Accuracy and Resource Estimations for Quantum Chemistry on a Near-Term Quantum Computer

Quantum simulation of quantum chemistry is one of the most compelling applications of quantum computing. It is of particular importance in areas ranging from materials science, biochemistry, and condensed matter physics. Here, we propose a full quantum eigensolver (FQE) algorithm to calculate the molecular ground energies and electronic structures using quantum gradient descent. Compared to existing classical-quantum hybrid methods such as variational quantum eigensolver (VQE), our method removes the classical optimizer and performs all the calculations on a quantum computer with faster convergence. The gradient descent iteration depth has a favorable complexity that is logarithmically dependent on the system size and inverse of the precision. Moreover, the FQE can be further simplified by exploiting a perturbation theory for the calculations of intermediate matrix elements and obtaining results with a precision that satisfies the requirement of chemistry application. The full quantum eigensolver can be implemented on a near-term quantum computer. With the rapid development of quantum computing hardware, the FQE provides an efficient and powerful tool to solve quantum chemistry problems.

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What is Quantum Computing and How it Works

10.47363/jmsmr/2020(2)104 ◽

2020 ◽

pp. 1-5

Author(s):

Bahman Zohuri ◽

◽

Farhang Mossavar Rahmani ◽

Keyword(s):

Artificial Intelligence ◽

Quantum Computing ◽

Quantum Computer ◽

Time Frame ◽

Basic Unit ◽

Next Generation ◽

Intel Corporation ◽

Encrypt Data ◽

Near Term ◽

Incremental Step

Companies such as Intel as a pioneer in chip design for computing are pushing the edge of computing from its present Classical Computing generation to the next generation of Quantum Computing. Along the side of Intel corporation, companies such as IBM, Microsoft, and Google are also playing in this domain. The race is on to build the world’s first meaningful quantum computer—one that can deliver the technology’s long-promised ability to help scientists do things like develop miraculous new materials, encrypt data with near-perfect security and accurately predict how Earth’s climate will change. Such a machine is likely more than a decade away, but IBM, Microsoft, Google, Intel, and other tech heavyweights breathlessly tout each tiny, incremental step along the way. Most of these milestones involve packing more quantum bits, or qubits—the basic unit of information in a quantum computer—onto a processor chip ever. But the path to quantum computing involves far more than wrangling subatomic particles. Such computing capabilities are opening a new area into dealing with the massive sheer volume of structured and unstructured data in the form of Big Data, is an excellent augmentation to Artificial Intelligence (AI) and would allow it to thrive to its next generation of Super Artificial Intelligence (SAI) in the near-term time frame.

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Error mitigation with Clifford quantum-circuit data

Quantum ◽

10.22331/q-2021-11-26-592 ◽

2021 ◽

Vol 5 ◽

pp. 592

Author(s):

Piotr Czarnik ◽

Andrew Arrasmith ◽

Patrick J. Coles ◽

Lukasz Cincio

Keyword(s):

State Energy ◽

Quantum Computer ◽

Quantum Circuit ◽

Training Data ◽

Quantum Circuits ◽

Accurate Estimation ◽

Error Mitigation ◽

Order Of Magnitude ◽

Quantum Observables ◽

Near Term

Achieving near-term quantum advantage will require accurate estimation of quantum observables despite significant hardware noise. For this purpose, we propose a novel, scalable error-mitigation method that applies to gate-based quantum computers. The method generates training data {Xinoisy,Xiexact} via quantum circuits composed largely of Clifford gates, which can be efficiently simulated classically, where Xinoisy and Xiexact are noisy and noiseless observables respectively. Fitting a linear ansatz to this data then allows for the prediction of noise-free observables for arbitrary circuits. We analyze the performance of our method versus the number of qubits, circuit depth, and number of non-Clifford gates. We obtain an order-of-magnitude error reduction for a ground-state energy problem on 16 qubits in an IBMQ quantum computer and on a 64-qubit noisy simulator.

