Related papers: Real-Valued Somewhat-Pseudorandom Unitaries
A new iterative low complexity algorithm has been presented for computing the Walsh-Hadamard transform (WHT) of an $N$ dimensional signal with a $K$-sparse WHT, where $N$ is a power of two and $K = O(N^\alpha)$, scales sub-linearly in $N$…
Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a…
Motivated by the study of Polyakov lines in gauge theories, Hanada and Watanabe recently presented a conjectured formula for the distribution of eigenphases of Haar-distributed random SU(N) matrices ($\beta$=2), supported by explicit…
The Kirkwood-Dirac (KD) quasiprobability distribution is known for its role in quantum metrology, thermodynamics, as well as quantum foundations. In this work we classify unitary evolutions that preserve KD positivity. We identify…
The singular values of products of standard complex Gaussian random matrices, or sub-blocks of Haar distributed unitary matrices, have the property that their probability distribution has an explicit, structured form referred to as a…
A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably…
Many quantum algorithms, to compute some property of a unitary $U$, require access not just to $U$, but to $cU$, the unitary with a control qubit. We show that having access to $cU$ does not help for a large class of quantum problems. For a…
We propose the concept of pseudorandom states and study their constructions, properties, and applications. Under the assumption that quantum-secure one-way functions exist, we present concrete and efficient constructions of pseudorandom…
Existence of the eigenvalues of the discrete-time quantum walks is deeply related to localization of the walks. We revealed the distributions of the eigenvalues given by the splitted generating function method (the SGF method) of the…
This thesis discusses the young fields of quantum pseudo-randomness and quantum learning algorithms. We present techniques for derandomising algorithms to decrease randomness resource requirements and improve efficiency. One key object in…
We determine the limiting empirical singular value distribution for random unitary matrices with Haar distribution and discrete Fourier transform (DFT) matrices when a random set of columns and rows is removed.
Given the Hamiltonian, the evaluation of unitary operators has been at the heart of many quantum algorithms. Motivated by existing deterministic and random methods, we present a hybrid approach, where Hamiltonians with large amplitude are…
This paper initiates the study of hidden variables from the discrete, abstract perspective of quantum computing. For us, a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another, into a…
Physical Unclonable Functions (PUFs) leverage inherent, non-clonable physical randomness to generate unique input-output pairs, serving as secure fingerprints for cryptographic protocols like authentication. Quantum PUFs (QPUFs) extend this…
We present an infinite number of construction schemes involving unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not previously been described. Our results rely on biunitary…
$k$-Uniform states are fundamental to quantum information and computing, with applications in multipartite entanglement and quantum error-correcting codes (QECCs). Prior work has primarily focused on constructing exact $k$-uniform states or…
Randomisation is widely used in quantum algorithms to reduce the number of quantum gates and ancillary qubits required. A range of randomised algorithms, including eigenstate property estimation by spectral filters, Hamiltonian simulation,…
We present a hybrid quantum-classical framework for simulating generic matrix functions more amenable to early fault-tolerant quantum hardware than standard quantum singular-value transformations. The method is based on randomization over…
We analyze the set of real and complex Hadamard matrices with additional symmetry constrains. In particular, we link the problem of existence of maximally entangled multipartite states of $2k$ subsystems with $d$ levels each to the set of…
For a polynomial ring over a commutative ring of positive characteristic, we define on the associated de Rham-Witt complex a set of functions, and show that they are pseudovaluations in the sense of Davis, Langer and Zink. To achieve it, we…