Final Report Summary - THECOSINT (Theory of Quantum Computation and Many-Body Simulation with Novel Quantum Technologies)
Quantum mechanics is an uneasy branch of science. It eludes our daily intuition and defies our comprehension of the physical world. But despite this quite blurry scenario, quantum mechanics has a lot to offer. We know that classical systems can compute, and we exploit this in our day-to-day life: a huge amount of bits of information are stored and processed everyday in the classical electrical circuits of our computers, mobile phones, and alike. A similar computation can happen at the quantum level as well: electrons, photons, and elementary particles can store 'quantum bits' of information, and when they interact those quantum bits can be processed. The exciting fact is that quantum systems can compute in an extraordinary way, much better than their classical counterpart - as we are now learning. By 'hacking' the computational power of the blurry quantum world, we could build quantum computers which store and process information at an unparalleled level. Problems that nowadays might puzzle our ordinary computers for years could be solved in the blink of an eye by these extraordinary quantum machines. The impact of this 'quantum information' revolution could be huge, reaching into every corner of our lives. From unconditionally secure communication to complex modelling for material and drug engineering, there are plenty of possibilities.
In order to make this promise a reality, it is necessary to identify, among the many quantum systems present in nature, some that can be controlled at will; thus providing the physical support for quantum information processing. But nature seems jealous of her secretes, and no definitive front-runner has been identified so far. This exciting search has been the main motivation of the project THECOSINT.
In particular, an approach alternative with respect to 'quantum bits' is given by the so called 'quantum modes' (also dubbed continuous variables). Whereas the former are quantum systems that can assume two states only (like two polarisation states of light), the latter can span over much more states (possibly infinite, similar to the infinite gradients of colours that light can assume). Unfortunately, insofar technological obstacles avoided to control a number of quantum modes large enough to really exploit the computational power of the quantum world. However, crucial experimental advances are rapidly changing this scenario. Inspired by this, the main objective of my proposal has been to devise novel schemes suited for emerging quantum-mode technologies, with the ultimate vision of exploiting the full power of quantum information.
In particular, the project has been developed in the three main goals identified in the original proposal and hereby summarised:
1) The first objective of the project was to single out the benefits that may be offered by some recently emerged quantum technologies (e.g. circuit quantum electrodynamics, optomechanical oscillators, and trapped ions). Specifically, the first task was to individuate useful effective interactions and to design proper measurement schemes suited for emerging technologies.
2) The second objective was to consider many-body continuous variable systems in connection to simulators and quantum thermodynamics. A specific objective was to study the thermal properties of many-body continuous variable systems that challenge some standard thermodynamic concepts, like local intensive temperature.
3) The third objective was to seek for novel approaches to quantum computation over continuous variables suited for implementation with novel technologies. In particular, a major aim was to introduce approaches suited to continuous variable systems encoded in confined forms - as the latter emerge naturally in the mentioned novel technologies.
In strict relation to all the above objectives, the main scientific outcomes of the project have been:
i) The introduction of novel approaches to quantum computation over continuous quantum variable
In the context of quantum computation over continuous variables, an entire spectrum of new possibilities was opened few years ago by the landmark discovery of a paradigm of computation - dubbed measurement-based quantum computation - that works as follows: first a set of quantum modes is prepared in the so-called cluster state; then, the specific computation proceeds as a sequence of local measurements that consume the cluster-state entanglement as the main resource of the computation. From an implementation perspective, the main effort resides in the preparation of the initial cluster. In this context, a major outcome of the present project has been to propose of an alternative approach to produce the cluster state, based on the introduction of a set of gapped and local Hamiltonians whose unique ground state is the continuous variable cluster state. This approach makes 'adiabatic state generation' possible: the cluster state can be prepared by first cooling down the system to zero temperature and then switching on the interactions so that the system is adiabatically driven toward the ground state of the cluster Hamiltonian. This approach is naturally better suited for state preparations at large scales and for continuous variables encoded in a confined form in the mentioned novel technologies. Another outcome of the present project has been the introduction of a second novel approach to quantum computation over continuous variables named 'sequential quantum computation'. In the standard approach, the cluster is first built and then consumed along the computation via local measurements. However, the creation of the whole cluster at the beginning of the computation is not strictly necessary. In other words the cluster might be created and immediately consumed step after step during the computation. This sequential approach relaxes the requirement of preserving the coherence of such a massively entangled state along the computation and might be helpful in reducing the detrimental effect of noise. In the present project, as said, a new theoretical framework for sequential quantum computation has been introduced. The feasibility of this approach in the physical setting of novel quantum technologies has also been recently approached.
