Simon Benjamin's

The hamiltonian simulation is to simulate the dynamics of the system, given some Hamiltonian. The conventional way of the Hamiltonian simulation is the Trotter decomposition. We discretize the simulated time to small time steps, like the classical Runge–Kutta method. Although if we increase the steps of the discretization, we can in principle reduce the algorithmic error, the physical error like dephasing increases linearly to the number of the Trotter steps. Therefore, there are an optimised Read more…

For quantum error correction, if the error rate of our physical components is below a certain error threshold, we can decrease the overall computational error indefinitely by scaling up the code. To obtain the value of such a threshold, we need to simulate the quantum error correction circuit, which can only be done efficiently classically if there are only Pauli errors occurring in the circuit. Twirling is a technique that ‘twirl’ out the irregularity of an arbitrary Read more…

Place an elastic ball in a box and shake it. What is the total energy of the ball? In classical physics, it can be any number which depends on how hard you shook. Shake a tiny bit harder and you’ll add a tiny bit more energy. Bound quantum systems behave differently. They have discrete energy spectra. Place a quantum particle in a box, excite it, and measure the total energy – you’ll find there are a Read more…

Simon Benjamin was recently featured on the Y Combinator blog, a seed accelerator which has seeded companies like Dropbox, Airbnb, Reddit and Twitch. In the episode, which you can view here, Simon discusses the different approaches for constructing and scaling a quantum computer.

“Imaginary time is a genuine scientific concept. One can picture it in the following way. One can think of ordinary, real, time as a horizontal line. On the left, one has the past, and on the right, the future. But there’s another kind of time in the vertical direction. This is called imaginary time, because it is not the kind of time we normally experience. But in a sense, it is just as real, as Read more…

These days, a lot of groups are trying to fabricate small sized quantum circuits with tens of qubits, and some useful algorithms to use them are proposed. To make the best of such circuits, we have to suppress the noise in the quantum circuits and we have proposed useful error suppression methods, without using conventional fault tolerant error correction techniques. For more details, please see the attached link. https://arxiv.org/abs/1712.09271