Quantum computing simulation through reduction and decomposition optimizations with a case study of Shor's algorithm (original) (raw)
Related papers
2017
Due to the expansion of transformations and read/write memory states by tensor products in multidimensional quantum applications, the exponential increase in temporal and spatial complexities constitutes one of the main challenges for quantum computing simulations. Simulation of these systems is important in order to develop and test new quantum algorithms. This work presents reduction and decomposition optimizations for the Distributed Geometric Machine environment. By exploring properties as the sparsity of the Identity operator and partiality of dense unitary transformations, better storage and distribution of quantum information are achieved. The main improvements are implemented by decreasing replication and void elements inherited from quantum operators. In the evaluation of this proposal, Shor's algorithm considering 2n+3 qubits in the order-finding quantum algorithm was simulated up to 25 qubits over CPU, sequentially and in parallel, and over GPU. Results confirm that temporal complexity is reduced. When comparing our implementations running on the same hardware with LIQUi| , academic release version, our new simulator was faster and allowed for the simulation of more qubits.
The exponential increase in the temporal and spatial complexities is one of the main challenges in the widespread use of quantum algorithm simulation, especially in dense quantum transformations (QTs) such as the Hadamard transformation (H), which has found wide applications in computer and communication science and also comprising the simplest quantum universal set of QTs. The main reason for these costs is the expansion of QTs by using tensor product in multi-dimension quantum applications. In this work, new optimizations for the execution of reduction and decomposition based on the Identity operator are introduced in the Distributed Geometric Machine framework (D-GM). Instead of executing the quantum transformation in a single step, they are divided in sub-quantum transformations and only the values different from Identity transformations are stored. Mixed Partial Processes provide control over the increase in the size of read/write memory states in the calculation of a QT, thus contributing to increase the scalability of applications regarding hardware-GPUs memory limit. In the evaluation of this D-GM extension, Hadamard Transformations were simulated up to 28 qubits applications over a single GPU. Our new simulator is 10, 829x faster and allows for the simulation of more qubits when compared to our previous implementation running on the same GPU.
State-of-the-art quantum computing simulators: Features, optimizations, and improvements for D-GM
Neurocomputing, 2019
Quantum computing is strongly limited by physical implementations of quantum computers. Currently, development of quantum computing algorithms is carried out by analytic or simulation procedures while quantum computers are not widely available. Although quantum computing simulation is parallel by nature, spatial and temporal complexity are major performance hazards. The exponential increase in memory and global access to quantum states in simulations limit not only the number of qubits but also quantum transformations. Considering these scenarios, six quantum simulators are studied, in order to find out their main features and simulation results considering implementations classified in single/multiple processor and accelerator architectures. The main strategies used to improve performance in these architectures provide relevant parameters for the development of the new extension of the Distributed Geometric Machine environment proposed in this paper. Shor's and Grover's algorithms are simulated and compared to previous D-GM results and to LIQUi| 's simulator, showing improvements as relative speedups up to 22.2× in relation to the previous version and up to 910.46× when compared to LIQUi| .
Optimizing Quantum Simulation for Heterogeneous Computing: a Hadamard Transformation Study
The D-GM execution environment improves distributed simulation of quantum algorithms in heterogeneous computing environments comprising both multi-core CPUs and GPUs. The main contribution of this work consists in the optimization of the environment VirD- GM, conceived in three steps: (i) the theoretical studies and implementation of the abstractions of the Mixed Partial Process defined in the qGM model, focusing on the reduction of the memory consumption regarding multidimensional QTs; (ii) the distributed/parallel implementation of such abstractions allowing its execution on clusters of GPUs; (iii) and optimizations that predict multiplications by zero-value of the quantum states/transformations, implying reduction in the number of computations. The results obtained in this work embrace the distribute/parallel simulation of Hadamard gates up to 21 qubits, showing scalability with the increase in the number of computing nodes.
General-purpose parallel simulator for quantum computing
Physical Review A, 2002
With current technologies, it seems to be very difficult to implement quantum computers with many qubits. It is therefore of importance to simulate quantum algorithms and circuits on the existing computers. However, for a large-size problem, the simulation often requires more computational power than is available from sequential processing. Therefore, the simulation methods using parallel processing are required.