ii) The analysis of the role played by quantum correlations in the emergence of thermodynamics quantities in continuous variable many-body systems
In the present project, the concept of temperature in a setting beyond the standard thermodynamics prescriptions has been considered. Namely, rather than restricting to standard coarse-grained measurements, one can consider observers able to master any possible quantum measurement - a scenario that might be relevant at nanoscopic scales for novel quantum technologies. In this setting, the project focussed on quantum systems of coupled harmonic oscillators and studied the question of whether the temperature is an intensive quantity. On one hand, instances in which this approximation is not valid have been identified; on the other hand, these investigation also showed that the standard thermodynamics result is recovered for coarse-grained measurements. In particular, the role that entanglement and quantum correlations play in this scenario has been analysed in details, showing that in general the thermodynamic paradigm of local intensive temperature applies whenever entanglement is not present in the system. The results of this project extend the applicability of the concept of temperature and assess its limits of validity, to a scenario beyond the standard one and that might be relevant for future technologies at mesoscopic and nanoscopic scale.
iii) The introduction of new measurement schemes for novel quantum technologies hosting quantum continuous variables
In the context of the novel quantum technologies mentioned above, an important question concerns extraction of the relevant information there encoded in the form of continuous variables. In general, quantum state reconstruction - also dubbed quantum state tomography - tries to estimate the state of a quantum system using measurements on an ensemble of identical copies of it. The advances of quantum information with continuous variables have been traditionally related to the exquisite control that is experimentally achievable for travelling light qumodes. This naturally led to a huge research effort in the reconstruction of travelling qumodes, for which a general framework based on quadrature measurements has been established. However, when those measurements are not available - as it is the case for qumodes confined in novel technologies - the framework itself is not directly applicable. A major objective achieved in this project was to devise a novel scheme for quantum tomography of a network of confined continuous variables. This is the first scheme specifically devised to this goal. In addition, it requires only minimal access to the system: instead of accessing all the oscillators in the network, access to a single one suffices. Tomography with minimal access is not only of theoretical interest. In fact, accessibility problems often plague experiments and the results of the project are expected to be useful for experimental applications.
iv) The characterisation of quantum correlations that are believed to be essential for advanced computational tasks such as quantum computation and simulation
A major question in quantum information is the characterisation of quantum correlations and their relation to the so-called quantum speed up that is achieved when quantum systems, rather than classical systems, are used to perform some information tasks (e.g. quantum computation). In this context, major results have been obtained during the project concerning the two most employed quantifiers of correlations beyond entanglement: non-classicality and the quantum discord. The former was established more than half a century ago, stemming from the notions of quantum phase space and quasiprobability distributions. The latter is instead mainly based on the information-theoretic aspects of quantum correlations. In this project those two approaches have been compared, investigating in particular whether physical constraints emerging from the former can bring new insight in the assessment of quantum correlations beyond the purely information-theoretic aspects of the latter. As a result, it has been found that this is indeed the case: the notion of nonclassical correlations springing from physical considerations on the quantum phase space is maximally inequivalent to that emerging from information-theoretic arguments. This, in particular, suggests that there are other quantum correlations in nature than those revealed by entanglement and quantum discord.
In order to make this promise a reality, it is necessary to identify, among the many quantum systems present in nature, some that can be controlled at will; thus providing the physical support for quantum information processing. But nature seems jealous of her secretes, and no definitive front-runner has been identified so far. This exciting search has been the main motivation of the project THECOSINT.
In particular, an approach alternative with respect to 'quantum bits' is given by the so called 'quantum modes' (also dubbed continuous variables). Whereas the former are quantum systems that can assume two states only (like two polarisation states of light), the latter can span over much more states (possibly infinite, similar to the infinite gradients of colours that light can assume). Unfortunately, insofar technological obstacles avoided to control a number of quantum modes large enough to really exploit the computational power of the quantum world. However, crucial experimental advances are rapidly changing this scenario. Inspired by this, the main objective of my proposal has been to devise novel schemes suited for emerging quantum-mode technologies, with the ultimate vision of exploiting the full power of quantum information.
In particular, the project has been developed in the three main goals identified in the original proposal and hereby summarised:
1) The first objective of the project was to single out the benefits that may be offered by some recently emerged quantum technologies (e.g. circuit quantum electrodynamics, optomechanical oscillators, and trapped ions). Specifically, the first task was to individuate useful effective interactions and to design proper measurement schemes suited for emerging technologies.
2) The second objective was to consider many-body continuous variable systems in connection to simulators and quantum thermodynamics. A specific objective was to study the thermal properties of many-body continuous variable systems that challenge some standard thermodynamic concepts, like local intensive temperature.
3) The third objective was to seek for novel approaches to quantum computation over continuous variables suited for implementation with novel technologies. In particular, a major aim was to introduce approaches suited to continuous variable systems encoded in confined forms - as the latter emerge naturally in the mentioned novel technologies.
