Quantum algorithm and quantum circuit for A-optimal projection: Dimensionality reduction
نویسندگان
چکیده
منابع مشابه
Limitations on Quantum Dimensionality Reduction
The Johnson-Lindenstrauss Lemma is a classic result which implies that any set of n real vectors can be compressed to O(log n) dimensions while only distorting pairwise Euclidean distances by a constant factor. Here we consider potential extensions of this result to the compression of quantum states. We show that, by contrast with the classical case, there does not exist any distribution over q...
متن کاملQuantum Ternary Circuit Synthesis Using Projection Operations
Basic logic gates and their operations in ternary quantum domain are involved in the synthesis of ternary quantum circuits. Only a few works define ternary algebra for ternary quantum logic realization. In this paper, a ternary logic function is expressed in terms of projection operations including a new one. A method to realize new multi-qutrit ternary gates in terms of generalized ternary gat...
متن کاملDimensionality Reduction Using a Randomized Projection Algorithm: Preliminary Results
We describe an implementation and experiments with a low-distortion randomized projection algorithm [LINI94] that can reduce the number of dimensions in the data by a considerable amount. The performance of the randomized algorithm is compared with that of a popular technique---Principal Component Analysis (PCA). The experiments show that the randomized projection algorithm consistently outperf...
متن کاملSystematic Dimensionality Reduction for Quantum Walks: Optimal Spatial Search and Transport on Non-Regular Graphs
Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that confine the dynamics to a smaller subspace of the full Hilbert space. In this work, we use invariant subspace methods, that can be computed systematically u...
متن کاملQuantum Circuit Optimization by Hadamard Gate Reduction
Due to its fault-tolerant gates, the Clifford+T library consisting of Hadamard (denoted by H), T , and CNOT gates has attracted interest in the synthesis of quantum circuits. Since the implementation of T gates is expensive, recent research is aiming at minimizing the use of such gates. It has been shown that T -depth optimizations can be implemented efficiently for circuits consisting only of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review A
سال: 2019
ISSN: 2469-9926,2469-9934
DOI: 10.1103/physreva.99.032311