With small quantum computers becoming a reality, first applications are eagerly sought. Quantum chemistry presents spectrum of computational problems, from relatively easy to classically intractable. Algorithms for the easiest these have been run on computers. But an urgent question is, how well will algorithms scale go beyond what is possible classically? This review strategies employed construct chemistry, with goal that eventually answer presently inaccessible questions, example, in...

One of the key applications for quantum computers will be simulation other systems that arise in chemistry, materials science, etc, order to accelerate process discovery. It is important ask: Can this achieved using near future processors, modest size and under imperfect control, or must it await more distant era large-scale fault-tolerant computing? Here we propose a variational method involving closely integrated classical coprocessors. We presume all operations coprocessor are prone...

It is vital to minimise the impact of errors for near-future quantum devices that will lack resources full fault tolerance. Two error mitigation (QEM) techniques have been introduced recently, namely extrapolation [Li2017,Temme2017] and quasi-probability decomposition [Temme2017]. To enable practical implementation these ideas, here we account inevitable imperfections in experimentalist's knowledge model itself. We describe a protocol systematically measuring effect so as design efficient...

Quantum computers can exploit a Hilbert space whose dimension increases exponentially with the number of qubits. In experiment, quantum supremacy has recently been achieved by Google team using noisy intermediate-scale (NISQ) device over 50 However, question what be implemented on NISQ devices is still not fully explored, and discovering useful tasks for such topic considerable interest. Hybrid quantum-classical algorithms are regarded as well-suited execution combining classical computers,...

The variational method is a versatile tool for classical simulation of variety quantum systems. Great efforts have recently been devoted to its extension computing efficiently solving static many-body problems and simulating real imaginary time dynamics. In this work, we first review the conventional principles, including Rayleigh-Ritz problems, Dirac Frenkel principle, McLachlan's time-dependent We focus on dynamics discuss connections three principles. Previous works mainly unitary...

In artificial systems, quantum superposition and entanglement typically decay rapidly unless cryogenic temperatures are used. Could life have evolved to exploit such delicate phenomena? Certain migratory birds the ability sense very subtle variations in Earth's magnetic field. Here we apply information theory widely accepted "radical pair" model analyze recent experimental observations of avian compass. We find that sustained this living system for at least tens microseconds, exceeding...

The quantum superposition principle states that an entity can exist in two different simultaneously, counter to our 'classical' intuition. Is it possible understand a given system's behaviour without such concept? A test designed by Leggett and Garg rule out this possibility. test, originally intended for macroscopic objects, has been implemented various systems. However date no experiment employed the 'ideal negative result' measurements are required most robust test. Here we introduce...

In most of physics it is normal to obtain information by analysis noisy data. The paradigm quantum computing has been a simplified version this -- one measurement two-level system gives bit reliable about the result computation. But real-world computers do not work way: noisiness evolution also requires good strategies for extracting information. This review covers many error-mitigation used in present-day processors. These make much more feasible useful results before fault tolerance achieved.

A distillation protocol is developed that enhances entanglement between distant nodes of a quantum network.

Variational algorithms may enable classically intractable simulations on near-future quantum computers. However, their potential is limited by hardware errors. It therefore crucial to develop efficient ways mitigate these Here, we propose a stabilizerlike method which enables the detection of up 60%-80% depolarizing Our suitable for near-term hardware. Simulations show that our can significantly benefit calculations subject both stochastic and correlated noise, especially when combined with...

Calculating the energy spectrum of a quantum system is an important task, for example to analyse reaction rates in drug discovery and catalysis. There has been significant progress developing algorithms calculate ground state molecules on near-term computers. However, calculating excited energies attracted comparatively less attention, it currently unclear what optimal method is. We introduce low depth, variational algorithm sequentially states general Hamiltonians. Incorporating recently...