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Quantum Attacks on Bitcoin, and How to Protect Against Them

Ledger ◽

10.5195/ledger.2018.127 ◽

2018 ◽

Vol 3 ◽

Cited By ~ 17

Author(s):

Divesh Aggarwal ◽

Gavin Brennen ◽

Troy Lee ◽

Miklos Santha ◽

Marco Tomamichel

Keyword(s):

At Risk ◽

Quantum Computer ◽

Alternative Proof ◽

Quantum Computers ◽

Signature Scheme ◽

Area At Risk ◽

Signature Schemes ◽

Near Term ◽

Financial Transactions ◽

Large Quantum

The key cryptographic protocols used to secure the internet and financial transactions of today are all susceptible to attack by the development of a sufficiently large quantum computer. One particular area at risk is cryptocurrencies, a market currently worth over 100 billion USD. We investigate the risk posed to Bitcoin, and other cryptocurrencies, by attacks using quantum computers. We find that the proof-of-work used by Bitcoin is relatively resistant to substantial speedup by quantum computers in the next 10 years, mainly because specialized ASIC miners are extremely fast compared to the estimated clock speed of near-term quantum computers. On the other hand, the elliptic curve signature scheme used by Bitcoin is much more at risk, and could be completely broken by a quantum computer as early as 2027, by the most optimistic estimates. We analyze an alternative proof-of-work called Momentum, based on finding collisions in a hash function, that is even more resistant to speedup by a quantum computer. We also review the available post-quantum signature schemes to see which one would best meet the security and efficiency requirements of blockchain applications.

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Next steps of quantum transport in Majorana nanowire devices

Nature Communications ◽

10.1038/s41467-019-13133-1 ◽

2019 ◽

Vol 10 (1) ◽

Cited By ~ 29

Author(s):

Hao Zhang ◽

Dong E. Liu ◽

Michael Wimmer ◽

Leo P. Kouwenhoven

Keyword(s):

Material Science ◽

Quantum Computer ◽

Condensed Matter ◽

Fundamental Aspect ◽

Semiconductor Nanowire ◽

Quantum Operations ◽

Zero Modes ◽

Ongoing Effort ◽

Gate Control ◽

Near Term

Abstract Majorana zero modes are localized quasiparticles that obey non-Abelian exchange statistics. Braiding Majorana zero modes forms the basis of topologically protected quantum operations which could, in principle, significantly reduce qubit decoherence and gate control errors at the device level. Therefore, searching for Majorana zero modes in various solid state systems is a major topic in condensed matter physics and quantum computer science. Since the first experimental signature observed in hybrid superconductor-semiconductor nanowire devices, this field has witnessed a dramatic expansion in material science, transport experiments and theory. While making the first topological qubit based on these Majorana nanowires is currently an ongoing effort, several related important transport experiments are still being pursued in the near term. These will not only serve as intermediate steps but also show Majorana physics in a more fundamental aspect. In this perspective, we summarize these key Majorana experiments and the potential challenges.

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Qubit Coupled Cluster Method: A Systematic Approach to Quantum Chemistry on a Quantum Computer

Journal of Chemical Theory and Computation ◽

10.1021/acs.jctc.8b00932 ◽

2018 ◽

Vol 14 (12) ◽

pp. 6317-6326 ◽

Cited By ~ 30

Author(s):

Ilya G. Ryabinkin ◽

Tzu-Ching Yen ◽

Scott N. Genin ◽

Artur F. Izmaylov

Keyword(s):

Quantum Chemistry ◽

Systematic Approach ◽

Quantum Computer ◽

Cluster Method ◽

Coupled Cluster ◽

Coupled Cluster Method

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Application of Quantum Computing to Biochemical Systems: A Look to the Future

Frontiers in Chemistry ◽

10.3389/fchem.2020.587143 ◽

2020 ◽

Vol 8 ◽

Author(s):

Hai-Ping Cheng ◽

Erik Deumens ◽

James K. Freericks ◽

Chenglong Li ◽

Beverly A. Sanders

Keyword(s):

