Related papers: Cartan Decomposition of SU(2^n), Constructive Cont…
Quantum circuits currently constitute a dominant model for quantum computation. Our work addresses the problem of constructing quantum circuits to implement an arbitrary given quantum computation, in the special case of two qubits. We…
I introduce compact quantum group extensions associated with the $q$-deformations of the classical compact groups $USp(2n)$, $O(n,\mathbb{R})$ and $SO(2n,\mathbb{R})$. Motivated by the relationship between $SU_q(n)$ and $U_q(n)$, I study…
Efficient verification of the functioning of quantum devices is a key to the development of quantum technologies, but is a daunting task as the system size increases. Here we propose a simple and general framework for verifying unitary…
The creation of composite quantum gates that implement quantum response functions $\hat{U}(\theta)$ dependent on some parameter of interest $\theta$ is often more of an art than a science. Through inspired design, a sequence of $L$…
We address the characterization of two-qubit gates, focusing on bounds to precision in the joint estimation of the three parameters that define their Cartan decomposition. We derive the optimal probe states that jointly maximize precision,…
We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2^n)$, in particular composition, algebraic and topological closedness and connectedness. It extends prior work on…
We present a general, systematic, and efficient method for decomposing any given exponential operator of bosonic mode operators, describing an arbitrary multi-mode Hamiltonian evolution, into a set of universal unitary gates. Although our…
Future quantum devices often rely on favourable scaling with respect to the system components. To achieve desirable scaling, it is therefore crucial to implement unitary transformations in an efficient manner. We develop an upper bound for…
Controlled unitary gates are a basic element in many quantum algorithms. Converting a general unitary $U$ with a known decomposition into its controlled version, controlled-$U$, can introduce a large overhead in terms of the depth of the…
A unitary 2-design can be viewed as a quantum analogue of a 2-universal hash function: it is indistinguishable from a truly random unitary by any procedure that queries it twice. We show that exact unitary 2-designs on n qubits can be…
Unitary operations are the building blocks of quantum programs. Our task is to design effcient or optimal implementations of these unitary operations by employing the intrinsic physical resources of a given n-qubit system. The most common…
We demonstrate that in a coupled two-qubit system any single-qubit gate can be decomposed into two conditional two-qubit gates and that any conditional two-qubit gate can be implemented by a manipulation analogous to that used for a…
We consider a class of random quantum circuits where at each step a gate from a universal set is applied to a random pair of qubits, and determine how quickly averages of arbitrary finite-degree polynomials in the matrix elements of the…
We propose a method for quantum computation which uses control of spin-orbit coupling in a linear array of single electron quantum dots. Quantum gates are carried out by pulsing the exchange interaction between neighboring electron spins,…
The controllability property of the unitary propagator of an N-level quantum mechanical system subject to a single control field is described using the structure theory of semisimple Lie algebras. Sufficient conditions are provided for the…
Variational algorithms require architectures that naturally constrain the optimization space to run efficiently. Geometric quantum machine learning achieves this goal by encoding group structure into parameterized quantum circuits to…
We propose a quantum analogue of Bluestein's algorithm (QBA) that implements an exact $N$-point Quantum Fourier Transform (QFT) for arbitrary $N$. Our construction factors the $N$-dimensional QFT unitary into three diagonal quadratic-phase…
The Quantum Fourier transform (QFT) is a key ingredient in most quantum algorithms. We have compared various spin-based quantum computing schemes to implement the QFT from the point of view of their actual time-costs and the accuracy of the…
We show that it is possible to reduce the number of two-qubit gates needed for the construction of an arbitrary controlled-unitary transformation by up to two times using a tunable controlled-phase gate. On the platform of linear optics,…
We present an architecture of QCPU(Quantum Central Processing Unit), based on the discrete quantum gate set, that can be programmed to approximate any n-qubit computation in a deterministic fashion. It can be built efficiently to implement…