scholarly journals May a Dissipative Environment Be Beneficial for Quantum Annealing?

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 26
Author(s):  
Gianluca Passarelli ◽  
Giulio Filippis ◽  
Vittorio Cataudella ◽  
Procolo Lucignano
Keyword(s):  
Low Temperature ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Spin Model ◽  
Quantum Master Equation ◽  
Quantum Annealing ◽  
Classical Counterpart ◽  
Speed Up ◽  
Fully Connected ◽  
Dissipative Environment

We discuss the quantum annealing of the fully-connected ferromagnetic p-spin model in a dissipative environment at low temperature. This model, in the large p limit, encodes in its ground state the solution to the Grover’s problem of searching in unsorted databases. In the framework of the quantum circuit model, a quantum algorithm is known for this task, providing a quadratic speed-up with respect to its best classical counterpart. This improvement is not recovered in adiabatic quantum computation for an isolated quantum processor. We analyze the same problem in the presence of a low-temperature reservoir, using a Markovian quantum master equation in Lindblad form, and we show that a thermal enhancement is achieved in the presence of a zero temperature environment moderately coupled to the quantum annealer.

scholarly journals Qulacs: a fast and versatile quantum circuit simulator for research purpose

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 559
Author(s):  
Yasunari Suzuki ◽  
Yoshiaki Kawase ◽  
Yuya Masumura ◽  
Yuria Hiraga ◽  
Masahiro Nakadai ◽  
...  
Keyword(s):  
Fault Tolerant ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Research Purpose ◽  
Numerical Techniques ◽  
Circuit Simulator ◽  
Speed Up ◽  
Near Term

To explore the possibilities of a near-term intermediate-scale quantum algorithm and long-term fault-tolerant quantum computing, a fast and versatile quantum circuit simulator is needed. Here, we introduce Qulacs, a fast simulator for quantum circuits intended for research purpose. We show the main concepts of Qulacs, explain how to use its features via examples, describe numerical techniques to speed-up simulation, and demonstrate its performance with numerical benchmarks.

scholarly journals Dissipative environment may improve the quantum annealing performances of the ferromagnetic p -spin model

2018 ◽  
Vol 97 (2) ◽  
Author(s):  
G. Passarelli ◽  
G. De Filippis ◽  
V. Cataudella ◽  
P. Lucignano
Keyword(s):  
Spin Model ◽  
Quantum Annealing ◽  
Dissipative Environment

scholarly journals Quantum-enhanced analysis of discrete stochastic processes

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Carsten Blank ◽  
Daniel K. Park ◽  
Francesco Petruccione
Keyword(s):  
Monte Carlo ◽  
Stochastic Processes ◽  
Importance Sampling ◽  
Wide Spectrum ◽  
Quantum Algorithm ◽  
Random Variable ◽  
Estimation Algorithm ◽  
Quantum Circuit ◽  
Monte Carlo Sampling ◽  
Speed Up

AbstractDiscrete stochastic processes (DSP) are instrumental for modeling the dynamics of probabilistic systems and have a wide spectrum of applications in science and engineering. DSPs are usually analyzed via Monte-Carlo methods since the number of realizations increases exponentially with the number of time steps, and importance sampling is often required to reduce the variance. We propose a quantum algorithm for calculating the characteristic function of a DSP, which completely defines its probability distribution, using the number of quantum circuit elements that grows only linearly with the number of time steps. The quantum algorithm reduces the Monte-Carlo sampling to a Bernoulli trial while taking all stochastic trajectories into account. This approach guarantees the optimal variance without the need for importance sampling. The algorithm can be further furnished with the quantum amplitude estimation algorithm to provide quadratic speed-up in sampling. The Fourier approximation can be used to estimate an expectation value of any integrable function of the random variable. Applications in finance and correlated random walks are presented. Proof-of-principle experiments are performed using the IBM quantum cloud platform.

scholarly journals Practical Quantum Computing

2021 ◽  
Vol 2 (1) ◽  
pp. 1-35
Author(s):  
Adrien Suau ◽  
Gabriel Staffelbach ◽  
Henri Calandra
Keyword(s):  
Wave Equation ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Equation Solving ◽  
Small Quantum ◽  
Quantum Wave ◽  
Variational Algorithms ◽  
The One

