scholarly journals Efficient universal quantum circuits

2010 ◽  
Vol 10 (1&2) ◽  
pp. 16-27
Author(s):  
D. Bera ◽  
S. Fenner ◽  
F. Green ◽  
S. Homer
Keyword(s):  
Blow Up ◽  
General Purpose ◽  
Quantum Circuits ◽  
Computational Power ◽  
Universal Quantum

Universal circuits can be viewed as general-purpose simulators for central classes of circuits and can be used to capture the computational power of the circuit class being simulated. We define and construct quantum universal circuits which are efficient and has very little overhead in simulation. For depth we construct universal circuits whose depth is the same order as the circuits being simulated. For size, there is a log factor blow-up in the universal circuits constructed here which is nearly optimal.

scholarly journals Matchgates and classical simulation of quantum circuits

2008 ◽  
Vol 464 (2100) ◽  
pp. 3089-3106 ◽  
Author(s):  
Richard Jozsa ◽  
Akimasa Miyake
Keyword(s):  
Clifford Algebra ◽  
Point Of View ◽  
Quantum Circuits ◽  
Nearest Neighbour ◽  
Computational Power ◽  
Classical Simulation ◽  
Wigner Representation ◽  
Universal Quantum ◽  
The One ◽  
Qubit Gate

Let G ( A ,  B ) denote the two-qubit gate that acts as the one-qubit SU (2) gates A and B in the even and odd parity subspaces, respectively, of two qubits. Using a Clifford algebra formalism, we show that arbitrary uniform families of circuits of these gates, restricted to act only on nearest neighbour (n.n.) qubit lines, can be classically efficiently simulated. This reproduces a result originally proved by Valiant using his matchgate formalism, and subsequently related by others to free fermionic physics. We further show that if the n.n. condition is slightly relaxed, to allow the same gates to act only on n.n. and next n.n. qubit lines, then the resulting circuits can efficiently perform universal quantum computation. From this point of view, the gap between efficient classical and quantum computational power is bridged by a very modest use of a seemingly innocuous resource (qubit swapping). We also extend the simulation result above in various ways. In particular, by exploiting properties of Clifford operations in conjunction with the Jordan–Wigner representation of a Clifford algebra, we show how one may generalize the simulation result above to provide further classes of classically efficiently simulatable quantum circuits, which we call Gaussian quantum circuits.

scholarly journals Comparing quantum hybrid reinforcement learning to classical methods

2021 ◽  
Author(s):  
Maximilian Moll ◽  
Leonhard Kunczik
Keyword(s):  
Reinforcement Learning ◽  
Quantum Circuits ◽  
Memory Usage ◽  
Computational Power ◽  
Classical Domain ◽  
Q Learning ◽  
Optimal Behavior ◽  
Computational Speed ◽  
Complex Decision ◽  
Hybrid Reinforcement

AbstractIn recent history, reinforcement learning (RL) proved its capability by solving complex decision problems by mastering several games. Increased computational power and the advances in approximation with neural networks (NN) paved the path to RL’s successful applications. Even though RL can tackle more complex problems nowadays, it still relies on computational power and runtime. Quantum computing promises to solve these issues by its capability to encode information and the potential quadratic speedup in runtime. We compare tabular Q-learning and Q-learning using either a quantum or a classical approximation architecture on the frozen lake problem. Furthermore, the three algorithms are analyzed in terms of iterations until convergence to the optimal behavior, memory usage, and runtime. Within the paper, NNs are utilized for approximation in the classical domain, while in the quantum domain variational quantum circuits, as a quantum hybrid approximation method, have been used. Our simulations show that a quantum approximator is beneficial in terms of memory usage and provides a better sample complexity than NNs; however, it still lacks the computational speed to be competitive.

scholarly journals Efficient Universal Quantum Circuits

2009 ◽  
pp. 418-428 ◽  
Author(s):  
Debajyoti Bera ◽  
Stephen Fenner ◽  
Frederic Green ◽  
Steve Homer
Keyword(s):  
Quantum Circuits ◽  
Universal Quantum

scholarly journals Partial Compilation of ASP Programs

2019 ◽  
Vol 19 (5-6) ◽  
pp. 857-873 ◽  
Author(s):  
BERNARDO CUTERI ◽  
CARMINE DODARO ◽  
FRANCESCO RICCA ◽  
PETER SCHÜLLER
Keyword(s):  
Experimental Analysis ◽  
Ad Hoc ◽  
Blow Up ◽  
State Of The Art ◽  
Answer Set Programming ◽  
General Purpose ◽  
Combinatorial Problems ◽  
New Approach ◽  
Input Program ◽  
Evaluation Algorithm

AbstractAnswer Set Programming (ASP) is a well-known declarative formalism in logic programming. Efficient implementations made it possible to apply ASP in many scenarios, ranging from deductive databases applications to the solution of hard combinatorial problems. State-of-the-art ASP systems are based on the traditional ground&solve approach and are general-purpose implementations, i.e., they are essentially built once for any kind of input program. In this paper, we propose an extended architecture for ASP systems, in which parts of the input program are compiled into an ad-hoc evaluation algorithm (i.e., we obtain a specific binary for a given program), and might not be subject to the grounding step. To this end, we identify a condition that allows the compilation of a sub-program, and present the related partial compilation technique. Importantly, we have implemented the new approach on top of a well-known ASP solver and conducted an experimental analysis on publicly-available benchmarks. Results show that our compilation-based approach improves on the state of the art in various scenarios, including cases in which the input program is stratified or the grounding blow-up makes the evaluation unpractical with traditional ASP systems.

