scholarly journals Quantum-assisted quantum compiling

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 140 ◽  
Author(s):  
Sumeet Khatri ◽  
Ryan LaRose ◽  
Alexander Poremba ◽  
Lukasz Cincio ◽  
Andrew T. Sornborger ◽  
...  
Keyword(s):  
Cost Function ◽  
Quantum Dynamics ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Computers ◽  
Problem Size ◽  
Noise Mitigation ◽  
Classical Algorithm ◽  
Noise Resilience ◽  
Near Term

Compiling quantum algorithms for near-term quantum computers (accounting for connectivity and native gate alphabets) is a major challenge that has received significant attention both by industry and academia. Avoiding the exponential overhead of classical simulation of quantum dynamics will allow compilation of larger algorithms, and a strategy for this is to evaluate an algorithm's cost on a quantum computer. To this end, we propose a variational hybrid quantum-classical algorithm called quantum-assisted quantum compiling (QAQC). In QAQC, we use the overlap between a target unitaryUand a trainable unitaryVas the cost function to be evaluated on the quantum computer. More precisely, to ensure that QAQC scales well with problem size, our cost involves not only the global overlapTr(V†U)but also the local overlaps with respect to individual qubits. We introduce novel short-depth quantum circuits to quantify the terms in our cost function, and we prove that our cost cannot be efficiently approximated with a classical algorithm under reasonable complexity assumptions. We present both gradient-free and gradient-based approaches to minimizing this cost. As a demonstration of QAQC, we compile various one-qubit gates on IBM's and Rigetti's quantum computers into their respective native gate alphabets. Furthermore, we successfully simulate QAQC up to a problem size of 9 qubits, and these simulations highlight both the scalability of our cost function as well as the noise resilience of QAQC. Future applications of QAQC include algorithm depth compression, black-box compiling, noise mitigation, and benchmarking.

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

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.

scholarly journals Coreset Clustering on Small Quantum Computers

Electronics ◽  
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.

scholarly journals Quantum Attacks on Bitcoin, and How to Protect Against Them

Ledger ◽  
2018 ◽  
Vol 3 ◽  
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.

scholarly journals A random walk approach to quantum algorithms

2006 ◽  
Vol 364 (1849) ◽  
pp. 3407-3422 ◽  
Author(s):  
Vivien M Kendon
Keyword(s):  
Random Walk ◽  
Quantum Dynamics ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Walk ◽  
Quantum Random Walk ◽  
Small Quantum ◽  
Starting Point ◽  
Quantum Version ◽  
Speed Up

The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial; pure quantum dynamics is deterministic, so randomness only enters during the measurement phase, i.e. when converting the quantum information into classical information. The outcome of a quantum random walk is very different from the corresponding classical random walk owing to the interference between the different possible paths. The upshot is that quantum walkers find themselves further from their starting point than a classical walker on average, and this forms the basis of a quantum speed up, which can be exploited to solve problems faster. Surprisingly, the effect of making the walk slightly less than perfectly quantum can optimize the properties of the quantum walk for algorithmic applications. Looking to the future, even with a small quantum computer available, the development of quantum walk algorithms might proceed more rapidly than it has, especially for solving real problems.

scholarly journals Variational Quantum Computation of Excited States

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 156 ◽  
Author(s):  
Oscar Higgott ◽  
Daochen Wang ◽  
Stephen Brierley
Keyword(s):  
Excited State ◽  
Excited States ◽  
Quantum Algorithms ◽  
Reaction Rates ◽  
Mitigation Strategies ◽  
Quantum Computers ◽  
Error Mitigation ◽  
Near Term ◽  
Ground State Energies ◽  
High Depth

The calculation of excited state energies of electronic structure Hamiltonians has many important applications, such as the calculation of optical spectra and reaction rates. While low-depth quantum algorithms, such as the variational quantum eigenvalue solver (VQE), have been used to determine ground state energies, methods for calculating excited states currently involve the implementation of high-depth controlled-unitaries or a large number of additional samples. Here we show how overlap estimation can be used to deflate eigenstates once they are found, enabling the calculation of excited state energies and their degeneracies. We propose an implementation that requires the same number of qubits as VQE and at most twice the circuit depth. Our method is robust to control errors, is compatible with error-mitigation strategies and can be implemented on near-term quantum computers.

Hidden symmetry detection on a quantum computer

2007 ◽  
Vol 7 (1&2) ◽  
pp. 83-92
Author(s):  
R. Schutzhold ◽  
W.G. Unruh
Keyword(s):  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Computers ◽  
Self Similarity ◽  
Hidden Subgroup Problem ◽  
Hidden Symmetry ◽  
Speed Up ◽  
Subgroup Problem ◽  
Discrete Scale

The fastest quantum algorithms (for the solution of classical computational tasks) known so far are basically variations of the hidden subgroup problem with {$f(U[x])=f(x)$}. Following a discussion regarding which tasks might be solved efficiently by quantum computers, it will be demonstrated by means of a simple example, that the detection of more general hidden (two-point) symmetries {$V\{f(x),f(U[x])\}=0$} by a quantum algorithm can also admit an exponential speed-up. E.g., one member of this class of symmetries {$V\{f(x),f(U[x])\}=0$} is discrete self-similarity (or discrete scale invariance).