In strict relation to all the above objectives, the main scientific outcomes of the project have been:
i) The introduction of novel approaches to quantum computation over continuous quantum variable
In the context of quantum computation over continuous variables, an entire spectrum of new possibilities was opened few years ago by the landmark discovery of a paradigm of computation - dubbed measurement-based quantum computation - that works as follows: first a set of quantum modes is prepared in the so-called cluster state; then, the specific computation proceeds as a sequence of local measurements that consume the cluster-state entanglement as the main resource of the computation. From an implementation perspective, the main effort resides in the preparation of the initial cluster. In this context, a major outcome of the present project has been to propose of an alternative approach to produce the cluster state, based on the introduction of a set of gapped and local Hamiltonians whose unique ground state is the continuous variable cluster state. This approach makes 'adiabatic state generation' possible: the cluster state can be prepared by first cooling down the system to zero temperature and then switching on the interactions so that the system is adiabatically driven toward the ground state of the cluster Hamiltonian. This approach is naturally better suited for state preparations at large scales and for continuous variables encoded in a confined form in the mentioned novel technologies. Another outcome of the present project has been the introduction of a second novel approach to quantum computation over continuous variables named 'sequential quantum computation'. In the standard approach, the cluster is first built and then consumed along the computation via local measurements. However, the creation of the whole cluster at the beginning of the computation is not strictly necessary. In other words the cluster might be created and immediately consumed step after step during the computation. This sequential approach relaxes the requirement of preserving the coherence of such a massively entangled state along the computation and might be helpful in reducing the detrimental effect of noise. In the present project, as said, a new theoretical framework for sequential quantum computation has been introduced. The feasibility of this approach in the physical setting of novel quantum technologies has also been recently approached.
ii) The analysis of the role played by quantum correlations in the emergence of thermodynamics quantities in continuous variable many-body systems
In the present project, the concept of temperature in a setting beyond the standard thermodynamics prescriptions has been considered. Namely, rather than restricting to standard coarse-grained measurements, one can consider observers able to master any possible quantum measurement - a scenario that might be relevant at nanoscopic scales for novel quantum technologies. In this setting, the project focussed on quantum systems of coupled harmonic oscillators and studied the question of whether the temperature is an intensive quantity. On one hand, instances in which this approximation is not valid have been identified; on the other hand, these investigation also showed that the standard thermodynamics result is recovered for coarse-grained measurements. In particular, the role that entanglement and quantum correlations play in this scenario has been analysed in details, showing that in general the thermodynamic paradigm of local intensive temperature applies whenever entanglement is not present in the system. The results of this project extend the applicability of the concept of temperature and assess its limits of validity, to a scenario beyond the standard one and that might be relevant for future technologies at mesoscopic and nanoscopic scale.
iii) The introduction of new measurement schemes for novel quantum technologies hosting quantum continuous variables
In the context of the novel quantum technologies mentioned above, an important question concerns extraction of the relevant information there encoded in the form of continuous variables. In general, quantum state reconstruction - also dubbed quantum state tomography - tries to estimate the state of a quantum system using measurements on an ensemble of identical copies of it. The advances of quantum information with continuous variables have been traditionally related to the exquisite control that is experimentally achievable for travelling light qumodes. This naturally led to a huge research effort in the reconstruction of travelling qumodes, for which a general framework based on quadrature measurements has been established. However, when those measurements are not available - as it is the case for qumodes confined in novel technologies - the framework itself is not directly applicable. A major objective achieved in this project was to devise a novel scheme for quantum tomography of a network of confined continuous variables. This is the first scheme specifically devised to this goal. In addition, it requires only minimal access to the system: instead of accessing all the oscillators in the network, access to a single one suffices. Tomography with minimal access is not only of theoretical interest. In fact, accessibility problems often plague experiments and the results of the project are expected to be useful for experimental applications.
iv) The characterisation of quantum correlations that are believed to be essential for advanced computational tasks such as quantum computation and simulation
A major question in quantum information is the characterisation of quantum correlations and their relation to the so-called quantum speed up that is achieved when quantum systems, rather than classical systems, are used to perform some information tasks (e.g. quantum computation). In this context, major results have been obtained during the project concerning the two most employed quantifiers of correlations beyond entanglement: non-classicality and the quantum discord. The former was established more than half a century ago, stemming from the notions of quantum phase space and quasiprobability distributions. The latter is instead mainly based on the information-theoretic aspects of quantum correlations. In this project those two approaches have been compared, investigating in particular whether physical constraints emerging from the former can bring new insight in the assessment of quantum correlations beyond the purely information-theoretic aspects of the latter. As a result, it has been found that this is indeed the case: the notion of nonclassical correlations springing from physical considerations on the quantum phase space is maximally inequivalent to that emerging from information-theoretic arguments. This, in particular, suggests that there are other quantum correlations in nature than those revealed by entanglement and quantum discord.