesis, we started looking at different measurement strategies for testing quantum devices whose functionality can be described by a single parameter; we used a Bayesian approach to estimate this parameter, exploiting the information collected through measurements to update a conditional probability distribution, without the need of estimating expected values of observables. The problem of finding the optimal experimental design can be in this case translated in the optimization of a utility function, which usually guides the update process adaptively at each step; we tried to outperform this approach looking ahead not only at the next step, but at a few ones, in order to obtain an answer of correct or wrong functioning as soon as possible. Moreover, we chose the input state for the quantum channel considered minimizing the error probability given by the Chernoff distance between the outputs of an ideal and a faulty channel; finally, we considered two different final decision criteria and compared their efficiency.
Abstract This work develops a theoretical framework for scalable noise resilience in coupled-oscillator quantum processors by integrating non-local Lechner–Hauke–Zoller (LHZ) interactions with non-extensive Tsallis statistics. The study focuses on a system of three strongly coupled harmonic oscillators (TSCHO), each interacting with a bosonic bath, and truncating each oscillator to its two lowest energy levels, obtaining an effective eight-dimensional Hilbert space. The Hamiltonian is diagonalized, yielding eigenstates that include dark states, and squeezed parity-mixed states. Thermal non-equilibrium conditions are then introduced using Tsallis statistics, constructing a generalized initial density matrix parameterized by the entropic index q . The dissipative dynamics is described by a Lindblad master equation derived under the Born–Markov approximation, with bath-induced decay rates that incorporate a q -deformed Bose–Einstein distribution. The concurrence is computed for two and three-oscillator subsystems and compared as a function of time and temperature. Next, the LHZ architecture is incorporated by adding genuine three-body non-local interactions, and the corresponding dissipative coefficients are derived. The time evolution of entanglement and fidelity is simulated within the LHZ-protected subspace. Finally, a CNOT gate is applied to one of the subsystems which exhibits significant concurrence and its fidelity is evaluated across different q regimes and temperatures. The results demonstrate that scaling from two to three oscillators spontaneously generates asymmetric dissipation channels that protect specific subsystems. A counter-intuitive temperature assisted stabilization effect is validated: for q ≠ 1 , higher bath temperatures do not destroy entanglement but rather preserve it. In the LHZ architecture for TSCHO quantitative analysis shows that at low frequencies and elevated temperatures, the non-extensive regimes outperform the extensive one; however, at high frequencies, thermal effects are suppressed and the q = 1 regime remains dominant. The dissipatively protected CNOT gate achieves meaningful fidelity without the massive qubit overhead of conventional quantum error correction. While the numerical analysis is performed for three oscillators, the proposed framework is theoretically scalable to larger systems, and the underlying mechanisms—non-local parity protection and non-extensive thermodynamics—are general. Overall, this approach suggests a potential paradigm shift from fighting decoherence to engineering intrinsic noise resilience at the hardware level, establishing non-locality and non-extensive thermodynamics as physical resources for robust quantum information processing.
Separability and entanglement for n-qubits systems are quantified by using Hilbert-Schmidt (HS) decompositions in which the density matrices are decomposed into various terms representing certain one qubit, two-qubits,and larger qubits measurements. The present method is more general than previous methods for bipartite systems as it can be used for quantification of entanglement for large n-qubits systems.We demonstrate the use of such method by analyzing three qubits GHZ states, and three qubits general Bell states produced by a certain multiplications of Braid operators, operating on the computational basis of states. Quantum correlations are obtained by measuring all qubits of these systems, while a measurement of a part of the system gives only classical correlations. Quantification of entanglement for these systems is given by the use of HS decompositions.
Abstract Determining whether an unknown quantum state is entangled can be approached through quantum tomography and related algorithms. However, these methods are generally inefficient due to the NP-hardness of the problem. An alternative strategy is to treat it as a decision (or estimation) problem with a quantum data structure (Horodecki and Ekert 2002 Phys. Rev. Lett. 89 127902). Over the years, significant progress has been made: the two-qubit case is now fully understood, but for higher-dimensional systems only entanglement detection via negativity has been established. In this work, we propose schemes for measuring upper bounds on bipartite biconcurrence and concurrence, expressed as functions of a fixed (but arbitrary) unitary operation acting on a Hilbert space that is quadratically larger than the original state space. Independently, we provide a scheme for measuring a lower bound for concurrence. In the case of the states proportional to the projectors the schemes are getting significantly simpler and the upper bound on the biconcurrence, as well as the lower bound on the concurrence, become exact (up to experimental and numerical errors). This framework opens the door to tackling the separability problem using methods inspired by the variational quantum eigensolver.
Lechner-Hauke-Zoller (LHZ) parity embedding is one of the front-running methods for implementing difficult-to-engineer long-range interactions in quantum optimization problems. Continuous-time quantum walks are a leading approach for solving quantum optimization problems. Because they populate excited states, quantum walks can avoid the exponential gap-closing problems seen in other continuous-time techniques such as quantum annealing and adiabatic quantum computation. An important question, therefore, is how continuous-time quantum walks perform in combination with the LHZ parity embedding. By numerically simulating continuous-time quantum walks on four-, five-, and six-logical-qubit Sherrington-Kirkpatrick Ising spin glass instances embedded onto the LHZ parity embedding, we are able to verify the continued efficacy of heuristics used to estimate the optimal hopping rate and the numerical agreement with the theory behind the location of the lower bound of the LHZ parity constraint strength. In addition, by comparing several different LHZ-based decoding methods, we identified postreadout error correction techniques which improve the success probability of the quantum walk.
Lechner-Hauke-Zoller (LHZ) parity embedding is one of the front-running methods for implementing difficult-to-engineer long-range interactions in quantum optimization problems. Continuous-time quantum walks are a leading approach for solving quantum optimization problems. Because they populate excited states, quantum walks can avoid the exponential gap-closing problems seen in other continuous-time techniques such as quantum annealing and adiabatic quantum computation. An important question, therefore, is how continuous-time quantum walks perform in combination with the LHZ parity embedding. By numerically simulating continuous-time quantum walks on four-, five-, and six-logical-qubit Sherrington-Kirkpatrick Ising spin glass instances embedded onto the LHZ parity embedding, we are able to verify the continued efficacy of heuristics used to estimate the optimal hopping rate and the numerical agreement with the theory behind the location of the lower bound of the LHZ parity constraint strength. In addition, by comparing several different LHZ-based decoding methods, we identified postreadout error correction techniques which improve the success probability of the quantum walk.