The Autobiography of James Monroe

Use of global interactions in efficient quantum circuit constructions

“…In fact, it has been calculated numerically that the power p 1.4 opt = renders the maximum quality for the set of parameters considered in [34]. Fortunately, p = 1.4 is within the limits p 0, 3 Î [ ] [11,31]. Motivated by the previous discussion, we next suggest an extended method of the power law approximation of the exponential drop off that is useful for quantum Fourier arithmetic circuits.…”

“…The signs of ij c may furthermore be determined by the experiment such as the case in [1], disallowing their uniform assignment. It is, however, expected [11] that future trapped ions experiments will feature a fully controllable sign of the interaction, and this will not be an issue. Should the signs be uncontrollable, this provides an additional challenge, since the constructions in figures 1 and 2 rely on the ability to apply GMS gates with the inverted sign of the rotation angle.…”

“…Unfortunately, the exponential drop off in the strength of the interaction appears to be unnatural. Instead, the decrease in the strength of the interaction as a power of the distance d as d p , where p 0, 3 Î [ ] [11,31] seems more realistic. This leads to the question of how well the desired exponential drop off can be approximated with such physical-level global gates.…”

“…These may come in different flavors, including the addressable R , q f ( )rotations [1] of which at most two are needed to implement arbitrary single-qubit gate [10], or the addressable RZ rotation, which together with global RX and RY rotations also gives the single-qubit universality [7,8]. Depending on the specifics, the control apparatus may allow the application of an XX gate to a selectable pair of qubits [1], globally [4][5][6][7][8], or globally to a subset of qubits [11,12]. We furthermore note that the existing control apparatus described in reference [1] allows the application of the global Molmer-Sorensen (GMS) gates [11], however, to date, this approach has not been studied in detail.…”

“…Depending on the specifics, the control apparatus may allow the application of an XX gate to a selectable pair of qubits [1], globally [4][5][6][7][8], or globally to a subset of qubits [11,12]. We furthermore note that the existing control apparatus described in reference [1] allows the application of the global Molmer-Sorensen (GMS) gates [11], however, to date, this approach has not been studied in detail. In each case above, XX gate comes at a higher cost (expressed in terms of the duration and/or average fidelity) compared to the single-qubit gates.…”