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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.

Quantum computing for finance: overview and prospects

Quantum computing for finance: overview and prospects

Many financial services players are experimenting with quantum-computing so that they can be the first to start exploiting its benefits in speed-up and tractability. Algorithms have been developed for a wide range of finance related topics e.g. Monte Carlo simulation, portfolio optimization, anomaly (fraud) detection, market forecasting and reduction of slippage. In this paper Orus et al. provide a nice overview of most of these applications. Although the paper puts much emphasis on what has been done with quantum-annealers, applying the Quantum Approximate Optimization Algorithm (QAOA) lets us map all of them to universal-gate devices, which ensures that these applications stay relevant even when annealers become obsolete.

The coming quantum leap in computing

The coming quantum leap in computing

This report by The Boston Consulting Group, a strategy consulting firm, provides both an introductory status overview of current and near-term qubit technologies and of practical quantum-computing applications as well as a longer-term outlook of the quantum-computing market, which the authors (Massimo Russo et al.) estimate could be as large as $50bln by 2030. The report also provides some advice to corporates on how to prepare for the arrival of practical quantum-computing applications

Individual error correction applied to quantum-chemistry calculations using the VQE algorithm

Individual error correction applied to quantum-chemistry calculations using the VQE algorithm

Recently, promising experimental results have been shown for quantum-chemistry calculations using small, noisy quantum processors. As full scale fault-tolerant error correction is still many years away, near-term quantum computers will have a limited number of qubits, and each qubit will be noisy. Methods that reduce noise and correct errors without doing full error correction on every qubit will help extend the range of interesting problems that can be solved in the near-term. In this paper Otten et al. present a scheme for accounting (and removal) of errors in observables determined from quantum algorithms and apply this scheme to the variational quantum eigensolver algorithm, simulating the calculation of the ground state energy of equilibrium H2 and LiH in the presence of several noise sources, including amplitude damping, dephasing, thermal noise, and correlated noise. They show that their scheme provides a decrease in the needed quality of the qubits by up to two orders of magnitude.

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.

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