Enhancing the fidelity of two-qubit gates by measurements

Abstract

Dynamical decoupling techniques are the method of choice for increasing gate fidelities. While these methods have produced very impressive results in terms of decreasing local noise and increasing the fidelities of single qubit operations, dealing with the noise of two qubit gates has proven more challenging. The main obstacle is that the noise time scale is shorter than the two qubit gate itself so that refocusing methods do not work. We present a measurement and feedback based method to refocus two qubit gates which cannot be refocused by conventional methods. We analyze in detail this method for an error model which is relevant for trapped ions quantum information. Introduction -Shor's discovery of an algorithm[1] to break the RSA cryptosystem demonstrated that a quantum computer constitutes a promising system for tackling hard computational problems. However, it still remained unclear whether even conceptually a quantum computer can be constructed. One compelling reason is that even a minute error in each computational step would rapidly accumulate to a large error. Remarkably, the theory of quantum fault tolerance [2][3][4][5] showed that this intuition was wrong. Actually, in order for a quantum computer to output a correct result with and arbitrarily small probability of failure, each gate operation must only fail with a small probability below a certain threshold. Thus, the precise value of the error threshold is extremely important to the field of quantum computation. This has initiated an enormous effort to reduce gate infidelities below the fault tolerance threshold. Very good results have been achieved in various platforms, in particular in trapped ions, NV centers in diamond and superconducting devices.

Effects of gate errors in digital quantum simulations of fermionic systems

“…In this case, order 2  dj ( ) terms and products between dj and g n t can be neglected inside a Trotter step, consistent with the Trotter approximation. The optional assumption(iii) is motivated by the observation that single-qubit gates usually have a significantly better fidelity than two-qubit gates [19,[38][39][40][41]. In addition, there are examples, e.g., the Hubbard model with equal on-site energies, which can be simulated using only two-qubit gates.…”

“…The optional assumption (iii) is motivated by the observation that single-qubit gates usually have a significantly better fidelity than two-qubit gates, which are more difficult to optimize [19,[36][37][38][39]. Furthermore, we note that, e.g., the Hubbard model with equal on-site energies can be simulated using only two-qubit gates.…”