In my previous post on superconducting qubits, we have seen how a flux qubit represents a qubits state as a superposition of currents in a superconducting loop. Even though flux qubits have been implemented and used successfully, most research groups today focus on different types of qubits using a charge qubit as an archetype. Charge … Continue reading Superconducting qubits – on islands, charge qubits and the transmon

# Category: Mathematics

# Superconducting qubits – the flux qubit

In the last post, we have discussed the basic idea of superconducting qubits - implement circuits in which a supercurrent flows that can be described by a quantum mechanical wave function, and use two energy levels of the resulting quantum system as a qubit. Today, we will look in some more detail into one possible … Continue reading Superconducting qubits – the flux qubit

# NMR based quantum computing: gates and state preparation

In my last post on NMR based quantum computing, we have seen how an individual qubit can be implemented based on NMR technology. However, just having a single qubit is of course not really helpful - what we are still missing is the ability to initialize several qubits and to realize interacting quantum gates. These … Continue reading NMR based quantum computing: gates and state preparation

# Single qubit NMR based quantum computation

In the previous post, we have sketched the basic ideas behind NMR based quantum computation. In this post, we will discuss single qubits and single qubit operations in more depth. The rotating frame of reference In NMR based quantum computing, quantum gates are realized by applying oscillating magnetic fields to our probe. As an oscillating … Continue reading Single qubit NMR based quantum computation

# Quantum error correction: the surface code

In my previous post on quantum error correction, we have looked at the toric code which is designed for a rather theoretical case - a grid of qubits on a torus. In reality, qubits are more likely to be arranged in a planar geometry. Luckily, a version of the toric codes that works well in … Continue reading Quantum error correction: the surface code

# Quantum phase estimation – the quantum algorithm Swiss army knife

When you are faced with a problem in linear algebra and have absolutely no idea what to do, an eigenvalue decomposition is the one thing that you would typically try first. In the world of quantum algorithms, the situation is similar - finding the eigenvalues of a matrix is a central building block of many … Continue reading Quantum phase estimation – the quantum algorithm Swiss army knife

# Quantum error correction with stabilizer codes

In our previous discussion of quantum error correction, we have assumed that quantum gates can act on any two physical qubits. In reality, however, this is not true - only nearby qubits and interact, and our error correction needs to take the geometric arrangements of the qubits into account. The link between these geometric constraints … Continue reading Quantum error correction with stabilizer codes