scholarly journals Anticoncentration theorems for schemes showing a quantum speedup

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 65 ◽  
Author(s):  
Dominik Hangleiter ◽  
Juan Bermejo-Vega ◽  
Martin Schwarz ◽  
Jens Eisert
Keyword(s):  
Information Science ◽  
Quantum Computers ◽  
Translation Invariant ◽  
Computational Advantage ◽  
Spatial Dimensions ◽  
Universal Quantum ◽  
Closing The Gap ◽  
State Of Affairs ◽  
Random Circuits ◽  
Quantum Speedup

One of the main milestones in quantum information science is to realise quantum devices that exhibit an exponential computational advantage over classical ones without being universal quantum computers, a state of affairs dubbed quantum speedup, or sometimes "quantum computational supremacy". The known schemes heavily rely on mathematical assumptions that are plausible but unproven, prominently results on anticoncentration of random prescriptions. In this work, we aim at closing the gap by proving two anticoncentration theorems and accompanying hardness results, one for circuit-based schemes, the other for quantum quench-type schemes for quantum simulations. Compared to the few other known such results, these results give rise to a number of comparably simple, physically meaningful and resource-economical schemes showing a quantum speedup in one and two spatial dimensions. At the heart of the analysis are tools of unitary designs and random circuits that allow us to conclude that universal random circuits anticoncentrate as well as an embedding of known circuit-based schemes in a 2D translation-invariant architecture.

scholarly journals Design Space Exploration of Hybrid Quantum–Classical Neural Networks

Electronics ◽  
2021 ◽  
Vol 10 (23) ◽  
pp. 2980
Author(s):  
Muhammad Kashif ◽  
Saif Al-Kuwari
Keyword(s):  
Neural Networks ◽  
Design Space Exploration ◽  
Design Space ◽  
Space Exploration ◽  
Quantum Computers ◽  
Computational Advantage ◽  
Systematic Methodology ◽  
Universal Quantum ◽  
Speed Up ◽  
Hybrid Neural Networks

The unprecedented success of classical neural networks and the recent advances in quantum computing have motivated the research community to explore the interplay between these two technologies, leading to the so-called quantum neural networks. In fact, universal quantum computers are anticipated to both speed up and improve the accuracy of neural networks. However, whether such quantum neural networks will result in a clear advantage on noisy intermediate-scale quantum (NISQ) devices is still not clear. In this paper, we propose a systematic methodology for designing quantum layer(s) in hybrid quantum–classical neural network (HQCNN) architectures. Following our proposed methodology, we develop different variants of hybrid neural networks and compare them with pure classical architectures of equivalent size. Finally, we empirically evaluate our proposed hybrid variants and show that the addition of quantum layers does provide a noticeable computational advantage.

scholarly journals Universal Qudit Hamiltonians

2021 ◽  
Author(s):  
Stephen Piddock ◽  
Ashley Montanaro
Keyword(s):  
State Energy ◽  
Entangled State ◽  
Quantum Computers ◽  
List Type ◽  
Universal Family ◽  
Finite Dimensional ◽  
Universal Quantum ◽  
Aklt Model ◽  
Almost All ◽  
Natural Way

AbstractA family of quantum Hamiltonians is said to be universal if any other finite-dimensional Hamiltonian can be approximately encoded within the low-energy space of a Hamiltonian from that family. If the encoding is efficient, universal families of Hamiltonians can be used as universal analogue quantum simulators and universal quantum computers, and the problem of approximately determining the ground-state energy of a Hamiltonian from a universal family is QMA-complete. One natural way to categorise Hamiltonians into families is in terms of the interactions they are built from. Here we prove universality of some important classes of interactions on qudits (d-level systems): We completely characterise the k-qudit interactions which are universal, if augmented with arbitrary Hermitian 1-local terms. We find that, for all $$k \geqslant 2$$ k ⩾ 2 and all local dimensions $$d \geqslant 2$$ d ⩾ 2 , almost all such interactions are universal aside from a simple stoquastic class. We prove universality of generalisations of the Heisenberg model that are ubiquitous in condensed-matter physics, even if free 1-local terms are not provided. We show that the SU(d) and SU(2) Heisenberg interactions are universal for all local dimensions $$d \geqslant 2$$ d ⩾ 2 (spin $$\geqslant 1/2$$ ⩾ 1 / 2 ), implying that a quantum variant of the Max-d-Cut problem is QMA-complete. We also show that for $$d=3$$ d = 3 all bilinear-biquadratic Heisenberg interactions are universal. One example is the general AKLT model. We prove universality of any interaction proportional to the projector onto a pure entangled state.

