In principle a quantum system could be used to simulate another quantum system. The purpose of such a simulation would be to obtain information about problems which are difficult to simulate on a classical computer due to the exponential increase of the Hilbert space with the size of the system, and which cannot be readily measured or controlled in an experiment. A quantum simulator is, however, an open quantum system that will interact with the surrounding environment, which in this case are other particles in the system, and will be implemented using imperfect controls, making it subject to noise. It has been suggested that noise does not need to be controlled to the same extent as it must be for general quantum information processing. However, the effects of noise in quantum simulations are not well understood and how best to treat them in most cases is not known. In the present work we study an existing quantum algorithm for the simulation of the one-dimensional Fano-Anderson model. This algorithm was proposed for a liquid-state NMR device. We examine models of noise in the evolution using different initial states in the original model. We also add interacting spins to simulate realistic situation where an environment of spins is present. We find that states which are entangled with their environment, and sometimes correlated but not necessarily entangled have an evolution which is described by maps which are not completely positive. We discuss the conditions for this to occur and also the implications.
In principle a quantum system could be used to simulate another quantum system. The purpose of such a simulation would be to obtain information about problems which are difficult to simulate on a classical computer due to the exponential increase of the Hilbert space with the size of the system, and which cannot be readily measured or controlled in an experiment. A quantum simulator is, however, an open quantum system that will interact with the surrounding environment, which in this case are other particles in the system, and will be implemented using imperfect controls, making it subject to noise. It has been suggested that noise does not need to be controlled to the same extent as it must be for general quantum information processing. However, the effects of noise in quantum simulations are not well understood and how best to treat them in most cases is not known. In the present work we study an existing quantum algorithm for the simulation of the one-dimensional Fano-Anderson model. This algorithm was proposed for a liquid-state NMR device. We examine models of noise in the evolution using different initial states in the original model. We also add interacting spins to simulate realistic situation where an environment of spins is present. We find that states which are entangled with their environment, and sometimes correlated but not necessarily entangled have an evolution which is described by maps which are not completely positive. We discuss the conditions for this to occur and also the implications.
In principle, a quantum system could be used to simulate another quantum system. The purpose of such a simulation would be to obtain information about problems which are difficult to simulate on a classical computer due to the exponential increase of the Hilbert space with the size of the system and which cannot be readily measured or controlled in an experiment. The system will interact with the surrounding environment and with the other particles in the system, and be implemented using imperfect controls, making it subject to noise. It has been suggested that noise does not need to be controlled to the same extent as it must be for general quantum computing. However, the effects of noise in quantum simulations are not well understood and how best to treat them in most cases is not known. In this paper we study an existing quantum algorithm for simulating the one-dimensional Fano-Anderson model using a liquid-state NMR device. We examine models of noise in the evolution using different initial states in the original model. We also add interacting spins to simulate a realistic situation where an environment of spins is present. We find that states which are entangled with their environment, and sometimes correlated but not necessarily entangled, have an evolution which is described by maps which are not completely positive. We discuss the conditions for this to occur and also the implications.
Recently developed quantum algorithms suggest that in principle, quantum computers can solve problems such as simulation of physical systems more efficiently than classical computers. Much remains to be done to implement these conceptual ideas into actual quantum computers. As a small-scale demonstration of their capability, we simulate a simple many-fermion problem, the Fano-Anderson model, using liquid-state nuclear magnetic resonance (NMR). We carefully designed our experiment so that the resource requirement would scale up polynomially with the size of the quantum system to be simulated. The experimental results obtained give us an insight to the quantum control required when simulating quantum systems with NMR techniques. The simulation of other physical systems, with different particle statistics, is also discussed.
