Abstract
We study the achievements of quantum circuits comprised of several one- and two-qubit gates subject to dissipation and dephasing. Quantum process matrices are determined for the basic one- and two-qubit gate operations and concatenated to yield the process matrix of the combined quantum circuit. Examples are given of process matrices obtained by a Monte Carlo wavefunction analysis of Rydberg blockade gates in neutral atoms. Our analysis is ideally suited to compare different implementations of the same process. In particular, we show that the three-qubit Toffoli gate facilitated by the simultaneous interaction between all atoms may be accomplished with higher fidelity than a concatenation of one- and two-qubit gates.
Highlights
Since the first proposals were made to use quantum effects for computing purposes there has been a strong focus on how errors and imperfections may harm and even prevent successful application of quantum computing
In Section, we introduce the Rydberg blockade gate scheme for quantum computing with neutral atoms
6 Conclusion In conclusion, we have presented an efficient method to compute the accumulation of errors in quantum circuits comprised of several few-qubit gates
Summary
Since the first proposals were made to use quantum effects for computing purposes there has been a strong focus on how errors and imperfections may harm and even prevent successful application of quantum computing. We will show that, provided dissipation and decoherence acts locally and is uncorrelated over the quantum computing register χ -matrices calculated once for one- and two-qubit gates can be concatenated, see Figure , to characterize circuits built from many of these gates. The system is propagated stochastically using the Monte Carlo wave function method, which on average reproduces results of a master equation evolution [ – ] Process characterization using this approach has a number of advantages: First, for large D, an adequate ensemble of wave functions is easier to store and evolve than density matrices. Since useful quantum gates require excellent fidelity, jumps are rare and a single deterministic ‘no-jump’ wave function suffices to provide a good estimate and rigorous bound on the process matrices describing the evolution [ ]. The assessment of how errors accumulate becomes a function of the width and depth of the quantum circuit
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