Improving Emulation of Quantum Algorithms using Space-Efficient Hardware Architectures
2019 IEEE 30th International Conference on Application-specific Systems, Architectures and Processors (ASAP), 2019
With rapid advancement in quantum computing technology, continuous efforts are being directed to simulation and emulation of quantum algorithms on classical platforms. A well-known limitation to classical emulation of quantum circuits is scalability. Existing hardware emulators implement gate-based circuit models of quantum circuits that result in heavy resource utilization and degrade the scalability of the system. Also, current quantum emulation hardware use fixedpoint arithmetic, which has an adverse effect on accuracy when the system is scaled up. In this work, we employ a complexmultiply-and-accumulate (CMAC) and lookup-based emulation approach that greatly reduces resource utilization and improves system scalability in terms of number of emulated qubits. We demonstrate emulation of up to 16 fully-entangled qubits which is highest among existing work. We design fully-pipelined, highthroughput hardware architectures that use floating-point precision for higher accuracy. Experime...
Towards a Novel Environment for Simulation of Quantum Computing
Computer Science, 2015
In this paper, we analyze existing quantum computer simulation techniques and their realizations to minimize the impact of the exponential complexity of simulated quantum computations. As a result of this investigation, we propose a quantum computer simulator with an integrated development environment-QuIDE-supporting the development of algorithms for future quantum computers. The simulator simplifies building and testing quantum circuits and understanding quantum algorithms in an efficient way. The development environment provides flexibility of source code edition and ease of the graphical building of circuit diagrams. We also describe and analyze the complexity of algorithms used for simulation as well as present performance results of the simulator as well as results of its deployment during university classes.
The Fraunhofer quantum computing simulator
Frontiers in Artificial Intelligence and Applications
Fraunhofer FIRST develops a computing service and collaborative workspace providing a convenient tool for simulation and investigation of quantum algorithms. To broaden the twenty qubit limit of workstation-based simulations to the next qubit decade we provide a dedicated high memorized Linux cluster with fast Myrinet interconnection network together with a adapted parallel simulator engine. This simulation service supplemented by a collaborative workspace is usable everywhere via web interface and integrates both hardware and software as collaboration and investigation platform for the quantum community. The modular design of our simulator engine enables the application of various implementations and simulation techniques and is open for extensions motivated by the experience of the users. The beta test version realizes all common one, two and three qubit gates, arbitrary one and two bit gates, orthogonal measurements as well as special gates like Oracle, Modulo function and Quantum Fourier Transformation. The main focus of our project is the simulation of experimentally realizations of quantum algorithms which will make it feasible to understand the differences between real and ideal quantum devices and open the view for new algorithms and applications. That's why the simulator also can work with arbitrary Hamiltonians yielding its unitary transformation, spectrum and eigenvectors. To realize the various simulation tasks we integrate various implementations. The test version is able to simulate small quantum circuits and Hamiltonians exactly, the latter through the use of a standard diagonalization procedure. Circuits up to thirty qubits can be simulated exactly as well; Hamiltonians of that size, however, have to be approximated according to the Trotter formulae. For a restricted gate set we also develop a tensor-sum implementation, which makes it feasible to investigate circuits with up to sixty qubits.
Classical simulation of quantum algorithms using the tensor product representation
Using the tensor product representation in the density matrix renormalization group, we show that a quantum circuit of Grover's algorithm, which has one-qubit unitary gates, generalized Toffoli gates, and projective measurements, can be efficiently simulated by a classical computer. It is possible to simulate quantum circuits with several ten qubits.
Simulation of Quantum Gates on a Novel GPU Architecture
2007
Quantum computers aim to achieve a huge reduction of the time required for solving problems with an exponential complexity, but their simulation in conventional computers results itself on a problem with a similar complexity. As this limits considerably the dimensions of the quantum computer we can simulate, multiprocessor architectures are an almost obliged tool when tackling with such simulations. In