Related papers: Interfacing with Hamiltonian Dynamics
We present a quantum algorithm for the dynamical simulation of time-dependent Hamiltonians. Our method involves expanding the interaction-picture Hamiltonian as a sum of generalized permutations, which leads to an integral-free Dyson series…
We demonstrate how structured decompositions of unitary operators can be employed to derive control schemes for finite-level quantum systems that require only sequences of simple control pulses such as square wave pulses with finite rise…
The capacity to custom tailor the properties of quantum matter and materials is a central requirement for enlarging their range of possible functionalities. A particularly promising route is the use of driving protocols to engineer specific…
Gate-based universal quantum computation is formulated in terms of two types of operations: local single-qubit gates, which are typically easily implementable, and two-qubit entangling gates, whose faithful implementation remains one of the…
Some two qubit interactions are singly sufficient for universal quantum computation but not without the use of an ancilla. Recent schemes for universal quantum computation have focused on hybrid physical systems using ancillae. In them, the…
In this dissertation I analyze Hamiltonian control of $d$-dimensional quantum systems as realized in alkali atomic spins. Alkali atoms provide an ideal platform for studies of quantum control due to the extreme precision with which the…
Here is discussed the Hamiltonian approach to construction of deterministic universal (in approximate sense) programmable quantum circuits with qubits or any other quantum systems with dimension of Hilbert space is $n \ge 2$.
We present pulse sequences for two-qubit gates acting on encoded qubits for exchange-only quantum computation. Previous work finding such sequences has always required numerical methods due to the large search space of unitary operators…
We present a general method which expresses a unitary operator by the product of operators allowed by the Hamiltonian of spin-1/2 systems. In this method, the generator of an operator is found first, and then the generator is expanded by…
Quantum computation is a promising emerging technology, and by utilizing the principles of quantum mechanics, it is expected to achieve faster computations than classical computers for specific problems. There are two distinct architectures…
Extensions of average Hamiltonian theory to quantum computation permit the design of arbitrary Hamiltonians, allowing rotations throughout a large Hilbert space. In this way, the kinematics and dynamics of any quantum system may be…
Starting with the basic control system model often employed in NMR pulse design, we derive more realistic control system models taking into account effects such as off-resonant excitation for systems with fixed inter-qubit coupling…
We derive an integral expression for the filter-transfer function of an arbitrary one-qubit gate through the use of dynamical invariant theory and Hamiltonian reverse engineering. We use this result to define a cost function which can be…
Engineering effective Hamiltonians is essential for advancing quantum technologies including quantum simulation, sensing, and computing. This paper presents a general framework for effective Hamiltonian engineering, enabling robust,…
The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wavefunctions that are relevant in the behavior of the system under study. Hamiltonian symmetries are an important…
When can a quantum system of finite dimension be used to simulate another quantum system of finite dimension? What restricts the capacity of one system to simulate another? In this paper we complete the program of studying what simulations…
Quantum pseudorandomness, also known as unitary designs, comprise a powerful resource for quantum computation and quantum engineering. While it is known in theory that pseudorandom unitary operators can be constructed efficiently, realizing…
Measurement-based quantum computation utilizes an initial entangled resource state and proceeds with subsequent single-qubit measurements. It is implicitly assumed that the interactions between qubits can be switched off so that the…
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of…
A digital quantum simulator is an envisioned quantum device that can be pro- grammed to efficiently simulate any other local system. We demonstrate and investigate the digital approach to quantum simulation in a system of trapped ions.…