One of the most promising suggested applications of quantum computing is solving classically intractable chemistry problems. This may help to answer unresolved questions about phenomena such as high temperature superconductivity, solid-state physics, transition metal catalysis, and certain biochemical reactions. In turn, this increased understanding may help us to refine, and perhaps even one day design, new compounds of scientific and industrial importance. However, building a sufficiently large quantum computer will be a difficult scientific challenge. As a result, developments that enable these problems to be tackled with fewer quantum resources should be considered important. Driven by this potential utility, quantum computational chemistry is rapidly emerging as an interdisciplinary field requiring knowledge of both quantum computing and computational chemistry. This review provides a comprehensive introduction to both computational chemistry and quantum computing, bridging the current knowledge gap. Major developments in this area are reviewed, with a particular focus on near-term quantum computation. Illustrations of key methods are provided, explicitly demonstrating how to map chemical problems onto a quantum computer, and how to solve them. The review concludes with an outlook on this nascent field.

Quantum computational chemistry

The simple act of slowly varying the parameters of a quantum system so that it remains always in its ground state is extremely rich from an information processing point of view. For an ideal, closed system, this adiabatic evolution is equivalent to full quantum computation, and it is convenient for establishing quantum algorithms for optimization. This review presents adiabatic quantum algorithms, proves the closed-system equivalence of the adiabatic and circuit models of quantum computation, reviews the placement of adiabatic quantum computation in the more general classification of computational complexity theory, and discusses the case of ``stoquastic'' quantum evolutions.

Adiabatic quantum computation

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete-time quantum walks.

Quantum walks: a comprehensive review

Noisy quantum computers can in principle perform reliable quantum computations, but truly scalable systems require noise levels lower than are presently achieved. Still, moderate-complexity computations can be performed. This review discusses what is possible in this ``noisy intermediate scale'' quantum (NISQ) era. Topic areas include the simulation of many-body physics and chemistry, combinatorial optimization, and machine learning. It is evident that the NISQ era has produced new paradigms for programming that will be built upon as quantum computers are further perfected. 

/pdf/noisy-intermediate-scale-quantum-algorithms-204m0vt3.pdf

Noisy intermediate-scale quantum algorithms

Quantum control is concerned with active manipulation of physical and chemical processes on the atomic and molecular scale. This work presents a perspective of progress in the field of control over quantum phenomena, tracing the evolution of theoretical concepts and experimental methods from early developments to the most recent advances. Among numerous theoretical insights and technological improvements that produced the present state-of- the-art in quantum control, there have been several breakthroughs of foremost importance. On the technology side, the current experimental successes would be impossible without the development of intense femtosecond laser sources and pulse shapers. On the theory side, the two most critical insights were (i) realizing that ultrafast atomic and molecular dynamics can be controlled via manipulation of quantum interferences and (ii) understanding that optimally shaped ultrafast laser pulses are the most effective means for producing the desired quantum interference patterns in the controlled system. Finally, these theoretical and experimental advances were brought together by the crucial concept of adaptive feedback control (AFC), which is a laboratory procedure employing measurement-driven, closed-loop optimization to identify the best shapes of femtosecond laser control pulses for steering quantum dynamics towards the desired objective. Optimization in AFC experiments is guided by a learning algorithm, with stochastic methods proving to be especially effective. AFC of quantum phenomena has found numerous applications in many areas of the physical and chemical sciences, and this paper reviews the extensive experiments. Other subjects discussed include quantum optimal control theory, quantum control landscapes, the role of theoretical control

https://iopscience.iop.org/article/10.1088/1367-2630/12/7/075008/pdf

Control of quantum phenomena: past, present and future

We provide an intuitive platform for engineering exciton transfer dynamics. We show that careful consideration of the spectral density, which describes the system-bath interaction, leads to opportunities to engineer exciton transfer. Since excitons in nanostructures are proposed for use in quantum information processing and artificial photosynthetic designs, our approach paves the way for engineering a wide range of desired exciton dynamics. We carefully describe the validity of the model and use experimentally relevant material parameters to show counter-intuitive examples of directed exciton transfer in a linear chain of quantum dots.

/pdf/engineering-directed-excitonic-energy-transfer-4g2ltr0d6g.pdf

Engineering directed excitonic energy transfer

Sombrero adiabatic quantum computation

In this paper we explore the use of a quantum optimization algorithm for obtaining low-energy conformations of protein models. We discuss mappings between protein models and optimization variables, which are in turn mapped to a system of coupled quantum bits. General strategies are given for constructing Hamiltonians to be used to solve optimization problems of physical, chemical, or biological interest via quantum computation by adiabatic evolution. As an example, we implement the Hamiltonian corresponding to the hydrophobic-polar model for protein folding. Furthermore, we present an approach to reduce the resulting Hamiltonian to two-body terms gearing toward an experimental realization.

/pdf/construction-of-model-hamiltonians-for-adiabatic-quantum-1kranxfbxe.pdf

Construction of model Hamiltonians for adiabatic quantum computation and its application to finding low-energy conformations of lattice protein models

Adiabatic quantum computation (AQC) is a universal model for quantum computation which seeks to transform the initial ground state of a quantum system into a final ground state encoding the answer to a computational problem. AQC initial Hamiltonians conventionally have a uniform superposition as ground state. We diverge from this practice by introducing a simple form of heuristics: the ability to start the quantum evolution with a state which is a guess to the solution of the problem. With this goal in mind, we explain the viability of this approach and the needed modifications to the conventional AQC (CAQC) algorithm. By performing a numerical study on hard-to-satisfy 6 and 7 bit random instances of the satisfiability problem (3-SAT), we show how this heuristic approach is possible and we identify that the performance of the particular algorithm proposed is largely determined by the Hamming distance of the chosen initial guess state with respect to the solution. Besides the possibility of introducing educated guesses as initial states, the new strategy allows for the possibility of restarting a failed adiabatic process from the measured excited state as opposed to restarting from the full superposition of states as in CAQC. The outcome of the measurement can be used as a more refined guess state to restart the adiabatic evolution. This concatenated restart process is another heuristic that the CAQC strategy cannot capture.

pdf/a-study-of-heuristic-guesses-for-adiabatic-quantum-3j5y6hd6r0.pdf

A study of heuristic guesses for adiabatic quantum computation

We provide an intuitive platform for engineering exciton transfer dynamics. We show that careful consideration of the spectral density, which describes the system-bath interaction, leads to opportunities to engineer the transfer of an exciton. Since excitons in nanostructures are proposed for use in quantum information processing and artificial photosynthetic designs, our approach paves the way for engineering a wide range of desired exciton dynamics. We carefully describe the validity of the model and use experimentally relevant material parameters to show counter-intuitive examples of a directed exciton transfer in a linear chain of quantum dots.

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Papers

Engineering directed excitonic energy transfer

Sombrero adiabatic quantum computation

Construction of model Hamiltonians for adiabatic quantum computation and its application to finding low-energy conformations of lattice protein models

A study of heuristic guesses for adiabatic quantum computation

Engineering directed excitonic energy transfer