Guang Hao Low

Fixed-Point Quantum Search with an Optimal Number of Queries

Grovers quantum search and its generalization, quantum amplitude amplification, provide a quadratic advantage over classical algorithms for a diverse set of tasks but are tricky to use without knowing beforehand what fraction λ of the initial state is comprised of the target states. In contrast, fixed-point search algorithms need only a reliable lower bound on this fraction but, as a consequence, lose the very quadratic advantage that makes Grovers algorithm so appealing. Here we provide the first version of amplitude amplification that achieves fixed-point behavior without sacrificing the quantum speedup. Our result incorporates an adjustable bound on the failure probability and, for a given number of oracle queries, guarantees that this bound is satisfied over the broadest possible range of λ.

Laser-induced charging of microfabricated ion traps

Electrical charging of metal surfaces due to photoelectric generation of carriers is of concern in trapped ion quantum computation systems, due to the high sensitivity of the ions’ motional quantum states to deformation of the trapping potential. The charging induced by typical laser frequencies involved in Doppler cooling and quantum control is studied here, with microfabricated surface-electrode traps made of aluminum, copper, and gold, operated at 6 K with a single Sr+ ion trapped 100 μm above the trap surface. The lasers used are at 370, 405, 460, and 674 nm, and the typical photon flux at the trap is 1014 photons/cm2/sec. Charging is detected by monitoring the ion’s micromotion signal, which is related to the number of charges created on the trap. A wavelength and material dependence of the charging behavior is observed: Lasers at lower wavelengths cause more charging, and aluminum exhibits more charging than copper or gold. We describe the charging dynamic based on a rate-equation approach.

Hamiltonian simulation with optimal sample complexity

We investigate the sample complexity of Hamiltonian simulation: how many copies of an unknown quantum state are required to simulate a Hamiltonian encoded by the density matrix of that state? We show that the procedure proposed by Lloyd, Mohseni, and Rebentrost [Nat. Phys., 10(9):631–633, 2014] is optimal for this task. We further extend their method to the case of multiple input states, showing how to simulate any Hermitian polynomial of the states provided. As applications, we derive optimal algorithms for commutator simulation and orthogonality testing, and we give a protocol for creating a coherent superposition of pure states, when given sample access to those states. We also show that this sample-based Hamiltonian simulation can be used as the basis of a universal model of quantum computation that requires only partial swap operations and simple single-qubit states.Quantum Software from Quantum StatesOne of the hallmarks of quantum computation is the storage and extraction of information within quantum systems. Recently, Lloyd, Mohseni and Rebentrost created a protocol to treat multiple identical copies of a quantum state as “quantum software”, specifying a quantum program to be run on any other state. They use this approach to do principal component analysis of the software state. Here, we expand on their results, providing protocols for running more-complex quantum programs specified by several different states. Our protocols can be used to analyze the relationship between different states (for example, deciding whether states are orthogonal) and to create new states (such as coherent linear combinations of two states). We also outline the optimality of Lloyd et al.’s original protocol, as well as our new protocols.

Quantum Inference on Bayesian Networks

Performing exact inference on Bayesian networks is known to be #P-hard. Typically approximate inference techniques are used instead to sample from the distribution on query variables given the values

Robust Calibration of a Universal Single-Qubit Gate-Set via Robust Phase Estimation

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Methodology of Resonant Equiangular Composite Quantum Gates

of evidence variables. Classically, a single unbiased sample is obtained from a Bayesian network on

Quantum Imaging by Coherent Enhancement

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Effects of electrode surface roughness on motional heating of trapped ions

variables with at most

Iterative precision measurement of branching ratios applied to 5P states in 88Sr

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Optimal Hamiltonian Simulation by Quantum Signal Processing

parents per node in time