Related papers: Efficient Quantum Tensor Product Expanders and k-d…
Quantum physical unclonable functions, or QPUFs, are rapidly emerging as theoretical hardware solutions to provide secure cryptographic functionalities such as key-exchange, message authentication, entity identification among others. Recent…
Although tensor networks are powerful tools for simulating low-dimensional quantum physics, tensor network algorithms are very computationally costly in higher spatial dimensions. We introduce quantum gauge networks: a different kind of…
A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…
A central problem in quantum computation is to understand which quantum circuits are useful for exponential speed-ups over classical computation. We address this question in the setting of query complexity and show that for almost any…
We analyze the quantum walk in higher spatial dimensions and compare classical and quantum spreading as a function of time. Tensor products of Hadamard transformations and the discrete Fourier transform arise as natural extensions of the…
We present a practical design framework for high-fidelity quantum control in coupled Kerr-nonlinear oscillators, directly addressing the challenge of spectral crowding. We show that systematic spectral degeneracies, which hinder selective…
Expander graphs are fundamental in both computer science and mathematics, with a wide array of applications. With quantum technology reshaping our world, quantum expanders have emerged, finding numerous uses in quantum information theory,…
Unitary t-designs are some of the most versatile tools in quantum information theory. Their applications range from randomized benchmarking and shadow tomography, to more fundamental ones such as emulating quantum chaos and establishing…
The quantum Fourier transform (QFT) is a powerful tool in quantum computing. The main ingredients of QFT are formed by the Walsh-Hadamard transform H and phase shifts P(.), both of which are 2x2 unitary matrices as operators on the…
This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field…
A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk. The quantum walker is a particle that moves from a given vertex to adjacent vertices in quantum superposition. Here we…
A complex projective $t$-design is a configuration of vectors which is ``evenly distributed'' on a sphere in the sense that sampling uniformly from it reproduces the moments of Haar measure up to order $2t$. We show that the set of all…
A quantum expander is a unital quantum channel that is rapidly mixing, has only a few Kraus operators, and can be implemented efficiently on a quantum computer. We consider the problem of estimating the mixing time (i.e., the spectral gap)…
We provide the first tensor network method for computing quantum weight enumerator polynomials in the most general form. If a quantum code has a known tensor network construction of its encoding map, our method is far more efficient, and in…
$k$-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…
We provide a generalization of the idea of unitary designs to cover finite averaging over much more general operations on quantum states. Namely, we construct finite averaging sets for averaging quantum states over arbitrary reductive Lie…
Epsilon-nets and approximate unitary $t$-designs are natural notions that capture properties of unitary operations relevant for numerous applications in quantum information and quantum computing. The former constitute subsets of unitary…
Randomness is a fundamental resource in quantum information, with crucial applications in cryptography, algorithms, and error correction. A central challenge is to construct unitary $k$-designs that closely approximate Haar-random unitaries…
Families of expander graphs were first constructed by Margulis from discrete groups with property (T). Within the framework of quantum information theory, several authors have generalised the notion of an expander graph to the setting of…
A t-design for quantum states is a finite set of quantum states with the property of simulating the Haar-measure on quantum states, w.r.t. any test that uses at most t copies of a state. We give efficient constructions for approximate…