Manifold algorithmic errors in quantum computers with static internal imperfections

Abstract

The inevitable existence of static internal imperfections and residual interactions in some quantum computer architectures results in internal decoherence, dissipation and destructive unitary shifts of active algorithms. By exact numerical simulations, we determine the relative importance and origin of these errors for a Josephson charge-qubit quantum computer. In particular we determine that the dynamics of a CNOT gate interacting with its idle neighboring qubits via native residual coupling behaves much like a perturbed kicked top in the exponential decay regime, where fidelity decay is only weakly dependent on perturbation strength. This means that retroactive removal of gate errors (whether unitary or non-unitary) may not be possible, and that effective error correction schemes must operate concurrently with the implementation of subcomponents of the gate.

Kraus decomposition for chaotic environments including time-dependent subsystem Hamiltonians

“…The CKD captures both these effects. The large magnitude of the infidelity in both cases is due to a coherent shift of the subsystem [3,4,5]. Detailed discussions of the reasons for the different behaviors for the different coupling are given in Ref.…”

“…Hence, it is sensitive to both unitary and non-unitary errors. Since the purity is insensitive to unitary effects, large deviations between purity and fidelity can be used as an indicator of unitary errors induced by the coherent shift process [3,4,5].…”

“…In other configurations, part of a QC can be employed to measure the strength of residual two-body interactions [3], and this knowledge may prove useful for error correction. Idle qubits can also be manipulated to improve performance of the active qubits [4,5]. In fact such self-interacting quantum systems have an exceedingly complex dynamics we are only beginning to explore.…”

“…Our test model [4,5] represents a two-qubit register performing a CNOT gate while interacting with neighboring idle qubits via static internal residual interactions. Statically flawed isolated QC models offer a prototypical example of a manipulated subsystem interacting with a self-interacting, possibly chaotic, environment wherein exact quantum dynamics can be readily obtained.…”

“…A statically flawed isolated quantum computer (QC) [1,2] can exhibit a rich variety of dynamical behaviors [3,4,5], many of which are detrimental to its operation. Large unitary shifts have been observed which can destroy the fidelity over the span of a single gate [3,4,5]. Non-unitary effects such as internal decoherence and dissipation can also affect performance [4,5].…”