Faster amplitude estimation

In this paper, we introduce an efficient algorithm for the quantum amplitude estimation task which is tailored for near-term quantum computers. The quantum amplitude estimation is an important problem which has various applications in fields such as quantum chemistry, machine learning, and finance. Because the well-known algorithm for the quantum amplitude estimation using the phase estimation does not work in near-term quantum computers, alternative approaches have been proposed in recent literature. Some of them provide a proof of the upper bound which almost achieves the Heisenberg scaling. However, the constant factor is large and thus the bound is loose. Our contribution in this paper is to provide the algorithm such that the upper bound of query complexity almost achieves the Heisenberg scaling and the constant factor is small.

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Amplitude estimation without phase estimation

Quantum Information Processing ◽

10.1007/s11128-019-2565-2 ◽

2020 ◽

Vol 19 (2) ◽

Cited By ~ 10

Author(s):

Yohichi Suzuki ◽

Shumpei Uno ◽

Rudy Raymond ◽

Tomoki Tanaka ◽

Tamiya Onodera ◽

...

Keyword(s):

Measurement Data ◽

Likelihood Estimation ◽

Estimation Algorithm ◽

Quantum Circuits ◽

Phase Estimation ◽

Amplitude Estimation ◽

Quantum Amplitude ◽

Phase Estimation Algorithm ◽

Near Term ◽

Quantum Speedup

AbstractThis paper focuses on the quantum amplitude estimation algorithm, which is a core subroutine in quantum computation for various applications. The conventional approach for amplitude estimation is to use the phase estimation algorithm, which consists of many controlled amplification operations followed by a quantum Fourier transform. However, the whole procedure is hard to implement with current and near-term quantum computers. In this paper, we propose a quantum amplitude estimation algorithm without the use of expensive controlled operations; the key idea is to utilize the maximum likelihood estimation based on the combined measurement data produced from quantum circuits with different numbers of amplitude amplification operations. Numerical simulations we conducted demonstrate that our algorithm asymptotically achieves nearly the optimal quantum speedup with a reasonable circuit length.

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Coreset Clustering on Small Quantum Computers

Electronics ◽

10.3390/electronics10141690 ◽

2021 ◽

Vol 10 (14) ◽

pp. 1690

Author(s):

Teague Tomesh ◽

Pranav Gokhale ◽

Eric R. Anschuetz ◽

Frederic T. Chong

Keyword(s):

Quantum Algorithms ◽

Quantum Computers ◽

Data Sets ◽

New Paradigm ◽

Data Set ◽

Small Quantum ◽

Natural Data ◽

Near Term ◽

Classical Computing ◽

Quantum Speedup

Many quantum algorithms for machine learning require access to classical data in superposition. However, for many natural data sets and algorithms, the overhead required to load the data set in superposition can erase any potential quantum speedup over classical algorithms. Recent work by Harrow introduces a new paradigm in hybrid quantum-classical computing to address this issue, relying on coresets to minimize the data loading overhead of quantum algorithms. We investigated using this paradigm to perform k-means clustering on near-term quantum computers, by casting it as a QAOA optimization instance over a small coreset. We used numerical simulations to compare the performance of this approach to classical k-means clustering. We were able to find data sets with which coresets work well relative to random sampling and where QAOA could potentially outperform standard k-means on a coreset. However, finding data sets where both coresets and QAOA work well—which is necessary for a quantum advantage over k-means on the entire data set—appears to be challenging.

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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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Modeling and simulating the noisy behavior of near-term quantum computers

Physical Review A ◽

10.1103/physreva.104.062432 ◽

2021 ◽

Vol 104 (6) ◽

Author(s):

Konstantinos Georgopoulos ◽

Clive Emary ◽

Paolo Zuliani

Keyword(s):

Quantum Computers ◽

Near Term

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Option Pricing using Quantum Computers

Quantum ◽

10.22331/q-2020-07-06-291 ◽

2020 ◽

Vol 4 ◽

pp. 291 ◽

Cited By ~ 4

Author(s):

Nikitas Stamatopoulos ◽

Daniel J. Egger ◽

Yue Sun ◽

Christa Zoufal ◽

Raban Iten ◽

...

Keyword(s):

Option Pricing ◽

Quantum Computer ◽

Quantum Circuits ◽

Quantum Computers ◽

Barrier Options ◽

Error Mitigation ◽

Quantum Device ◽

Amplitude Estimation ◽

Simulation Results ◽

Path Dependent

We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We put an emphasis on the implementation of the quantum circuits required to build the input states and operators needed by amplitude estimation to price the different option types. Additionally, we show simulation results to highlight how the circuits that we implement price the different option contracts. Finally, we examine the performance of option pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. We employ a simple, yet effective, error mitigation scheme that allows us to significantly reduce the errors arising from noisy two-qubit gates.

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Simulation of Condensed-Phase Spectroscopy with Near-Term Digital Quantum Computers

Journal of Chemical Theory and Computation ◽

10.1021/acs.jctc.1c00849 ◽

2021 ◽

Author(s):

Chee-Kong Lee ◽

Chang-Yu Hsieh ◽

Shengyu Zhang ◽

Liang Shi

Keyword(s):

Condensed Phase ◽

Quantum Computers ◽

Near Term

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Quantum simulations of materials on near-term quantum computers

npj Computational Materials ◽

10.1038/s41524-020-00353-z ◽

2020 ◽

Vol 6 (1) ◽

Cited By ~ 4

Author(s):

He Ma ◽

Marco Govoni ◽

Giulia Galli

Keyword(s):

Quantum Computers ◽

Quantum Simulations ◽

Near Term

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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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