Compiling gate networks on an Ising quantum computer

Here we describe a simple mechanical procedure for compiling a quantum gate network into the natural gates (pulses and delays) for an Ising quantum computer. The aim is not necessarily to generate the most efficient pulse sequence, but rather to develop an efficient compilation algorithm that can be easily implemented in large spin systems. The key observation is that it is not always necessary to refocus all the undesired couplings in a spin system. Instead, the coupling evolution can simply be tracked and then corrected at some later time. Although described within the language of NMR, the algorithm is applicable to any design of quantum computer based on Ising couplings.

Figure 1

An example of rescaling couplings between four qubits. The solid blocks indicate NOT gates (180° pulses).

Figure 2

An example quantum circuit, based on the algorithmic benchmark of Knill et al. [14]. White squares indicate ${90}_y^{°}$ pulses (pseudo-Hadamard gates), while black circles connected by control lines are Ising coupling gates with a target angle of 90° between the coupled qubits.

Figure 3

An example Ising quantum computer, described by indicating the strengths of the Ising couplings (measured in hertz) between all pairs of qubits; these couplings were chosen arbitrarily.

Figure 4

Sequence of refocusing pulses used to implement the circuit shown in Fig. 2 on the Ising quantum computer shown in Fig. 3. White squares indicate ${90}_y^{°}$ pulses as before, while white rectangles indicate NOT gates. These single-qubit gates are assumed to be instantaneous. The evolution periods are drawn approximately to scale, and the lengths of some periods (measured in microseconds) are indicated.