Quantum computation is a part of quantum information theory. By using quantum mechanical phenomena it is possible to speed up the solving of some problems with quantum algorithms over classical probabilistic algorithms. In some cases quantum algorithms can utilise quantum parallelism in order to speed up problem solving. In this thesis experiments on IBM quantum computers are compared with ideal error free simulations. In the first part quantum teleportation is shown in practice, similarly the performance of Deutsch–Jozsa, Bernstein–Vazirani, Simon’s and Grover’s search algorithms are shown in action on IBM quantum computers and each is compared against an ideal simulation. The last experiment shows how the binary success probability of an unsharp measurement using Lüders instrument can be improved by adding sequential measurements by using an ideal simulation and a simulation using simple noise model.
Quantum computation is a part of quantum information theory. By using quantum mechanical phenomena it is possible to speed up the solving of some problems with quantum algorithms over classical probabilistic algorithms. In some cases quantum algorithms can utilise quantum parallelism in order to speed up problem solving. In this thesis experiments on IBM quantum computers are compared with ideal error free simulations. In the first part quantum teleportation is shown in practice, similarly the performance of Deutsch–Jozsa, Bernstein–Vazirani, Simon’s and Grover’s search algorithms are shown in action on IBM quantum computers and each is compared against an ideal simulation. The last experiment shows how the binary success probability of an unsharp measurement using Lüders instrument can be improved by adding sequential measurements by using an ideal simulation and a simulation using simple noise model.
Quantum Computing is widely perceived to be one of the ways forward in the future of computation as the end of Moore’s law is almost here. Instead of using bits in classical computers, quantum computers manipulate qubits which are governed by the phenomena of superposition and entanglement. In this paper, we demonstrate the relevance of quantum computing in game theory and database search applications. Through a simple example of coin tossing, we show how it is possible to organise a game where one player adopting a quantum strategy is guaranteed to win. It is also shown that the other player, using a second coin (qubit), can subvert this action to award the wins to themselves without the first player’s knowledge. In another application, a modified Grover’s database search algorithm is applied to clone an arbitrary quantum state of a qubit to a duplicate qubit. In both cases, the comparison of simulated and actual results emphasises on the hardware limitations of the current error-prone quantum computers. The quantum computer programs are designed using quantum gates and simulated in the Quantum Information Software Kit before testing on the IBM Q 5.1 (ibmqx4) quantum computer.
In the past few years, IBM has expanded their Quantum Experience to include a high-level Python module called Qiskit as well as a 15-qubit machine (ibmq_16_melbourne). In order to evaluate IBM’s progress, we create an overview of the processes involved in developing and running an algorithm on IBM’s quantum machines. This includes exploring the new resources that IBM has made available recently including the Qiskit Python module. Then, we test textbook algorithms such as the Deutsch-Jozsa algorithm, Grover’s search algorithm, and Quantum Fourier Transform on ibmq_16_melbourne and compare the results with the output of a simulator. Constraints imposed by IBM’s Quantum Experience and significant differences between algorithm performance on IBM's quantum hardware and the simulator will be used to assess IBM’s quantum computing capabilities.
A long-standing aim of quantum information research is to understand what gives quantum computers their advantage. This requires separating problems that need genuinely quantum resources from those for which classical resources are enough. Two examples of quantum speed-up are the Deutsch–Jozsa and Simon’s problem, both efficiently solvable on a quantum Turing machine, and both believed to lack efficient classical solutions. Here we present a framework that can simulate both quantum algorithms efficiently, solving the Deutsch–Jozsa problem with probability 1 using only one oracle query, and Simon’s problem using linearly many oracle queries, just as expected of an ideal quantum computer. The presented simulation framework is in turn efficiently simulatable in a classical probabilistic Turing machine. This shows that the Deutsch–Jozsa and Simon’s problem do not require any genuinely quantum resources, and that the quantum algorithms show no speed-up when compared with their corresponding classical simulation. Finally, this gives insight into what properties are needed in the two algorithms and calls for further study of oracle separation between quantum and classical computation.
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.
A long-standing aim of quantum information research is to understand what gives quantum computers their advantage. This requires separating problems that need genuinely quantum resources from those for which classical resources are enough. Two examples of quantum speed-up are the Deutsch-Jozsa and Simon's problem, both efficiently solvable on a quantum Turing machine, and both believed to lack efficient classical solutions. Here we present a framework that can simulate both quantum algorithms efficiently, solving the Deutsch-Jozsa problem with probability 1 using only one oracle query, and Simon's problem using linearly many oracle queries, just as expected of an ideal quantum computer. The presented simulation framework is in turn efficiently simulatable in a classical probabilistic Turing machine. This shows that the Deutsch-Jozsa and Simon's problem do not require any genuinely quantum resources, and that the quantum algorithms show no speed-up when compared with their corresponding classical simulation. Finally, this gives insight into what properties are needed in the two algorithms, and calls for further study of oracle separation between quantum and classical computation.
We analyze the basic aspects of the quantum information theory, namely the quantum version
of the theory that is behind all the classical implementations like computers and communications.
We focus on quantum computation, defining its fundamental unit: the qubit,
namely a quantum two-level system that will be described in detail in this thesis. We then
concentrate on the possible transformations gates that can be applied to qubits, both unitary
and non-unitary ones.
The challenges in the construction of qubits are impressive: in particular, it is difficult to
isolate the system from the environment. This interaction is modeled by non-unitary transformations.
The characteristic times connected to these processes are the relaxation time, the
time in which a state decays in another state, and the decoherence time, the time in which
quantum coherence is lost. These times are fundamental in quantum computing since they
quantify how many operations can be performed on qubits and still obtain reliable results.
We measure these characteristic times on the IBM quantum processor ’ibmq_16_melbourne’
performing three different experiments: one for the relaxation time and two for the decoherence
time, namely Ramsey and Echo experiments.
Finally, we implement a quantum algorithm, an algorithm that uses the resources of quantum
mechanics, like entanglement. We focus on finding a protocol to define the quantum
version of the elementary cellular automata, the quantum elementary cellular automata, and
run it on the IBM processor. They are dynamical systems defined on a lattice in which the
evolution is defined using simple local update rules.
Comparing the physical results with theoretical expectations and noise-affected simulations
we show the performance of the IBM processor.