Dynamically corrected gates for qubits with always-on Ising couplings: Error model and fault tolerance with the toric code

Abstract

We describe how a universal set of dynamically-corrected quantum gates can be implemented using sequences of shaped decoupling pulses on any qubit network forming a sparse bipartite graph with always-on Ising interactions. These interactions are constantly decoupled except when they are needed for two-qubit gates. We analytically study the error operators associated with the constructed gates up to third order in the Magnus expansion, analyze these errors numerically in the unitary time evolution of small qubit clusters, and give a bound on high-order errors for qubits on a large square lattice. We prove that with a large enough toric code the present gate set can be used to implement fault-tolerant quantum memory.

High-fidelity quantum gates in Si/SiGe double quantum dots

“…5 (c) and (d)), problematic for longer quantum algorithms. Mitigation of these effects is still possible through advanced pulse shaping or composite pulse sequences [32], complex dynamical decoupling sequences [33], and reduction of the amplitude of the fluctuations, i.e., operating at a charge noise sweet spot. Also, a partial recovery of the fidelity is still achieved as the conditional spin flip during the frequency selective CNOT gate serves as a simple spin-echo sequence, decoupling the left spin and low-frequency charge noise if |Ψ R = |↑ .…”

Universal set of dynamically protected gates for bipartite qubit networks: Soft pulse implementation of the [[5,1,3]] quantum error-correcting code

“…[50] Each of these operators can be computed order-by-order in the time-dependent perturbation theory; in Ref. 50 we carried such an expansion up to third order. In each order of the series, the dependence on the pulse shape is encoded in terms of just a few coefficients [45][46][47]50].…”

“…Recently we made a substantial progress toward developing a combined DD/QEC coherence protection protocol by constructing a universal set of quantum gates based on soft-pulse DD sequences. [49,50] The gates are designed to work on a network of qubits with alwayson Ising couplings forming a sparse bipartite graph. In addition to providing accurate control, these gates also work as decoupling sequences, suppressing the effect of low-frequency phase noise to second order in the Magnus series.…”

“…We have also studied [50] the errors associated with the gates similar to those constructed in Ref. 49.…”

Concurrently optimized cooperative pulses in robust quantum control: application to broadband Ramsey-type pulse sequence elements

“…in NMR, ESR or optical spectroscopy with a large range of offset frequencies or highly inhomogeneous line widths, the performance of simple rectangular pulses is not satisfactory and improved performance can be achieved by using shaped or composite pulses [9,[11][12][13].Depending on the application, experimental limitations and imperfections that need to be taken into account include (a) limited pulse amplitude due to amplifier constraints, (b) limited pulse energy in order to reduce heating effects, which are of particular concern in medical applications [3], (c) scaling of the pulse amplitudes due to errors in pulse calibration or due to the spatial inhomogeneity of the control field [9, 14, 15], (d) amplitude and phase transients [16][17][18] and (e) noise on the control amplitude [19,20]. Many different approaches have been used to optimize robust pulses [9,[11][12][13][21][22][23][24][25][26][27][28][29][30]. In addition to pulse imperfections, noisy fluctuations of classical or quantum nature in the environment leads to relaxation losses.…”