One of the greatest challenges in the fields of quantum information processing and quantum technologies is the detailed coherent control over each and every constituent of quantum systems with an ever increasing number of particles. Within this endeavor, harnessing of many-body entanglement against the detrimental effects of the environment is a major pressing issue. Besides being an important concept from a fundamental standpoint, entanglement has been recognized as a crucial resource for quantum speed-ups or performance enhancements over classical methods. Understanding and controlling many-body entanglement in open systems may have strong implications in quantum computing, quantum simulations of many-body systems, secure quantum communication or cryptography, quantum metrology, our understanding of the quantum-to-classical transition, and other important questions of quantum foundations.In this paper we present an overview of recent theoretical and experimental efforts to underpin the dynamics of entanglement under the influence of noise. Entanglement is thus taken as a dynamic quantity on its own, and we survey how it evolves due to the unavoidable interaction of the entangled system with its surroundings. We analyze several scenarios, corresponding to different families of states and environments, which render a very rich diversity of dynamical behaviors.In contrast to single-particle quantities, like populations and coherences, which typically vanish only asymptotically in time, entanglement may disappear at a finite time. In addition, important classes of entanglement display an exponential decay with the number of particles when subject to local noise, which poses yet another threat to the already-challenging scaling of quantum technologies. Other classes, however, turn out to be extremely robust against local noise. Theoretical results and recent experiments regarding the difference between local and global decoherence are summarized. Control and robustness-enhancement techniques, scaling laws, statistical and geometrical aspects of multipartite-entanglement decay are also reviewed; all in order to give a broad picture of entanglement dynamics in open quantum systems addressed to both theorists and experimentalists inside and outside the field of quantum information.
One of the greatest challenges in the fields of quantum information processing and quantum technologies is the detailed coherent control over each and every constituent of quantum systems with an ever increasing number of particles. Within this endeavor, harnessing of many-body entanglement against the detrimental effects of the environment is a major pressing issue. Besides being an important concept from a fundamental standpoint, entanglement has been recognized as a crucial resource for quantum speed-ups or performance enhancements over classical methods. Understanding and controlling many-body entanglement in open systems may have strong implications in quantum computing, quantum simulations of many-body systems, secure quantum communication or cryptography, quantum metrology, our understanding of the quantum-to-classical transition, and other important questions of quantum foundations. In this paper we present an overview of recent theoretical and experimental efforts to underpin the dynamics of entanglement under the influence of noise. Entanglement is thus taken as a dynamic quantity on its own, and we survey how it evolves due to the unavoidable interaction of the entangled system with its surroundings. We analyze several scenarios, corresponding to different families of states and environments, which render a very rich diversity of dynamical behaviors. In contrast to single-particle quantities, like populations and coherences, which typically vanish only asymptotically in time, entanglement may disappear at a finite time. In addition, important classes of entanglement display an exponential decay with the number of particles when subject to local noise, which poses yet another threat to the already-challenging scaling of quantum technologies. Other classes, however, turn out to be extremely robust against local noise. Theoretical results and recent experiments regarding the difference between local and global decoherence are summarized. Control and robustness- enhancement techniques, scaling laws, statistical and geometrical aspects of multipartite-entanglement decay are also reviewed; all in order to give a broad picture of entanglement dynamics in open quantum systems addressed to both theorists and experimentalists inside and outside the field of quantum information.
The purpose of this study is to investigate the effects of noise in quantum simulation. An existing and simple model was used to simulate the results of the evolution of an initial quantum state. The results show that if all states align in z-axis, the dynamical map is completely positive, and the spin bath affected how fast the system evolved. If precessing states are considered, the dynamical map is non completely positive. Visualization of the Bloch vector was used to illustrate the process of the evolution of the quantum system.
All physical quantum systems are in contact with the external world which is inevitably a source of noise. It is therefore necessary to take into account this dissipation when designing controls that accomplish useful tasks in quantum information processing. This thesis is on that overlap of open quantum systems and control theory; it looks at what dynamics can happen with the use of external driving, and how this driving can be chosen to accomplish a desired goal. The first result looks at how a given quantum dissipator can be manipulated, using coherent controls, into replicating the action of a different type of noise. This results in no-go theorems for how noise can be transformed based on its isotropy, with applications in simulating open systems. Another way of doing simulations is to use only unitary dynamics over the system and a finite dimensional ancilla, and it is proved that there always exists a dilation Hamiltonian that replicates the noisy dynamics continuously in time. This also highlights the fact that adding controls on noise can result in a different evolution than if the controls were done on the under- lying system-environment level. A conjecture is introduced and studied which states that both approaches are equivalent in the special case of the controls commuting with the Lindbladian. A way around this difficulty is to use a quantum system to compute in situ which controls are best for achieving a desired task on itself. This problem is studied in the context of reaching entangling gates on a quantum simulator in order to upgrade it into a quantum computer. The experimental cost of doing so is found to be polynomial in the number of qubits in simulations. The same underlying principle is also used to find error correcting codes tailored to the dissipation in a system.