In the last few years, several quantum algorithms that try to address the problem of partial differential equation solving have been devised: on the one hand, “direct” quantum algorithms that aim at encoding the solution of the PDE by executing one large quantum circuit; on the other hand, variational algorithms that approximate the solution of the PDE by executing several small quantum circuits and making profit of classical optimisers. In this work, we propose an experimental study of the costs (in terms of gate number and execution time on a idealised hardware created from realistic gate data) associated with one of the “direct” quantum algorithm: the wave equation solver devised in [32]. We show that our implementation of the quantum wave equation solver agrees with the theoretical big-O complexity of the algorithm. We also explain in great detail the implementation steps and discuss some possibilities of improvements. Finally, our implementation proves experimentally that some PDE can be solved on a quantum computer, even if the direct quantum algorithm chosen will require error-corrected quantum chips, which are not believed to be available in the short-term.

scholarly journals Deep neural networks for quantum circuit mapping

2021 ◽  
Author(s):  
Giovanni Acampora ◽  
Roberto Schiattarella
Keyword(s):  
Neural Networks ◽  
Deep Neural Networks ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Machine Learning Techniques ◽  
Quantum Computers ◽  
Physical Constraints ◽  
Proper Mapping ◽  
Correct Execution

AbstractQuantum computers have become reality thanks to the effort of some majors in developing innovative technologies that enable the usage of quantum effects in computation, so as to pave the way towards the design of efficient quantum algorithms to use in different applications domains, from finance and chemistry to artificial and computational intelligence. However, there are still some technological limitations that do not allow a correct design of quantum algorithms, compromising the achievement of the so-called quantum advantage. Specifically, a major limitation in the design of a quantum algorithm is related to its proper mapping to a specific quantum processor so that the underlying physical constraints are satisfied. This hard problem, known as circuit mapping, is a critical task to face in quantum world, and it needs to be efficiently addressed to allow quantum computers to work correctly and productively. In order to bridge above gap, this paper introduces a very first circuit mapping approach based on deep neural networks, which opens a completely new scenario in which the correct execution of quantum algorithms is supported by classical machine learning techniques. As shown in experimental section, the proposed approach speeds up current state-of-the-art mapping algorithms when used on 5-qubits IBM Q processors, maintaining suitable mapping accuracy.

scholarly journals A strategy to speed up formation and strengthen activity of biofilms at low temperature

RSC Advances ◽  
2017 ◽  
Vol 7 (37) ◽  
pp. 22788-22796 ◽  
Author(s):  
Huizhi Hu ◽  
Junguo He ◽  
Huarong Yu ◽  
Jian Liu ◽  
Jie Zhang
Keyword(s):  
Low Temperature ◽  
Biofilm Reactors ◽  
Start Up ◽  
Long Time ◽  
Speed Up

The start-up period of biofilm reactors often takes a long time to obtain a mature and stable biofilm, especially at low temperature.

An FPGA-based quantum circuit emulation framework using heisenberg representation

2018 ◽  
Vol 16 (06) ◽  
pp. 1850052
Author(s):  
Y. H. Lee ◽  
M. Khalil-Hani ◽  
M. N. Marsono
Keyword(s):  
Large Scale ◽  
Scale Up ◽  
Quantum Circuit ◽  
Theoretical Research ◽  
Resource Requirement ◽  
Heisenberg Representation ◽  
Speed Up ◽  
Computing Platforms ◽  
Classical Computing

While physical realization of practical large-scale quantum computers is still ongoing, theoretical research of quantum computing applications is facilitated on classical computing platforms through simulation and emulation methods. Nevertheless, the exponential increase in resource requirement with the increase in the number of qubits is an inherent issue in classical modeling of quantum systems. In the effort to alleviate the critical scalability issue in existing FPGA emulation works, a novel FPGA-based quantum circuit emulation framework based on Heisenberg representation is proposed in this paper. Unlike previous works that are restricted to the emulations of quantum circuits of small qubit sizes, the proposed FPGA emulation framework can scale-up to 120-qubit on Altera Stratix IV FPGA for the stabilizer circuit case study while providing notable speed-up over the equivalent simulation model.

scholarly journals Hyper-optimized tensor network contraction

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 410
Author(s):  
Johnnie Gray ◽  
Stefanos Kourtis
Keyword(s):  
Computation Time ◽  
Quantum Circuit ◽  
Optimization Approach ◽  
Many Body ◽  
Tensor Networks ◽  
Randomized Protocols ◽  
Classical Simulation ◽  
Tensor Network ◽  
Speed Up ◽  
Many Body Systems

Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to tensor networks with irregular geometries. Finding the best possible contraction path for such networks is a central problem, with an exponential effect on computation time and memory footprint. In this work, we implement new randomized protocols that find very high quality contraction paths for arbitrary and large tensor networks. We test our methods on a variety of benchmarks, including the random quantum circuit instances recently implemented on Google quantum chips. We find that the paths obtained can be very close to optimal, and often many orders or magnitude better than the most established approaches. As different underlying geometries suit different methods, we also introduce a hyper-optimization approach, where both the method applied and its algorithmic parameters are tuned during the path finding. The increase in quality of contraction schemes found has significant practical implications for the simulation of quantum many-body systems and particularly for the benchmarking of new quantum chips. Concretely, we estimate a speed-up of over 10,000× compared to the original expectation for the classical simulation of the Sycamore `supremacy' circuits.

Quantum algorithm for MUSIC-based DOA estimation in hybrid MIMO systems

2021 ◽  
Author(s):  
Fan-Xu Meng ◽  
Ze-Tong Li ◽  
Xutao Yu ◽  
Zaichen Zhang
Keyword(s):  
Mimo Systems ◽  
Multiple Input Multiple Output ◽  
Quantum Algorithm ◽  
Doa Estimation ◽  
Quantum Circuit ◽  
Music Algorithm ◽  
Quantum Method ◽  
Sample Covariance ◽  
Input Multiple Output ◽  
Eigen Decomposition

Abstract The multiple signal classification (MUSIC) algorithm is a well-established method to evaluate the direction of arrival (DOA) of signals. However, the construction and eigen-decomposition of the sample covariance matrix (SCM) are computationally costly for MUSIC in hybrid multiple input multiple output (MIMO) systems, which limits the application and advancement of the algorithm. In this paper, we present a novel quantum method for MUSIC in hybrid MIMO systems. Our scheme makes the following three contributions. First, the quantum subroutine for constructing the approximate SCM is designed, along with the quantum circuit for the steering vector and a proposal for quantum singular vector transformation. Second, the variational density matrix eigensolver is proposed to determine the signal and noise subspaces utilizing the destructive swap test. As a proof of principle, we conduct two numerical experiments using a quantum simulator. Finally, the quantum labelling procedure is explored to determine the DOA. The proposed quantum method can potentially achieve exponential speedup on certain parameters and polynomial speedup on others under specific moderate circumstances, compared with their classical counterparts.

Quantum CFD Simulations for Heat Transfer Applications

2020 ◽  
Author(s):  
Chao Lu ◽  
Zhao Hu ◽  
Bei Xie ◽  
Ning Zhang
Keyword(s):  
Heat Transfer ◽  
Quantum Computing ◽  
Linear System ◽  
Linear Equation ◽  
Linear Systems ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Quantum Phase ◽  
Cfd Simulations ◽  
Analytical Result

Abstract In this paper, computational heat transfer (CHT) equations were solved using the state-of-art quantum computing (QC) technology. The CHT equations can be discretized into a linear equation set, which can be possibly solved by a QC system. The linear system can be characterized by Ax = b. The A matrix in this linear system is a Hermitian matrix. The linear system is then solved by using the HHL algorithm, which is a quantum algorithm to solve a linear system. The quantum circuit requires an Ancilla qubit, clock qubits, qubits for b and a classical bit to record the result. The process of the HHL algorithm can be described as follows. Firstly, the qubit for b is initialized into the phase as desire. Secondly, the quantum phase estimation (QPE) is used to determine the eigenvalues of A and the eigenvalues are stored in clock qubits. Thirdly, a Rotation gate is used to rotate the inversion of eigenvalues and information is passed to the Ancilla bit to do Pauli Y-rotation operation. Fourthly, revert the whole processes to untangle qubits and measure all of the qubits to output the final results for x. From the existing literature, a few 2 × 2 matrices were successfully solved with QC technology, proving the possibility of QC on linear systems [1]. In this paper, a quantum circuit is designed to solve a CHT problem. A simple 2 by 2 linear equation is modeled for the CHT problem and is solved by using the quantum computing. The result is compared with the analytical result. This result could initiate future studies on determining the quantum phase parameters for more complicated QC linear systems for CHT applications.

Sign in / Sign up

Export Citation Format

Share Document