## Final Report Summary - PACOMANEDIA (Partially Coherent Many-Body Nonequilibrium Dynamics for Information Applications)

Technologies that use bonafide quantum mechanical entities (i.e. systems which display uniquely quantum attributes such as superposition and entanglement) are on the rise, with varied applications in areas such as computation, communication, sensing and simulation. In most applications, a chip containing several quantum entities interacting with each other – a “quantum many-body system” is necessary. Controlling the interactions of each of these entities with each other individually in time is very challenging and that control itself has the potential to introduce errors. Motivated by this, in the current project, we have developed varied possibilities of implementing quantum technologies without extensive time-dependent control. It is a scenario in which interactions between quantum entities, be it quantum spins or particles hopping in lattices, remains fixed throughout the time evolution enacting a useful protocol. Additionally, any external control to the system is applied as a single time constant pulse to the system to enact the protocol. We can call this an automata style operation.

Under this scenario, we have developed automata to implement relevant three qubit (quantum bit) gates for quantum computation, particularly those required for arithmetic operations and error correction, by optimizing the permanent couplings between the qubits using machine learning. This has been dubbed “while you wait” computing where you simply let the time evolution of permanently interacting spins do the computation for you without controlling them actively in time. This has contributed to opening up a new area of applying classical machine learning to quantum problems.

We have also developed simple automata for the logic gates, Toffoli and Fredkin, required for classical reversible computation. This has been developed both as quantum automata of interacting quantum spins, as well as classical automata of interacting nano-magnets. This will potentially enable low dissipation computation beyond the current state of art. We have also found permanently interacting quantum dopants in a line can convey spin information from one end to another through their stable thermal equilibrium states and the fact that this flow of information can be gated by a small magnetic field. Such a quantum automata could be an important component as a data-bus in classical magnetic logic.

We have found novel data-buses also for scaling up quantum computers. For example quantum entanglement between distant sites can serve this aim. So we have designed automata from chains of permanently interacting spins which create an extensive amount of entanglement as a result of their dynamics, namely the maximum possible in a spin chain – a rainbow pattern of entanglement. This automaton has also been tested in a photonic chip experiment. Moreover we have found that electrons arranging each other in a crystal because of their repulsion in a gated semiconductor can act as a data bus conveying information encoded in spins from one end to another.

In the context of atoms hopping in lattices, we have found automata which make the atoms exhibit the same processes as photons on a chip, and, using the additional fact that atoms can interact, found applications of these automata in atom based quantum computation and quantum sensing.

Aside the above, the project has also identified new types of analog simulators of quantum many-body systems and various ways of using and measuring quantum entanglement inspired quantities to identify phases of many-body systems and the transitions between them.

Under this scenario, we have developed automata to implement relevant three qubit (quantum bit) gates for quantum computation, particularly those required for arithmetic operations and error correction, by optimizing the permanent couplings between the qubits using machine learning. This has been dubbed “while you wait” computing where you simply let the time evolution of permanently interacting spins do the computation for you without controlling them actively in time. This has contributed to opening up a new area of applying classical machine learning to quantum problems.

We have also developed simple automata for the logic gates, Toffoli and Fredkin, required for classical reversible computation. This has been developed both as quantum automata of interacting quantum spins, as well as classical automata of interacting nano-magnets. This will potentially enable low dissipation computation beyond the current state of art. We have also found permanently interacting quantum dopants in a line can convey spin information from one end to another through their stable thermal equilibrium states and the fact that this flow of information can be gated by a small magnetic field. Such a quantum automata could be an important component as a data-bus in classical magnetic logic.

We have found novel data-buses also for scaling up quantum computers. For example quantum entanglement between distant sites can serve this aim. So we have designed automata from chains of permanently interacting spins which create an extensive amount of entanglement as a result of their dynamics, namely the maximum possible in a spin chain – a rainbow pattern of entanglement. This automaton has also been tested in a photonic chip experiment. Moreover we have found that electrons arranging each other in a crystal because of their repulsion in a gated semiconductor can act as a data bus conveying information encoded in spins from one end to another.

In the context of atoms hopping in lattices, we have found automata which make the atoms exhibit the same processes as photons on a chip, and, using the additional fact that atoms can interact, found applications of these automata in atom based quantum computation and quantum sensing.

Aside the above, the project has also identified new types of analog simulators of quantum many-body systems and various ways of using and measuring quantum entanglement inspired quantities to identify phases of many-body systems and the transitions between them.