scholarly journals Optimizing quantum heuristics with meta-learning

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Max Wilson ◽  
Rachel Stromswold ◽  
Filip Wudarski ◽  
Stuart Hadfield ◽  
Norm M. Tubman ◽  
...  
Keyword(s):  
Quantum Algorithms ◽  
Evolutionary Strategies ◽  
Quantum Computers ◽  
Parameter Setting ◽  
Present Evidence ◽  
Machine Learning Methods ◽  
Meta Learning ◽  
Global Optima ◽  
Near Term ◽  
Important Indication

AbstractVariational quantum algorithms, a class of quantum heuristics, are promising candidates for the demonstration of useful quantum computation. Finding the best way to amplify the performance of these methods on hardware is an important task. Here, we evaluate the optimization of quantum heuristics with an existing class of techniques called “meta-learners.” We compare the performance of a meta-learner to evolutionary strategies, L-BFGS-B and Nelder-Mead approaches, for two quantum heuristics (quantum alternating operator ansatz and variational quantum eigensolver), on three problems, in three simulation environments. We show that the meta-learner comes near to the global optima more frequently than all other optimizers we tested in a noisy parameter setting environment. We also find that the meta-learner is generally more resistant to noise, for example, seeing a smaller reduction in performance in Noisy and Sampling environments, and performs better on average by a “gain” metric than its closest comparable competitor L-BFGS-B. Finally, we present evidence that indicates the meta-learner trained on small problems will generalize to larger problems. These results are an important indication that meta-learning and associated machine learning methods will be integral to the useful application of noisy near-term quantum computers.

scholarly journals Quantum Algorithms for Solving Ordinary Differential Equations via Classical Integration Methods

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 502
Author(s):  
Benjamin Zanger ◽  
Christian B. Mendl ◽  
Martin Schulz ◽  
Martin Schreiber
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Optimization Problems ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
High Order ◽  
Quantum Computers ◽  
Integration Methods ◽  
Linear Ordinary Differential Equations ◽  
Legendre Collocation Method

Identifying computational tasks suitable for (future) quantum computers is an active field of research. Here we explore utilizing quantum computers for the purpose of solving differential equations. We consider two approaches: (i) basis encoding and fixed-point arithmetic on a digital quantum computer, and (ii) representing and solving high-order Runge-Kutta methods as optimization problems on quantum annealers. As realizations applied to two-dimensional linear ordinary differential equations, we devise and simulate corresponding digital quantum circuits, and implement and run a 6th order Gauss-Legendre collocation method on a D-Wave 2000Q system, showing good agreement with the reference solution. We find that the quantum annealing approach exhibits the largest potential for high-order implicit integration methods. As promising future scenario, the digital arithmetic method could be employed as an "oracle" within quantum search algorithms for inverse problems.

scholarly journals Fisher Information in Noisy Intermediate-Scale Quantum Applications

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 539
Author(s):  
Johannes Jakob Meyer
Keyword(s):  
Fisher Information ◽  
Quantum Algorithms ◽  
Quantum Fisher Information ◽  
Quantum Systems ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Quantum Devices ◽  
Intermediate Scale ◽  
Quantum Sensing ◽  
Near Term

The recent advent of noisy intermediate-scale quantum devices, especially near-term quantum computers, has sparked extensive research efforts concerned with their possible applications. At the forefront of the considered approaches are variational methods that use parametrized quantum circuits. The classical and quantum Fisher information are firmly rooted in the field of quantum sensing and have proven to be versatile tools to study such parametrized quantum systems. Their utility in the study of other applications of noisy intermediate-scale quantum devices, however, has only been discovered recently. Hoping to stimulate more such applications, this article aims to further popularize classical and quantum Fisher information as useful tools for near-term applications beyond quantum sensing. We start with a tutorial that builds an intuitive understanding of classical and quantum Fisher information and outlines how both quantities can be calculated on near-term devices. We also elucidate their relationship and how they are influenced by noise processes. Next, we give an overview of the core results of the quantum sensing literature and proceed to a comprehensive review of recent applications in variational quantum algorithms and quantum machine learning.

scholarly journals Simulating quantum many-body dynamics on a current digital quantum computer

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Adam Smith ◽  
M. S. Kim ◽  
Frank Pollmann ◽  
Johannes Knolle
Keyword(s):  
Quantum Dynamics ◽  
Quantum Computer ◽  
Quantum Computers ◽  
Many Body ◽  
Time Dynamics ◽  
Effects Of Disorder ◽  
Body Dynamics ◽  
Many Body Quantum Dynamics ◽  
Universal Quantum

AbstractUniversal quantum computers are potentially an ideal setting for simulating many-body quantum dynamics that is out of reach for classical digital computers. We use state-of-the-art IBM quantum computers to study paradigmatic examples of condensed matter physics—we simulate the effects of disorder and interactions on quantum particle transport, as well as correlation and entanglement spreading. Our benchmark results show that the quality of the current machines is below what is necessary for quantitatively accurate continuous-time dynamics of observables and reachable system sizes are small comparable to exact diagonalization. Despite this, we are successfully able to demonstrate clear qualitative behaviour associated with localization physics and many-body interaction effects.

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