Related papers: Unitary synthesis with optimal brick wall circuits
We consider the problem of deciding if a set of quantum one-qudit gates $\mathcal{S}=\{g_1,\ldots,g_n\}\subset G$ is universal, i.e if the closure $\overline{<\mathcal{S}>}$ is equal to $G$, where $G$ is either the special unitary or the…
In this paper we consider circuit synthesis for n-wire linear reversible circuits using the C-NOT gate library. These circuits are an important class of reversible circuits with applications to quantum computation. Previous algorithms,…
Integrability is an exceptional property believed to hold only for systems with fine-tuned parameters. Contrary, we explicitly show that in homogeneous nearest-neighbor qubit circuits with a U(1) symmetry, i.e., circuits that repeatedly…
We describe a simple algorithm for computing the canonical basis of any finite-dimensional $U_{q}(sp_{2n})$-module.
We establish connections between state tomography, pseudorandomness, quantum state synthesis, and circuit lower bounds. In particular, let $\mathfrak{C}$ be a family of non-uniform quantum circuits of polynomial size and suppose that there…
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 first consider various methods for the indirect implementation of unitary gates. We apply these methods to rederive the universality of 4-qubit measurements based on a scheme much simpler than Nielsen's original construction…
The architecture of circuital quantum computers requires computing layers devoted to compiling high-level quantum algorithms into lower-level circuits of quantum gates. The general problem of quantum compiling is to approximate any unitary…
We give a novel procedure for approximating general single-qubit unitaries from a finite universal gate set by reducing the problem to a novel magnitude approximation problem, achieving an immediate improvement in sequence length by a…
Quantum algorithms for unstructured search problems rely on the preparation of a uniform superposition, traditionally achieved through Hadamard gates. However, this incidentally creates an auxiliary search space consisting of nonsensical…
We provide two simple universality criteria. Our first criterion states that $\mathcal{S}\subset G_d:=U(d)$ is universal if and only if $\mathcal{S}$ forms a $\delta$-approximate $t(d)$-design, where $t(2)=6$ and $t(d)=4$ for $d\geq3$. Our…
The paper studies the global convergence of the block Jacobi me\-thod for symmetric matrices. Given a symmetric matrix $A$ of order $n$, the method generates a sequence of matrices by the rule $A^{(k+1)}=U_k^TA^{(k)}U_k$, $k\geq0$, where…
We develop a method to synthesize a class of entangling multi-qubit gates for a quantum computing platform with fixed Ising-type interaction with all-to-all connectivity. The only requirement on the flexibility of the interaction is that it…
Kliuchnikov, Maslov, and Mosca proved in 2012 that a $2\times 2$ unitary matrix $V$ can be exactly represented by a single-qubit Clifford+$T$ circuit if and only if the entries of $V$ belong to the ring $\mathbb{Z}[1/\sqrt{2},i]$. Later…
We present a classical simulation method for fermionic quantum systems which, without loss of generality, can be represented by parity-preserving circuits made of two-qubit gates in a brick-wall structure. We map such circuits to a…
We consider one dimensional quantum circuits of the brickwork type, where the fundamental quantum gate is dual unitary. Such models are solvable: the dynamical correlation functions of the infinite temperature ensemble can be computed…
Symmetry plays a crucial role in the design and analysis of quantum protocols. This result shows a canonical circuit decomposition of a $(G \times H)$-invariant quantum comb for compact groups $G$ and $H$ using the corresponding…
In this paper a storage method and a context-aware circuit simulation idea are presented for the sum of block diagonal matrices. Using the design technique for a generalized circuit for the Hamiltonian dynamics through the truncated series,…
We show the applicability of the Cartan decomposition of Lie algebras to quantum circuits. This approach can be used to synthesize circuits that can efficiently implement any desired unitary operation. Our method finds explicit quantum…
We consider the implementation of two-qubit unitary transformations by means of CNOT gates and single-qubit unitary gates. We show, by means of an explicit quantum circuit, that together with local gates three CNOT gates are necessary and…