Measurement-Based Interference in Quantum Computation

Hans J. Briegel, Dan E. Browne, Wolfgang Dür +2 more

You-Yang Xu

The interference has been measured by the visibility in two-level systems, which, however, does not work for multi-level systems. We generalize a measure of the interference based on decoherence process, consistent with the visibility in qubit systems. By taking cluster states as examples, we show in the one-way quantum computation that the gate fidelity is proportional to the interference of the measured qubit and is inversely proportional to the interference of all register qubits. We also find that the interference increases with the number of the computing steps. So we conjecture that the interference may be the source of the speedup of the one-way quantum computation.

Gerard J Milburn, Cassius D'Helon

Santanu Pattanayak

In 1981 Richard Feynman proposed the idea that a computer built of quantum mechanical elements obeying quantum mechanical laws can perform efficient simulations of quantum systems. Quantum computing works on the laws of quantum mechanical properties such as superposition, entanglement, and interference. Unlike in classical computing, in quantum computers a register can exist in all possible states at once due to its superposition properties. It is only when a quantum system is measured that we observe one of the possible states. Such a system is advantageous since, when measured, each state can appear with a certain probability encoded in the state prior to the measurement. Quantum computing works by increasing the probability of the desired state to a sufficiently high value so that the desired state can be obtained with high confidence with a minimal number of measurements. In this regard, quantum interference, which results from quantum superposition, plays a big role since it allows probability amplitudes corresponding to a given state to interfere and cancel each other. This property of quantum interference biases the measurement to a set of states that we desire as the outcome of quantum algorithms. Similarly, quantum entanglement allows one to create a strong correlation between quantum objects, especially qubits, to the advantage of quantum algorithms, as you will see throughout this chapter.

Daniel Braun, Bertrand Georgeot

We study the importance of interference for the performance of Shor's factoring algorithm and Grover's search algorithm using a recently proposed interference measure. To this aim we introduce systematic unitary errors, random unitary errors, and decoherence processes in these algorithms. We show that unitary errors which destroy the interference destroy the efficiency of the algorithm, too. However, unitary errors may also create useless additional interference. In such a case the total amount of interference can increase, while the efficiency of the quantum computation decreases. For decoherence due to phase flip errors, interference is destroyed for small error probabilities, and converted into destructive interference for error probabilities approaching 1, leading to success probabilities which can even drop below the classical value. Our results show that in general, interference is necessary in order for a quantum algorithm to outperform classical computation, but large amounts of interference are not sufficient and can even lead to destructive interference with worse than classical success rates.

Dan E. Browne, Janet Anders