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Quantum-computing related developments

On this page we post about interesting quantum-computing related research and news which we are following.

Comparison of quantum computing methods for simulating the Hamiltonian of H2O

Comparison of quantum computing methods for simulating the Hamiltonian of H2O

In this paper Bian et al. compare four different quantum simulation methods to simulate the ground state energy of the Hamiltonian for the water molecule on a quantum computer, being 1) the phase estimation algorithm based on Trotter decomposition, 2) phase estimation based on the direct implementation of the Hamiltonian, 3) direct measurement based on the implementation of the Hamiltonian and 4) the variational quantum eigensolver (classical-quantum hybrid) algorithm. They compare a.o. the required number of qubits, gate-complexity, accuracy/error. 

Quantum Algorithm Implementations for Beginners

Quantum Algorithm Implementations for Beginners

In this paper, Patrick J. Coles et al., aim to explain the principles of quantum programming straight-forward algebra that makes understanding the underlying quantum mechanics optional (but still fascinating). The authors give an introduction to quantum computing algorithms and their implementation on real quantum hardware and survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. They show how these algorithms can be implemented on an actual quantum-processor (in this case an IBM QPU) and in each case discuss the results of the implementation with respect to differences of the results on a simulator (QVM) or the actual processor (QPU).

Quantum chemistry calculations using the VQE algorithm on a trapped-ion quantum simulator

Quantum chemistry calculations using the VQE algorithm on a trapped-ion quantum simulator

Efficient quantum simulations of classically intractable instances of the associated electronic structure problem promise breakthroughs in our understanding of basic chemistry and could revolutionize research into new materials, pharmaceuticals, and industrial catalysts. In Quantum Computational Chemistry solutions, the Variational Quantum Eigensolver (VQE) algorithm offers a hybrid classical-quantum, and thus low quantum circuit depth, alternative to the Phase Estimation algorithm used to measure the ground-state energy of a molecular Hamiltonian. In this paper, Hempel et al. use a digital quantum simulator based on trapped ions to experimentally investigate the VQE algorithm for the calculation of molecular ground state energies of two simple molecules  (H2 and LiH) and experimentally demonstrate and compare different encoding methods using up to four qubits. 

Survey of photonic quantum information processing

Survey of photonic quantum information processing

In this paper Flamini et al. provide a comprehensive overview of the current (March 2018) state of the art in the field of photonic quantum information processing including quantum communication and photonic quantum simulation.

Quantum-assisted unsupervised learning (cluster analysis)

Quantum-assisted unsupervised learning (cluster analysis)

Clustering is a form of unsupervised machine learning, where instances are organized into groups whose members share similarities. The assignments are, in contrast to classification, not known a priori, but generated by the algorithm. In this paper, Neukart et al.  present an algorithm for quantum-assisted cluster analysis (QACA) that makes use of the topological properties of a D-Wave 2000Q quantum processing unit (QPU). They explain how the problem can be expressed as a quadratic unconstrained binary optimization (QUBO) problem, and show that the introduced quantum-assisted clustering algorithm is, regarding accuracy, equivalent to commonly used classical clustering algorithms.

Classical-quantum hybrid algorithm for machine learning with NISQ devices

Classical-quantum hybrid algorithm for machine learning with NISQ devices

Quantum machine learning (QML) algorithms based on the Harrow-Hassidim- Lloyd (HHL) algorithm rely on quantum phase estimation which requires high circuit-depth. To allow QML on current noisy intermediate scale quantum (NISQ) devices classical-quantum hybrid algorithms have been suggested applying low-depth circuits like quantum variational eigensolvers and quantum approximate optimization. Such hybrid algorithms typically divide the ML problem into two parts, each part to be performed either classically or on a quantum-computer. In this paper, Mitarai et al. present a new hybrid framework, called quantum circuit learning (QCL), which is easily realizable on current NISQ devices. Under QCL a circuit learns by providing input data, while iteratively tuning the circuit parameters to give the desired output. They show that QCL is able to learn nonlinear functions and perform simple classification tasks. They also show that a 6-qubit circuit is capable of learning dynamics of a 10-spin system with a fully connected Ising Hamiltonian, implying that QCL could be well suited for learning complex many-body systems.

Quantum algorithm outperforming Grover for exact optimization of a.o. MAX-2-SAT

Quantum algorithm outperforming Grover for exact optimization of a.o. MAX-2-SAT

In this paper, Matthew Hastings presents a quantum algorithm to exactly solve certain problems in combinatorial optimization, including weighted MAX-2-SAT.  While the time required is still exponential, the algorithm provably outperforms Grover's algorithm assuming a mild condition on the number of low energy states of the target Hamiltonian.

Quantum circuit design for training perceptron models

Quantum circuit design for training perceptron models

The perceptron algorithm dates back to the late 1950s and is an algorithm for supervised learning of binary classifiers. In a 2016 paper, Wiebe et al. proposed a quantum algorithm (based on Grover’s quantum-search approach), which can quadratically speed-up the training of a perceptron. In this paper, Zheng et al. describe their design for a quantum-circuit to implement the training-algorithm of Wiebe et al. They also analyze the resource requirements (qubits and gates) and demonstrate the feasibility of their quantum-circuit by testing it on the ibmqx5 (a 16 qubit universal gate quantum processor developed by IBM)

100+ trapped-ions in cryogenically pumped architecture

100+ trapped-ions in cryogenically pumped architecture

Atomic ions can be trapped by electric fields in ultra-high vacuum and then laser-cooled to extremely low temperatures. The internal states of such a trapped ion can be used to encode a qubit. Such qubit systems have very long coherence times and their internal states can be precisely manipulated using lasers, and measured efficiently. Current, room temperature, systems are limited to 50 ions to to collisions with background gas. At cryogenic temperatures (4K) , most of the residual background gas is trapped enabling further scale-up of ion-trap systems. In this paper, Pagano et al. present experimental results from a trapped ion system with such cryogenic-pumping, which enables them to trap over 100 ions in a linear configuration for hours, paving the way for future quantum simulation of spin models that are intractable with classical computer modelling.

Hyper- and hybrid entanglement

Hyper- and hybrid entanglement

Usually quantum information is encoded into a single, well-controlled degree of freedom, such as a spin. In some cases, however, establishing so called hyper-entanglement among several degrees-of-freedom (e.g. photon path, polarization and angular momentum), can be beneficial, e.g. improve the capacity of dense coding in linear optics.  In this paper, Li et al. propose a scheme that allows to combine both (single degree-of-freedom) entanglement and hyper-entanglement. Specifically, they show how two identical, initially separated particles can become spin-entangled, momenta-entangled and spin-and-momenta-hyper-entangled.

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