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We consider a composite open quantum system consisting of a fast subsystem coupled to a slow one. Using the time-scale separation, we develop an adiabatic elimination technique to derive at any order the reduced model describing the slow…
Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between non-degenerate instantaneous eigen-energy levels in such a…
We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum…
Suppression of diabatic transitions in quantum adiabatic evolution stands as a significant challenge for ground state preparations. Counterdiabatic driving has been proposed to compensate for diabatic losses and achieve shortcut to…
An operator-valued quantum phase space formula is constructed. The phase space formula of Quantum Mechanics provides a natural link between first and second quantization, thus contributing to the understanding of quantization problem. By…
A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed…
In adiabatic quantum computing the aim is to track an eigenstate as the Hamiltonian changes. In the usual setup this is achieved using the natural time-dependent Hamiltonian evolution of the system and the main technical tool is the…
Quantum adiabatic evolutions find a broad range of applications in quantum physics and quantum technologies. The traditional form of the quantum adiabatic theorem limits the speed of adiabatic evolution by the minimum energy gaps of the…
We study temporal behavior of a quantum system under a slow external perturbation, which drives the system across a second order quantum phase transition. It is shown that despite the conventional adiabaticity conditions are always violated…
We describe tensor network algorithms to optimize quantum circuits for adiabatic quantum computing. To suppress diabatic transitions, we include counterdiabatic driving in the optimization and utilize variational matrix product operators to…
A quantum system will stay near its instantaneous ground state if the Hamiltonian that governs its evolution varies slowly enough. This quantum adiabatic behavior is the basis of a new class of algorithms for quantum computing. We test one…
In recent quantum algorithmic developments, a feedback-based approach has shown promise for preparing quantum many-body system ground states and solving combinatorial optimization problems. This method utilizes quantum Lyapunov control to…
Bounds to the speed of evolution of a quantum system are of fundamental interest in quantum metrology, quantum chemical dynamics and quantum computation. We derive a time-energy uncertainty relation for open quantum systems undergoing a…
The anomalous dynamical evolution and the crossing of nonadiabatic energy levels are investigated for exactly solvable time-dependent quantum systems through a reverse-engineering scheme. By exploiting a typical driven model, we elucidate…
We consider the problem of energy cost needed for acceleration (deceleration) of the evolution of a quantum system using the Masuda-Nakamura fast forward protocol. In particular, we focus on dynamics by considering models for a quantum box…
We propose a method to speed up the quantum adiabatic algorithm using catalysis by many-body delocalization. This is applied to random-field antiferromagnetic Ising spin models. The algorithm is catalyzed in such a way that the evolution…
A major drawback of adiabatic quantum computing (AQC) is fulfilling the energy gap constraint, which requires the total evolution time to scale inversely with the square of the minimum energy gap. Failure to satisfy this condition violates…
We discuss the quantization of an unstable field through the construction of a "one-particle Hilbert space." The system considered here is a neutral scalar field evolving over a globally hyperbolic static spacetime and subject to a…
We develop new protocols for high-fidelity single qubit gates that exploit and extend theoretical ideas for accelerated adiabatic evolution. Our protocols are compatible with qubit architectures with highly isolated logical states, where…
Quantum scrambling describes the spreading of local information into many degrees of freedom in quantum systems. This provides the conceptual connection among diverse phenomena ranging from thermalizing quantum dynamics to models of black…