scholarly journals A diagrammatic approach to variational quantum ansatz construction

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 596
Author(s):  
Y. Herasymenko ◽  
T.E. O'Brien
Keyword(s):  
Ground State ◽  
Quantum Algorithms ◽  
Transverse Field ◽  
Quantum Correlations ◽  
Ferromagnetic Phase ◽  
Target System ◽  
Good Convergence ◽  
Size Extensivity ◽  
Minimum Number ◽  
Near Term

Variational quantum eigensolvers (VQEs) are a promising class of quantum algorithms for preparing approximate ground states in near-term quantum devices. Minimizing the error in such an approximation requires designing ansatzes using physical considerations that target the studied system. One such consideration is size-extensivity, meaning that the ground state quantum correlations are to be compactly represented in the ansatz. On digital quantum computers, however, the size-extensive ansatzes usually require expansion via Trotter-Suzuki methods. These introduce additional costs and errors to the approximation. In this work, we present a diagrammatic scheme for the digital VQE ansatzes, which is size-extensive but does not rely on Trotterization. We start by designing a family of digital ansatzes that explore the entire Hilbert space with the minimum number of free parameters. We then demonstrate how one may compress an arbitrary digital ansatz, by enforcing symmetry constraints of the target system, or by using them as parent ansatzes for a hierarchy of increasingly long but increasingly accurate sub-ansatzes. We apply a perturbative analysis and develop a diagrammatic formalism that ensures the size-extensivity of generated hierarchies. We test our methods on a short spin chain, finding good convergence to the ground state in the paramagnetic and the ferromagnetic phase of the transverse-field Ising model.

scholarly journals Algorithmic Error Mitigation Scheme for Current Quantum Processors

Quantum ◽  
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.

scholarly journals QUANTUM DISCORD AND RELATED MEASURES OF QUANTUM CORRELATIONS IN FINITE XY CHAINS

2012 ◽  
Vol 27 (01n03) ◽  
pp. 1345033 ◽  
Author(s):  
N. CANOSA ◽  
L. CILIBERTI ◽  
R. ROSSIGNOLI
Keyword(s):  
Ground State ◽  
Quantum Discord ◽  
Nearest Neighbor ◽  
Full Range ◽  
Transverse Field ◽  
Quantum Correlations ◽  
Spin Chains ◽  
Crucial Importance ◽  
Spin Pairs ◽  
Fully Connected

We examine the quantum correlations of spin pairs in the ground state of finite XY chains in a transverse field, by evaluating the quantum discord as well as other related entropic measures of quantum correlations. A brief review of the latter, based on generalized entropic forms, is also included. It is shown that parity effects are of crucial importance for describing the behavior of these measures below the critical field. It is also shown that these measures reach full range in the immediate vicinity of the factorizing field, where they become independent of separation and coupling range. Analytical and numerical results for the quantum discord, the geometric discord and other measures in spin chains with nearest neighbor coupling and in fully connected spin arrays are also provided.

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 Demonstrating a Continuous Set of Two-qubit Gates for Near-term Quantum Algorithms

2020 ◽  
Vol 125 (12) ◽  
Author(s):  
B. Foxen ◽  
C. Neill ◽  
A. Dunsworth ◽  
P. Roushan ◽  
B. Chiaro ◽  
...  
Keyword(s):  
Quantum Algorithms ◽  
Near Term

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.

The spin-coupled valence bond theory of molecular electronic structure. I. Basic theory and application to the 2 Σ + states of BeH

1980 ◽  
Vol 371 (1747) ◽  
pp. 525-552 ◽  
Keyword(s):  
Electronic Structure ◽  
Ground State ◽  
Valence Bond ◽  
Present Theory ◽  
Hamiltonian Matrix ◽  
Molecular Electronic ◽  
Good Convergence ◽  
Valence Bond Theory ◽  
Bond Theory ◽  
Molecular Electronic Structure

The spin-coupled valence bond theory of molecular electronic structure is developed, according to which the single configuration spin-coupled theory is reformulated so as to yield both ground and excited orbitals. These orbitals are subsequently used to generate v.b. structures, the Hamiltonian matrix of which is diagonalized as in the conventional v.b. method. The fundamental feature of the excited spin-coupled orbitals is that, except those with the highest energy, they retain the characteristic distorted atomic form of the ground state orbitals, and correspondingly possess negative orbital energies. This leads to compact and rapidly convergent wavefunctions for the ground and lower-lying excited states, thus overcoming one of the basic drawbacks of the original v.b. theory. The theory is applied to the 2 ∑ + states of BeH by using 53, 71 and 80 structures of this kind. Very good convergence is found for the lowest six states, and the total energy of the ground state is below that given by a very large m.o.c.i. calculation. The present theory is thus a powerful and flexible alternative to m.o.c.i. calculations but using about an order of magnitude fewer functions.

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