Related papers: Oracular Approximation of Quantum Multiplexors and…
Constructing general programmable circuits to be able to run any given unitary operator efficiently on a quantum processor is of fundamental importance. We present a new quantum circuit design technique resulting two general programmable…
A mathematical proposition with a trainable pair, operator and quantum circuit, are introduced to approximate functions expressed as cubic Taylor polynomials, numerical simulations illustrate three cases.
We improve previous estimates for matrices belonging to the quantum annulus or to the numerical annulus.
This paper is dedicated to the problem of verification of matrices for unitary similarity. For the case of nonderogatory matrices, we have been able to present the new solution for this problem based on geometric approach. The main…
Let G be a finite subgroup of unitary matrices acting on the space of $N$-qubits. We associate with G a uniform quantum channel QU from the space on $N$-qubits to itself. We give a quantum algorithm to approximate this channel by…
Quantum oracles play key roles in the studies of quantum computation and quantum information. But implementing quantum oracles efficiently with universal quantum gates is a hard work. Motivated by genetic programming, this paper proposes a…
In this introductory course we sketch the framework of quantum probability in order to discuss open quantum systems, in particular the damped harmonic oscillator.
Although quantum circuits have been ubiquitous for decades in quantum computing, the first complete equational theory for quantum circuits has only recently been introduced. Completeness guarantees that any true equation on quantum circuits…
We present numerical evidence that a simple variational improvement of the ordinary perturbation theory of the quantum anharmonic oscillator can give a convergent sequence of approximations even in the extreme strong coupling limit, the…
Quantum simulation promises to address many challenges in fields ranging from quantum chemistry to material science, and high-energy physics, and could be implemented in noisy intermediate-scale quantum devices. A challenge in building good…
We introduce the first complete equational theory for quantum circuits. More precisely, we introduce a set of circuit equations that we prove to be sound and complete: two circuits represent the same unitary map if and only if they can be…
Within the general context of the architecture in quantum computer design, this paper aims is to provide a general strategy to obtain a block-matrix representation of quantum gates applied to qubits placed in arbitrary positions over an…
In this paper, we extend past work done on the application of the mathematics of category theory to quantum information science. Specifically, we present a realization of a dagger-compact category that can model finite-dimensional quantum…
We define and study a new type of quantum oracle, the quantum conditional oracle, which provides oracle access to the conditional probabilities associated with an underlying distribution. Amongst other properties, we (a) obtain speed-ups…
Building on the established methods for superconducting circuit quantization, we present a new theoretical framework for approximate numerical simulation of Josephson quantum circuits. Simulations based on this framework provide access to a…
It is an established fact that for many of the interesting problems quantum algorithms based on queries of the standard oracle bring no significant improvement in comparison to known classical algorithms. It is conceivable that there are…
We provide a constructive algorithm to find the best separable approximation to an arbitrary density matrix of a composite quantum system of finite dimensions. The method leads to a condition of separability and to a measure of…
We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…
Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. We prove a prominent conjecture by Brown and Susskind about how random quantum circuits' complexity…
We establish an isomorphism between quantum circuits and a subspace of polyatomic molecules, which suggests that molecules can be used as descriptors of quantum circuits for quantum machine learning. Our numerical results show that the…