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Synthesis lectures on computer architecture

Simulation of Quantum Computation

Tzvetan S. Metodi, Arvin I. Faruque, Frederic T. Chong

Published Jan 1, 2011• 1 citation
Publisher
DOI
10.1007/978-3-031-01731-5_5

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Quantum computing is based on the exploitation of quantum effects to perform some important computations more efficiently than ever possible on classical computers. Well known quantum algorithms are Shors polynomial time factoring algorithm and Grovers data base search scheme. Their potential is due to the parallelism of a quantum computation increasing exponentially with the size of the computing device. IBM has succeeded in building a first working quantum computing device with up to 7 qubits based on NMR technology, however, the construction of large multi-qubit systems appears to become extremely difficult due to the loss of coherence of the quantum states. Like the design process of modern microprocessors which is carried out by means of sophisticated software, modelling and simulation of the entire QC device is even more relevant. Simulation is required in order to understand the functioning of quantum algorithms, to construct novel quantum algorithms, to write quantum programs, to teach quantum computing, to construct real quantum computers, to understand and fight de-coherence and to understand and control the influence of the environment. Since quantum parallelism increases exponentially with the size of the quantum computer, parallel supercomputers are required for realistic simulations. I intend to give an introduction into the simulation of quantum computers using conventional computers. The simulation is based on a generic physical model of quantum computer hardware. Issues like parallel gate level simulators, modelling of QCs, simulators for physical quantum computers are addressed.
Noisy Quantum Computing (QC) simulation on a classical machine is very time consuming since it requires Monte Carlo simulation with a large number of error-injection trials to model the effect of random noises. Orthogonal to existing QC simulation optimizations, we aim to accelerate the simulation by eliminating the redundant computation among those Monte Carlo simulation trials. We observe that the intermediate states of many trials can often be the same. Once these states are computed in one trial, they can be temporarily stored and reused in other trials. However, storing such states will consume significant memory space. To leverage the shared intermediate states without introducing too much storage overhead, we propose to statically generate and analyze the Monte Carlo simulation simulation trials before the actual simulation. Those trials are reordered to maximize the overlapped computation between two consecutive trials. The states that cannot be reused in follow-up simulation are dropped, so that we only need to store a few states. Experiment results show that the proposed optimization scheme can save on average 80% computation with only a small number of state vectors stored. In addition, the proposed simulation scheme demonstrates great scalability as more computation can be saved with more simulation trials or on future QC devices with reduced error rates.
Quantum Computing (QC) research has gained a lot of momentum recently due to several theoretical analyses that indicate that QC is significantly more efficient at solving certain classes of problems than classical computing. While experimental validation will ultimately be required, the primitive nature of current QC hardware leaves practical testing limited to trivial examples. Thus, a robust simulator is needed to study complex QC issues. Most QC simulators model ideal operations, and thus cannot predict the actual time required to execute an algorithm or quantify the effects of errors in the calculation. We have developed a novel QC simulator that models physical hardware implementations. This simulator not only allows the accurate simulation of quantum algorithms on various hardware implementations, but also takes an important step towards providing a framework to determine their true performance and vulnerability to errors.