Related papers: Partition of 3-qubits using local gates
Quantum squaring operation is a useful building block in implementing quantum algorithms such as linear regression, regularized least squares algorithm, order-finding algorithm, quantum search algorithm, Newton Raphson division, Euclidean…
We show that any unimodular real 3-qubit gate can be expressed as the product of at most 14 CNOT gates plus single-qubit gates, improving on the bound of 16 CNOTs due to Wei and Di. Our method uses the exotic triality symmetry of…
Noisy intermediate-scale quantum (NISQ) computers have gate errors and decoherence, limiting the depth of circuits that can be implemented on them. A strategy for NISQ algorithms is to reduce the circuit depth at the expense of increasing…
We propose a universal quantum computing scheme in which the orthogonal qubit states $|0>$ and $|1>$ are identical in their single-particle spin and charge properties. Each qubit is contained in a single quantum dot and gate operations are…
We consider the task of deciding whether an unknown qubit state falls in a prescribed neighborhood of a reference state. We assume that several copies of the unknown state are given and apply a unitary operation pairwise on them combined…
In quantum control theory, a question of fundamental and practical interest is how an arbitrary unitary transformation can be decomposed into minimum number of elementary rotations for implementation, subject to various physical…
Given a finite group G with a bilocal representation, we investigate the bipartite entanglement in the state constructed from the group algebra of G acting on a separable reference state. We find an upper bound for the von Neumann entropy…
A set of orthogonal product states of a composite Hilbert space is genuinely nonlocal if the states are locally indistinguishable across any bipartition. In this work, we construct a minimal set of party asymmetry genuine nonlocal set in…
All quantum gates with one and two qubits may be described by elements of $Spin$ groups due to isomorphisms $Spin(3) \simeq SU(2)$ and $Spin(6) \simeq SU(4)$. However, the group of $n$-qubit gates $SU(2^n)$ for $n > 2$ has bigger dimension…
Hardware efficient transpilation of quantum circuits to a quantum devices native gateset is essential for the execution of quantum algorithms on noisy quantum computers. Typical quantum devices utilize a gateset with a single two-qubit…
An error-corrected quantum processor will require millions of qubits, accentuating the advantage of nanoscale devices with small footprints, such as silicon quantum dots. However, as for every device with nanoscale dimensions, disorder at…
Single qubit rotations and two-qubit CNOT operations are crucial ingredients for universal quantum computing. While high fidelity single qubit operations have been achieved using the electron spin degree of freedom, realizing a robust CNOT…
In this note we present explicit canonical forms for all the elements in the two-qubit CNOT-Dihedral group, with minimal numbers of controlled-S (CS) and controlled-X (CX) gates, using the generating set of quantum gates [X, T, CX, CS]. We…
Central in entanglement theory is the characterization of local transformations among pure multipartite states. As a first step towards such a characterization, one needs to identify those states which can be transformed into each other via…
The spin states of single electrons in gate-defined quantum dots satisfy crucial requirements for a practical quantum computer. These include extremely long coherence times, high-fidelity quantum operation, and the ability to shuttle…
In a recent work arXiv:2201.07655v2 we showed that there is a constant $\lambda >0$ such that it is possible to efficiently classically simulate a quantum system in which (i) qudits are placed on the nodes of a graph, (ii) each qudit…
We construct a quantum algorithm that creates the Laughlin state for an arbitrary number of particles $n$ in the case of filling fraction one. This quantum circuit is efficient since it only uses $n(n-1)/2$ local qudit gates and its depth…
We investigate genuinely entangled $N$-qubit states with no $N$-partite correlations in the case of symmetric states. Using a tensor representation for mixed symmetric states, we obtain a simple characterization of the absence of…
Quantum algorithms on near-term quantum processors are typically executed using shallow quantum circuits composed of one- and two-qubit gates. However, as circuit depth and gate number increase, gate imperfections and qubit decoherence…
The embedding of the $n$-qubit space into the $n$-fermion space with $2n$ modes is a widely used method in studying various aspects of these systems. This simple mapping raises a crucial question: does the embedding preserve the…