Kraus decomposition for chaotic environments including time-dependent subsystem Hamiltonians

Abstract

We derive an exact and explicit Kraus decomposition for the reduced density of a quantum system simultaneously interacting with time-dependent external fields and a chaotic environment of thermodynamic dimension. We test the accuracy of the Kraus decomposition against exact numerical results for a CNOT gate performed on two qubits of an (N +2)-qubit statically flawed isolated quantum computer. Here the N idle qubits comprise the finite environment. We obtain very good agreement even for small N .

Equilibration and asymptotic stationarity for non-Markovian master equations

“…Consider the model in section 2 with [B, H B ] = 0 which is similar to those considered in [2]. This model is readily solved numerically using a Kraus decomposition [27] which happens to be exact in this case. To complete the model, we set the parameters as in section 5 and sampled 10 5 eigenvalues of B uniformly from [−1, 1] and those corresponding to H B uniformly from [0, 5].…”

Exact reduced dynamics for a qubit in a precessing magnetic field and in contact with a heat bath

“…It is worth mentioning that the model with a similar properties was studied in Ref. [23], where the authors obtained the operator sum representation, yet the Kraus operator introduced therein involved the time chronological operator.…”

Manifold algorithmic errors in quantum computers with static internal imperfections

“…Hamiltonians similar to (6) were the focus of a number of previous studies [8][9][10] but obviously it is not the most general Hamiltonian for a qubit-based QC. Static one-body fluctuations are modeled by randomly and uniformly sampling coefficients from the interval…”

“…In this paper, we study the effects of one-and two-body static flaws on a quantum controlled-NOT (CNOT) gate performed on two qubits of a larger Josephson charge-qubit quantum computer (QC) [1,2]. The expected external decoherence time for this architecture allows up to 10 6 single-qubit operations, and hence issues of internal decoherence and other intrinsic errors are of paramount concern [3][4][5][6][8][9][10]. By internal decoherence, we mean errors in the basic structure of the QC such as incorrect qubit parameters or unwanted qubit-qubit interactions, while by external decoherence we refer to the effects of unwanted interactions with classical external fields and structures which are not part of the QC.…”

“…Suppression of decoherence with increasing intra-bath interactions has been explained in terms of a corresponding decline in the canonical variance of the bath coupling operator caused by the vanishing of off-diagonal matrix elements [3]. While this explanation is correct for the models considered in [3,4], and it is even possible to use the vanishing of off-diagonals to devise a numerical method for open quantum systems interacting with chaotic environments [5,6], a decline of variance cannot satisfactorily explain the suppression of decoherence in all cases. Here we consider zzas well as the native xx-type subsystem-bath interactions.…”