Related papers: Efficient classical simulations of quantum Fourier…
Quantum Fourier transform (QFT) is a widely used building block for quantum algorithms, whose scalable implementation is challenging in experiments. Here, we propose a protocol of quadratic quantum Fourier transform (QQFT), considering cold…
A framework to describe a broad class of physical operations (including unitary transformations, dissipation, noise, and measurement) in a quantum optics experiment is given. This framework provides a powerful tool for assessing the…
Quantum supremacy is the ability of quantum processors to outperform classical computers at certain tasks. In digital random quantum circuit approaches for supremacy, the output distribution produced is described by the Porter-Thomas (PT)…
We show that a classical algorithm efficiently simulating the modular exponentiation circuit, for certain product state input and with measurements in a general product state basis at the output, can efficiently simulate Shor's factoring…
Hamiltonian simulation is a promising application for quantum computers to achieve a quantum advantage. We present classical algorithms based on tensor network methods to optimize quantum circuits for this task. We show that, compared to…
Simulating quantum circuits is a computationally intensive task that relies heavily on tensor products and matrix multiplications, which can be inefficient. Recent advancements, eliminate the need for tensor products and matrix…
In this work we explore a correspondence between quantum circuits and low-degree polynomials over the finite field F_2. Any quantum circuit made up of Hadamard, Z, controlled-Z and controlled-controlled-Z gates gives rise to a degree-3…
In breakthrough work, Bravyi, Gosset, and K\"{o}nig (BGK) [Science, 2018] unconditionally proved that constant depth quantum circuits are more powerful than their classical counterparts. Their result is equivalent to saying that a…
Modern cryptography is largely based on complexity assumptions, for example, the ubiquitous RSA is based on the supposed complexity of the prime factorization problem. Thus, it is of fundamental importance to understand how a quantum…
The Fourier transform, known in classical analysis, and generalized in abstract harmonic analysis, can also be considered in the theory of locally compact quantum groups. In this note, I discuss some aspects of this more general Fourier…
Recently multiple families of spin chain models were found, which have a free fermionic spectrum,even though they are not solvable by a Jordan-Wigner transformation. Instead, the free fermions emerge as a result of a rather intricate…
Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability…
Classical simulators play a major role in the development and benchmark of quantum algorithms and practically any software framework for quantum computation provides the option of running the algorithms on simulators. However, the…
Investigating the classical simulability of quantum circuits provides a promising avenue towards understanding the computational power of quantum systems. Whether a class of quantum circuits can be efficiently simulated with a probabilistic…
Quantum computers are reaching a level where interactions between classical and quantum computations can happen in real-time. This marks the advent of a new, broader class of quantum circuits: dynamic quantum circuits. They offer a broader…
We show how the quantum fast Fourier transform (QFFT) can be made exact for arbitrary orders (first for large primes). For most quantum algorithms only the quantum Fourier transform of order $2^n$ is needed, and this can be done exactly.…
The Fermi-Hubbard model, a fundamental framework for studying strongly correlated phenomena could significantly benefit from quantum simulations when exploring non-trivial settings. However, simulating this problem requires twice as many…
Symmetries of the finite Heisenberg group represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. As is well known, these symmetries are properly expressed in terms of certain normalizer. This…
We present some basic integer arithmetic quantum circuits, such as adders and multipliers-accumulators of various forms, as well as diagonal operators, which operate on multilevel qudits. The integers to be processed are represented in an…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…