4,379 research outputs found
Unitary space-time modulation via Cayley transform
A prevoiusly proposed method for communicating with multiple antennas over block fading channels is unitary space-time modulation (USTM). In this method, the signals transmitted from the antennas, viewed as a matrix with spatial and temporal dimensions, form a unitary matrix, i.e., one with orthonormal columns. Since channel knowledge is not required at the receiver, USTM schemes are suitable for use on wireless links where channel tracking is undesirable or infeasible, either because of rapid changes in the channel characteristics or because of limited system resources. Previous results have shown that if suitably designed, USTM schemes can achieve full channel capacity at high SNR and, moreover, that all this can be done over a single coherence interval, provided the coherence interval and number of transmit antennas are sufficiently large, which is a phenomenon referred to as autocoding. While all this is well recognized, what is not clear is how to generate good performing constellations of (nonsquare) unitary matrices that lend themselves to efficient encoding/decoding. The schemes proposed so far either exhibit poor performance, especially at high rates, or have no efficient decoding algorithms. We propose to use the Cayley transform to design USTM constellations. This work can be viewed as a generalization, to the nonsquare case, of the Cayley codes that have been proposed for differential USTM. The codes are designed based on an information-theoretic criterion and lend themselves to polynomial-time (often cubic) near-maximum-likelihood decoding using a sphere decoding algorithm. Simulations suggest that the resulting codes allow for effective high-rate data transmission in multiantenna communication systems without knowing the channel. However, our preliminary results do not show a substantial advantage over training-based schemes
Making Laplacians commute
In this paper, we construct multimodal spectral geometry by finding a pair of
closest commuting operators (CCO) to a given pair of Laplacians. The CCOs are
jointly diagonalizable and hence have the same eigenbasis. Our construction
naturally extends classical data analysis tools based on spectral geometry,
such as diffusion maps and spectral clustering. We provide several synthetic
and real examples of applications in dimensionality reduction, shape analysis,
and clustering, demonstrating that our method better captures the inherent
structure of multi-modal data
Optimized Compilation of Aggregated Instructions for Realistic Quantum Computers
Recent developments in engineering and algorithms have made real-world
applications in quantum computing possible in the near future. Existing quantum
programming languages and compilers use a quantum assembly language composed of
1- and 2-qubit (quantum bit) gates. Quantum compiler frameworks translate this
quantum assembly to electric signals (called control pulses) that implement the
specified computation on specific physical devices. However, there is a
mismatch between the operations defined by the 1- and 2-qubit logical ISA and
their underlying physical implementation, so the current practice of directly
translating logical instructions into control pulses results in inefficient,
high-latency programs. To address this inefficiency, we propose a universal
quantum compilation methodology that aggregates multiple logical operations
into larger units that manipulate up to 10 qubits at a time. Our methodology
then optimizes these aggregates by (1) finding commutative intermediate
operations that result in more efficient schedules and (2) creating custom
control pulses optimized for the aggregate (instead of individual 1- and
2-qubit operations). Compared to the standard gate-based compilation, the
proposed approach realizes a deeper vertical integration of high-level quantum
software and low-level, physical quantum hardware. We evaluate our approach on
important near-term quantum applications on simulations of superconducting
quantum architectures. Our proposed approach provides a mean speedup of
, with a maximum of . Because latency directly affects the
feasibility of quantum computation, our results not only improve performance
but also have the potential to enable quantum computation sooner than otherwise
possible.Comment: 13 pages, to apper in ASPLO
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