Related papers: TARE: Block Encoding Linear Combinations of Pauli …
Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of near-term quantum devices. We introduce…
We formulate code concatenation as the action of a unitary quantum circuit on an expanding tree geometry and find that for certain classes of gates, applied identically at each node, a binary tree circuit encodes a single logical qubit with…
This paper describes a new method of data encoding which may be used in various modern digital, computer and telecommunication systems and devices. The method permits the compression of data for storage or transmission, allowing the exact…
Length generalization, the ability to generalize from small training context sizes to larger ones, is a critical challenge in the development of Transformer-based language models. Positional encoding (PE) has been identified as a major…
Quantum autoencoder is a quantum neural network model for compressing information stored in quantum states. However, one needs to process information stored in quantum circuits for many tasks in the emerging quantum information technology.…
Modular exponentiation (ME) operators are one of the fundamental components of Shor's algorithm, and the place where most of the quantum resources are deployed. I propose a method for constructing the ME operators that relies upon the…
Based on the controlled order rearrange encryption (CORE) for quantum key distribution using EPR pairs[Fu.G.Deng and G.L.Long Phys.Rev.A68 (2003) 042315], we propose the generalized controlled order rearrangement encryption (GCORE)…
There are several improvements proposed over the baseline Absolute Positional Encoding (APE) method used in original transformer. In this study, we aim to investigate the implications of inadequately representing positional encoding in…
Polynomial based approaches, such as the Mat-Dot and entangled polynomial codes (EPC) have been used extensively within coded matrix computations to obtain schemes with good recovery thresholds. However, these schemes are well-recognized to…
We study a quantum-algorithmic framework for parameterizing partial differential equations (PDEs). For a broad class of problems in which the discretized parameter field admits a diagonal representation, block-encodings of diagonal…
Quantum code surgery is a flexible and low overhead technique for performing logical measurements on quantum error-correcting codes, which generalises lattice surgery. In this work, we present a code surgery scheme, applicable to any qubit…
Linear maps that are not completely positive play a crucial role in the study of quantum information, yet their non-completely positive nature renders them challenging to realize physically. The core difficulty lies in the fact that when…
We present a general theory of entanglement-assisted quantum convolutional coding. The codes have a convolutional or memory structure, they assume that the sender and receiver share noiseless entanglement prior to quantum communication, and…
Positional encoding is a vital component of Transformer architectures, enabling models to incorporate sequence order into self-attention mechanisms. Rotary Positional Embeddings (RoPE) have become a widely adopted solution due to their…
We develop a generalized framework for constructing many-body-interaction operations either in linear time, or in logarithmic time with a linear number of ancilla qubits. Exact gate decompositions are given in particular for Pauli strings,…
An algorithm for constructing Tanner graphs of non-binary irregular quasi-cyclic LDPC codes is introduced. It employs a new method for selection of edge labels allowing control over the code's non-binary ACE spectrum and resulting in low…
Permutation codes are a class of structured vector quantizers with a computationally-simple encoding procedure based on sorting the scalar components. Using a codebook comprising several permutation codes as subcodes preserves the…
In this work we study the encoding of smooth, differentiable multivariate functions in quantum registers, using quantum computers or tensor-network representations. We show that a large family of distributions can be encoded as…
We present a software library for the commutation of Pauli operators through quantum Clifford circuits, which is called Pauli tracking. Tracking Pauli operators allows one to reduce the number of Pauli gates that must be executed on quantum…