Quantum Computing ◽

Physical System ◽

Quantum Computer ◽

Quantum Algorithms ◽

Active Regions ◽

Quantum Computers ◽

The Future ◽

Biochemical Systems ◽

Near Term ◽

Different Levels

Chemistry is considered as one of the more promising applications to science of near-term quantum computing. Recent work in transitioning classical algorithms to a quantum computer has led to great strides in improving quantum algorithms and illustrating their quantum advantage. Because of the limitations of near-term quantum computers, the most effective strategies split the work over classical and quantum computers. There is a proven set of methods in computational chemistry and materials physics that has used this same idea of splitting a complex physical system into parts that are treated at different levels of theory to obtain solutions for the complete physical system for which a brute force solution with a single method is not feasible. These methods are variously known as embedding, multi-scale, and fragment techniques and methods. We review these methods and then propose the embedding approach as a method for describing complex biochemical systems, with the parts not only treated with different levels of theory, but computed with hybrid classical and quantum algorithms. Such strategies are critical if one wants to expand the focus to biochemical molecules that contain active regions that cannot be properly explained with traditional algorithms on classical computers. While we do not solve this problem here, we provide an overview of where the field is going to enable such problems to be tackled in the future.

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Quantum chemistry beyond Born-Oppenheimer approximation on a quantum computer: A simulated phase estimation study

International Journal of Quantum Chemistry ◽

10.1002/qua.25176 ◽

2016 ◽

Vol 116 (18) ◽

pp. 1328-1336 ◽

Cited By ~ 6

Author(s):

Libor Veis ◽

Jakub Višňák ◽

Hiroaki Nishizawa ◽

Hiromi Nakai ◽

Jiří Pittner

Keyword(s):

Quantum Chemistry ◽

Quantum Computer ◽

Phase Estimation ◽

Oppenheimer Approximation

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Algorithmic Error Mitigation Scheme for Current Quantum Processors

Quantum ◽

10.22331/q-2021-07-01-492 ◽

2021 ◽

Vol 5 ◽

pp. 492

Author(s):

Philippe Suchsland ◽

Francesco Tacchino ◽

Mark H. Fischer ◽

Titus Neupert ◽

Panagiotis Kl. Barkoutsos ◽

...

Keyword(s):

Quantum Chemistry ◽

Ground State ◽

State Of The Art ◽

Quantum Algorithms ◽

Quantum Circuit ◽

Lanczos Method ◽

Error Mitigation ◽

Near Term ◽

The Impact ◽

Different Sources

We present a hardware agnostic error mitigation algorithm for near term quantum processors inspired by the classical Lanczos method. This technique can reduce the impact of different sources of noise at the sole cost of an increase in the number of measurements to be performed on the target quantum circuit, without additional experimental overhead. We demonstrate through numerical simulations and experiments on IBM Quantum hardware that the proposed scheme significantly increases the accuracy of cost functions evaluations within the framework of variational quantum algorithms, thus leading to improved ground-state calculations for quantum chemistry and physics problems beyond state-of-the-art results.

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Construction of a silicon-based solid state quantum computer

Quantum Information and Computation ◽

10.26421/qic1.s-8 ◽

2001 ◽

Vol 1 (Special) ◽

pp. 82-95

Author(s):

A.S. Dzurak ◽

M.Y. Simmons ◽

A.R. Hamilton ◽

R.G. Clark ◽

R. Brenner ◽

...

Keyword(s):

Large Scale ◽

Quantum Computer ◽

Atomic Scale ◽

Single Electron Transistor ◽

Epitaxial Silicon ◽

Top Down ◽

Bottom Up ◽

Near Term ◽

Silicon Based ◽

Coincidence Measurements

We discuss progress towards the fabrication and demonstration of a prototype silicon-based quantum computer. The devices are based on a precise array of 31P dopants embedded in 28Si. Fabrication is being pursued via two complementary pathways – a ‘top-down’ approach for near-term production of few-qubit demonstration devices and a ‘bottom-up’ approach for large-scale qubit arrays. The ‘top-down’ approach employs ion implantation through a multi-layer resist structure which serves to accurately register the donors to metal control gates and single-electron transistor (SET) read-out devices. In contrast the ‘bottom-up’ approach uses STM lithography and epitaxial silicon overgrowth to construct devices at an atomic scale. Techniques for qubit read-out, which utilise coincidence measurements on novel twin-SET devices, are also presented.

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