Related papers: Optimal control, geometry, and quantum computing
We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. Complexity is understood here as the shortest geodesic distance between the…
Coherent control errors, for which ideal Hamiltonians are perturbed by unknown multiplicative noise terms, are a major obstacle for reliable quantum computing. In this paper, we present a framework for analyzing the robustness of quantum…
Determining the ultimate limits of quantum communication, such as the quantum capacity of a channel and the distillable entanglement of a shared state, remains a central challenge in quantum information theory, primarily due to the…
Controlled gates are key components in various quantum algorithms. Improving on the prior work of Gosset et al., we show that, for an allowed error $\varepsilon$, $3\log_2(1/\varepsilon) + o(\log(1/\varepsilon))$ $T$ gates are sufficient to…
Many coherence transfer experiments in Nuclear Magnetic Resonance Spectroscopy, involving network of coupled spins, use temporary spin-decoupling to produce desired effective Hamiltonians. In this paper, we show that significant time can be…
Contemporary quantum computers encode and process quantum information in binary qubits (d = 2). However, many architectures include higher energy levels that are left as unused computational resources. We demonstrate a superconducting…
A new class of cost functionals for optimal control of quantum systems which produces controls which are sparse in frequency and smooth in time is proposed. This is achieved by penalizing a suitable time-frequency representation of the…
TThe problem of finding the resource free, closest local unitary, to any bipartite unitary gate $U$ is addressed. Previously discussed as a measure of nonlocality, the distance $K_D(U)$ to the nearest product unitary has implications for…
Geometric effects make evolution time vary for different evolution curves that connect the same two quantum states. Thus, it is important to be able to control along which path a quantum state evolve to achieve maximal speed in quantum…
Hamiltonian quantum gates controlled by classical electromagnetic fields form the basis of any realistic model of quantum computers. In this letter, we derive a lower bound on the field energy required to implement such gates and relate…
Experiments in coherent nuclear and electron magnetic resonance,and quantum computing in general correspond to control of quantum mechanical systems, guiding them from initial to final target states by unitary transformations. The control…
Optimization under the symplecticity constraint is an approach for solving various problems in quantum physics and scientific computing. Building on the results that this optimization problem can be transformed into an unconstrained problem…
Mathematical theory of the quantum systems control is based on some ideas of the optimal control theory. These ideas are developed here as applied to these systems. The results obtained meet the deficiencies in the basis and algorithms of…
Understanding entanglement cost in non-local quantum computation (NLQC) is relevant to complexity, cryptography, gravity, and other areas. This entanglement cost is largely uncharacterized; previous lower bound techniques apply to narrowly…
Ying conceived of using two or more small-capacity quantum computers to produce a larger-capacity quantum computing system by quantum parallel programming ([M. S. Ying, Morgan-Kaufmann, 2016]). In doing so, the main obstacle is separating…
The surface code is designed to suppress errors in quantum computing hardware and currently offers the most believable pathway to large-scale quantum computation. The surface code requires a 2-D array of nearest-neighbor coupled qubits that…
Many quantum algorithms can be written as a composition of unitaries, some of which can be exactly synthesized by a universal fault-tolerant gate set, while others can be approximately synthesized. A quantum compiler synthesizes each…
The processing of quantum information always has a cost in terms of physical resources such as energy or time. Determining the resource requirements is not only an indispensable step in the design of practical devices - the resources need…
We analyse the optimal times for implementing unitary quantum gates in a constrained finite dimensional controlled quantum system. The family of constraints studied is that the permitted set of (time dependent) Hamiltonians is the unit ball…
The quantum navigation problem of finding the time-optimal control Hamiltonian that transports a given initial state to a target state through quantum wind, that is, under the influence of external fields or potentials, is analysed. By…