We introduce QuEST, the Quantum Exact Simulation Toolkit, and compare it to ProjectQ, qHipster a recent distributed implementation of Quantum++. QuEST is first open source, hybrid multithreaded distributed, GPU accelerated simulator universal quantum circuits. Embodied as C library, designed so that user's code can be deployed seamlessly any platform from laptop supercomputer. capable simulating generic circuits general one two-qubit gates multi-qubit controlled gates, on pure mixed states,...

Variational quantum algorithms have been proposed to solve static and dynamic problems of closed many-body systems. Here we investigate variational simulation three general types tasks---generalised time evolution with a non-Hermitian Hamiltonian, linear algebra problems, open system dynamics. The algorithm for generalised provides unified framework simulation. In particular, show its application in solving systems equations matrix-vector multiplications by converting these algebraic into...

Achieving quantum computation has been a long-standing goal of physicists and engineers. Researchers conduct numerical simulations computer to show that ``clock speed'' kilohertz is possible with today's systems.

Quantum computers can in principle solve certain problems exponentially more quickly than their classical counterparts. We have not yet reached the advent of useful quantum computation, but when we do, it will affect nearly all scientific disciplines. In this review, examine how current algorithms could revolutionize computational biology and bioinformatics. There are potential benefits across entire field, from ability to process vast amounts information run machine learning far...

Abstract Imaginary time evolution is a powerful tool for studying quantum systems. While it possible to simulate with classical computer, the and memory requirements generally scale exponentially system size. Conversely, computers can efficiently systems, but not non-unitary imaginary evolution. We propose variational algorithm simulating on hybrid computer. use this find ground-state energy of many-particle systems; specifically molecular hydrogen lithium hydride, finding ground state high...

If NISQ-era quantum computers are to perform useful tasks, they will need employ powerful error mitigation techniques. Quasi-probability methods can permit perfect compensation at the cost of additional circuit executions, provided that nature model is fully understood and sufficiently local both spatially temporally. Unfortunately these conditions challenging satisfy. Here we present a method by which proper strategy instead be learned ab initio. Our training process uses multiple variants...

Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational tasks that are compatible with noisy intermediate-scale devices. We show the solutions of systems equations matrix-vector multiplications can be translated as ground states constructed Hamiltonians. Based on algorithms, introduce Hamiltonian morphing together an adaptive...

Recently the concept of quantum information has been introduced into game theory. Here we present first study games with more than two players. We discover that such can possess an alternative form equilibrium strategy, one which no analog either in traditional or even two-player games. In these ``coherent'' equilibria, entanglement shared among multiple players enables different kinds cooperative behavior: indeed it act as a contract, sense prevents from successfully betraying another.

We examine various realistic generalizations of the basic cellular automaton model describing traffic flow along a highway. In particular, we introduce slow-to-start rule which simulates possible delay before car pulls away from being stationary. Having discussed case bare highway, then consider presence junction. study effects acceleration, disorder, and behaviour on queue length at entrance to Interestingly, junction's efficiency is improved by introducing disorder imposing speed limit.

Quantum-Enhanced Measurement The single electron spin in a molecule, atom, or quantum dot precesses magnetic field and so can be used as sensor. As the number of spins sensor increases, too does sensitivity. Quantum mechanical entanglement ensemble should then allow sensitivity to increase much more than would expected from simple individual ensemble. Using highly symmetric trimethyl phosphite, molecule containing central P atom surrounded by nine hydrogen atoms, Jones et al. (p. 1166 ,...

A scalable quantum computer could be built by networking together many simple processor cells, thus avoiding the need to create a single complex structure. The difficulty is that realistic links are very error prone. solution for cells repeatedly communicate with each other and so purify any imperfections; however prior studies suggest themselves must then have prohibitively low internal rates. Here we describe method which even error-prone can perform purification: groups of generate shared...

Entangled states can potentially be used to outperform the standard quantum limit which every classical sensor is bounded by. However, entangled are very susceptible decoherence, and so it not clear whether one really create a superior technology via strategy subject effect of realistic noise. This paper presents an investigation how composed many spins affected by independent dephasing. We adopt general noise models including non-Markovian effects, in these performance depends crucially on...