2,402 research outputs found
Distillation protocols for Fourier states in quantum computing
Fourier states are multi-qubit registers that facilitate phase rotations in
fault-tolerant quantum computing. We propose distillation protocols for
constructing the fundamental, -qubit Fourier state with error at
a cost of Toffoli gates and Clifford gates, or any arbitrary
Fourier state using gates. We analyze these protocols with methods
from digital signal processing. These results suggest that phase kickback,
which uses Fourier states, could be the current lowest-overhead method for
generating arbitrary phase rotations.Comment: 18 pages, 4 figure
The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing
and protecting fragile qubits against the undesirable effects of quantum
decoherence. Similar to classical codes, hashing bound approaching QECCs may be
designed by exploiting a concatenated code structure, which invokes iterative
decoding. Therefore, in this paper we provide an extensive step-by-step
tutorial for designing EXtrinsic Information Transfer (EXIT) chart aided
concatenated quantum codes based on the underlying quantum-to-classical
isomorphism. These design lessons are then exemplified in the context of our
proposed Quantum Irregular Convolutional Code (QIRCC), which constitutes the
outer component of a concatenated quantum code. The proposed QIRCC can be
dynamically adapted to match any given inner code using EXIT charts, hence
achieving a performance close to the hashing bound. It is demonstrated that our
QIRCC-based optimized design is capable of operating within 0.4 dB of the noise
limit
Large-Alphabet Time-Frequency Entangled Quantum Key Distribution by means of Time-to-Frequency Conversion
We introduce a novel time-frequency quantum key distribution (TFQKD) scheme
based on photon pairs entangled in these two conjugate degrees of freedom. The
scheme uses spectral detection and phase modulation to enable measurements in
the temporal basis by means of time-to-frequency conversion. This allows
large-alphabet encoding to be implemented with realistic components. A general
security analysis for TFQKD with binned measurements reveals a close connection
with finite-dimensional QKD protocols and enables analysis of the effects of
dark counts on the secure key size.Comment: 14 pages, 3 figures, submitte
Complex additive geometric multilevel solvers for Helmholtz equations on spacetrees
We introduce a family of implementations of low-order, additive, geometric multilevel solvers for systems of Helmholtz equations arising from Schrödinger equations. Both grid spacing and arithmetics may comprise complex numbers, and we thus can apply complex scaling to the indefinite Helmholtz operator. Our implementations are based on the notion of a spacetree and work exclusively with a finite number of precomputed local element matrices. They are globally matrix-free. Combining various relaxation factors with two grid transfer operators allows us to switch from additive multigrid over a hierarchical basis method into a Bramble-Pasciak-Xu (BPX)-type solver, with several multiscale smoothing variants within one code base. Pipelining allows us to realize full approximation storage (FAS) within the additive environment where, amortized, each grid vertex carrying degrees of freedom is read/written only once per iteration. The codes realize a single-touch policy. Among the features facilitated by matrix-free FAS is arbitrary dynamic mesh refinement (AMR) for all solver variants. AMR as an enabler for full multigrid (FMG) cycling—the grid unfolds throughout the computation—allows us to reduce the cost per unknown. The present work primary contributes toward software realization and design questions. Our experiments show that the consolidation of single-touch FAS, dynamic AMR, and vectorization-friendly, complex scaled, matrix-free FMG cycles delivers a mature implementation blueprint for solvers of Helmholtz equations in general. For this blueprint, we put particular emphasis on a strict implementation formalism as well as some implementation correctness proofs
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