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 Entanglement marginal problems

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 589
Author(s):  
Miguel Navascués ◽  
Flavio Baccari ◽  
Antonio Acín
Keyword(s):  
Quantum State ◽  
System Size ◽  
Separable Extension ◽  
Translation Invariant ◽  
Time Space ◽  
Marginal Problem ◽  
Spatial Dimensions ◽  
A Chain ◽  
Reduced Density ◽  
Star Configuration

We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite programming relaxations of the set of quantum state marginals admitting a fully separable extension. We connect the completeness of each hierarchy to the resolution of an analog classical marginal problem and thus identify relevant experimental situations where the hierarchies are complete. For finitely many parties on a star configuration or a chain, we find that we can achieve an arbitrarily good approximation to the set of nearest-neighbour marginals of separable states with a time (space) complexity polynomial (linear) on the system size. Our results even extend to infinite systems, such as translation-invariant systems in 1D, as well as higher spatial dimensions with extra symmetries.

scholarly journals Assessing the quantumness of the annealing dynamics via Leggett Garg’s inequalities: a weak measurement approach

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
V. Vitale ◽  
G. De Filippis ◽  
A. de Candia ◽  
A. Tagliacozzo ◽  
V. Cataudella ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Quantum Computers ◽  
Quantum Annealing ◽  
Adiabatic Quantum Computation ◽  
Universal Quantum ◽  
Full Quantum ◽  
Measurement Approach ◽  
Coherent Behavior ◽  
Sizable Number

Abstract Adiabatic quantum computation (AQC) is a promising counterpart of universal quantum computation, based on the key concept of quantum annealing (QA). QA is claimed to be at the basis of commercial quantum computers and benefits from the fact that the detrimental role of decoherence and dephasing seems to have poor impact on the annealing towards the ground state. While many papers show interesting optimization results with a sizable number of qubits, a clear evidence of a full quantum coherent behavior during the whole annealing procedure is still lacking. In this paper we show that quantum non-demolition (weak) measurements of Leggett Garg inequalities can be used to efficiently assess the quantumness of the QA procedure. Numerical simulations based on a weak coupling Lindblad approach are compared with classical Langevin simulations to support our statements.

scholarly journals In situ upgrade of quantum simulators to universal computers

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 80 ◽  
Author(s):  
Benjamin Dive ◽  
Alexander Pitchford ◽  
Florian Mintert ◽  
Daniel Burgarth
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Strong Evidence ◽  
Logic Gates ◽  
Quantum Systems ◽  
Quantum Computers ◽  
Quantum Simulators ◽  
Universal Quantum ◽  
Classical Computer

Quantum simulators, machines that can replicate the dynamics of quantum systems, are being built as useful devices and are seen as a stepping stone to universal quantum computers. A key difference between the two is that computers have the ability to perform the logic gates that make up algorithms. We propose a method for learning how to construct these gates efficiently by using the simulator to perform optimal control on itself. This bypasses two major problems of purely classical approaches to the control problem: the need to have an accurate model of the system, and a classical computer more powerful than the quantum one to carry out the required simulations. Strong evidence that the scheme scales polynomially in the number of qubits, for systems of up to 9 qubits with Ising interactions, is presented from numerical simulations carried out in different topologies. This suggests that this in situ approach is a practical way of upgrading quantum simulators to computers.

scholarly journals A UNIVERSAL QUANTUM ESTIMATOR

2005 ◽  
Vol 03 (supp01) ◽  
pp. 123-132
Author(s):  
L. C. KWEK ◽  
K. W. CHOO ◽  
JIANGFENG DU ◽  
ARTUR K. EKERT ◽  
CAROLINA MOURA ALVES ◽  
...  
Keyword(s):  
Building Blocks ◽  
Quantum Gates ◽  
Quantum Computers ◽  
Quantum Networks ◽  
Modern Computer ◽  
Universal Quantum ◽  
Almost All

Almost all computational tasks in the modern computer can be designed from basic building blocks. These building blocks provide a powerful and efficient language for describing algorithms. In quantum computers, the basic building blocks are the quantum gates. In this tutorial, we will look at quantum gates that act on one and two qubits and briefly discuss how these gates can be used in quantum networks.

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