scholarly journals Probabilistic exact universal quantum circuits for transforming unitary operations

2019 ◽  
Vol 100 (6) ◽  
Author(s):  
Marco Túlio Quintino ◽  
Qingxiuxiong Dong ◽  
Atsushi Shimbo ◽  
Akihito Soeda ◽  
Mio Murao
Keyword(s):  
Quantum Circuits ◽  
Universal Quantum

scholarly journals Merlin-Arthur with efficient quantum Merlin and quantum supremacy for the second level of the Fourier hierarchy

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 106 ◽  
Author(s):  
Tomoyuki Morimae ◽  
Yuki Takeuchi ◽  
Harumichi Nishimura
Keyword(s):  
Quantum Computing ◽  
Polynomial Time ◽  
Probability Distributions ◽  
Quantum Circuits ◽  
Universal Models ◽  
Reversible Circuit ◽  
Universal Quantum ◽  
Quantum Polynomial ◽  
Output Probability ◽  
Probabilistic Polynomial Time

We introduce a simple sub-universal quantum computing model, which we call the Hadamard-classical circuit with one-qubit (HC1Q) model. It consists of a classical reversible circuit sandwiched by two layers of Hadamard gates, and therefore it is in the second level of the Fourier hierarchy. We show that output probability distributions of the HC1Q model cannot be classically efficiently sampled within a multiplicative error unless the polynomial-time hierarchy collapses to the second level. The proof technique is different from those used for previous sub-universal models, such as IQP, Boson Sampling, and DQC1, and therefore the technique itself might be useful for finding other sub-universal models that are hard to classically simulate. We also study the classical verification of quantum computing in the second level of the Fourier hierarchy. To this end, we define a promise problem, which we call the probability distribution distinguishability with maximum norm (PDD-Max). It is a promise problem to decide whether output probability distributions of two quantum circuits are far apart or close. We show that PDD-Max is BQP-complete, but if the two circuits are restricted to some types in the second level of the Fourier hierarchy, such as the HC1Q model or the IQP model, PDD-Max has a Merlin-Arthur system with quantum polynomial-time Merlin and classical probabilistic polynomial-time Arthur.

scholarly journals Quantum Natural Gradient

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 269 ◽  
Author(s):  
James Stokes ◽  
Josh Izaac ◽  
Nathan Killoran ◽  
Giuseppe Carleo
Keyword(s):  
Quantum Information ◽  
Gradient Descent ◽  
Information Geometry ◽  
General Purpose ◽  
Quantum Circuits ◽  
Descent Direction ◽  
Natural Gradient ◽  
Metric Tensor ◽  
Optimization Framework ◽  
Diagonal Approximation

A quantum generalization of Natural Gradient Descent is presented as part of a general-purpose optimization framework for variational quantum circuits. The optimization dynamics is interpreted as moving in the steepest descent direction with respect to the Quantum Information Geometry, corresponding to the real part of the Quantum Geometric Tensor (QGT), also known as the Fubini-Study metric tensor. An efficient algorithm is presented for computing a block-diagonal approximation to the Fubini-Study metric tensor for parametrized quantum circuits, which may be of independent interest.

scholarly journals Graphics card processing: accelerating profile-profile alignment

2012 ◽  
Vol 2 (4) ◽  
Author(s):  
Muhammad Hanif ◽  
Karl-Heinz Zimmermann
Keyword(s):  
Molecular Biology ◽  
General Purpose ◽  
Matrix Product ◽  
Fundamental Operation ◽  
Computational Power ◽  
Multiple Sequence ◽  
Average Speed ◽  
Order Of Magnitude ◽  
Speed Up ◽  
Profile Alignment

AbstractAlignment is the fundamental operation in molecular biology for comparing biomolecular sequences. The most widely used method for aligning groups of alignments is based on the alignment of the profiles corresponding to the groups. We show that profile-profile alignment can be significantly speeded up by general purpose computing on a modern commodity graphics card. Wavefront and matrix-matrix product approaches for implementing profile-profile alignment onto graphics processor are analyzed. The average speed-up obtained is one order of magnitude even when overheads are considered. Thus the computational power of graphics cards can be exploited to develop improved solutions for multiple sequence alignment.

scholarly journals Continuous Gravitational-Wave Data Analysis with General Purpose Computing on Graphic Processing Units

Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 218
Author(s):  
Iuri La Rosa ◽  
Pia Astone ◽  
Sabrina D’Antonio ◽  
Sergio Frasca ◽  
Paola Leaci ◽  
...  
Keyword(s):  
Data Analysis ◽  
General Purpose ◽  
Gpu Programming ◽  
Computational Power ◽  
Graphic Processing Units ◽  
New Approach ◽  
Multicore System ◽  
Speed Up ◽  
High Level ◽  
Graphic Processing

We present a new approach to searching for Continuous gravitational Waves (CWs) emitted by isolated rotating neutron stars, using the high parallel computing efficiency and computational power of modern Graphic Processing Units (GPUs). Specifically, in this paper the porting of one of the algorithms used to search for CW signals, the so-called FrequencyHough transform, on the TensorFlow framework, is described. The new code has been fully tested and its performance on GPUs has been compared to those in a CPU multicore system of the same class, showing a factor of 10 speed-up. This demonstrates that GPU programming with general purpose libraries (the those of the TensorFlow framework) of a high-level programming language can provide a significant improvement of the performance of data analysis, opening new perspectives on wide-parameter searches for CWs.

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