Related papers: Cyclic permutations for qudits in $d$ dimensions
We propose a new strategy to physically implement a universal set of quantum gates based on geometric phases accumulated in the nondegenerate eigenstates of a designated invariant operator in a periodic physical system. The system is driven…
We present an efficient family of quantum circuits for a fundamental primitive in quantum information theory, the Schur transform. The Schur transform on n d-dimensional quantum systems is a transform between a standard computational basis…
Although the quality of quantum bits (qubits) and quantum gates has been steadily improving, the available quantity of qubits has increased quite slowly. To address this important issue in quantum computing, we have demonstrated arbitrary…
We consider a generic elementary gate sequence which is needed to implement a general quantum gate acting on n qubits -- a unitary transformation with 4^n degrees of freedom. For synthesizing the gate sequence, a method based on the…
There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and 2-qubit CNOT gates. A CNOT gate is however…
We present a proof-of-principle demonstration of a method to characterize \textit{any} pure spatial qudit of arbitrary dimension $d$, which is based on the classic phase shift interferometry technique. In the proposed scheme a total of only…
We present quantum algorithms to realize geometric transformations (two-point swappings, symmetric flips, local flips, orthogonal rotations, and translations) based on an $n$-qubit normal arbitrary superposition state (NASS). These…
A scalable quantum information processing architecture based on silicon metal-oxide-semiconductor technology is presented, combining quantum hardware elements from planar and 3D silicon-on-insulator technologies. This architecture is…
Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm,…
We start with the simplest quantum system (a two-level system, i.e., a qubit) and discuss a one-to-one mapping of the quantum state in a two-dimensional Hilbert space to a vector in an eight dimensional probability space (probability…
Quantum computing can be realized with numerous different hardware platforms and computational protocols. A highly promising approach to foster scalability is to apply a photonic platform combined with a measurement-induced quantum…
We study a reduced quantum circuit computation paradigm in which the only allowable gates either permute the computational basis states or else apply a "global Hadamard operation", i.e. apply a Hadamard operation to every qubit…
Experimental realization of a universal set of quantum logic gates is the central requirement for implementation of a quantum computer. An all-geometric approach to quantum computation offered a paradigm for implementation where all the…
We study the generation of two-qudit entangling quantum logic gates using two techniques in quantum optimal control. We take advantage of both continuous, Lie-algebraic control and digital, Lie-group control. In both cases, the key is…
We show how to perform measurement-based quantum computing on qudits (high-dimensional quantum systems) using alternative resource states beyond the cluster state. Estimating overheads for gate decomposition, we find that generalizing…
Qudits hold great promise for efficient quantum computation and the simulation of high-dimensional quantum systems. Utilizing a local Hilbert space of dimension d > 2 is known to speed up certain quantum algorithms relative to their qubit…
With the advent of physical qubits exhibiting strong noise bias, it becomes increasingly relevant to identify which quantum gates can be efficiently implemented on error-correcting codes designed to address a single dominant error type.…
While thousands of experimental physicists and chemists are currently trying to build scalable quantum computers, it appears that simulation of quantum computation will be at least as critical as circuit simulation in classical VLSI design.…
Existing quantum compilers optimize quantum circuits by applying circuit transformations designed by experts. This approach requires significant manual effort to design and implement circuit transformations for different quantum devices,…
Nonadiabatic geometric quantum computation is dedicated to the realization of high-fidelity and robust quantum gates, which are necessary for fault-tolerant quantum computation. However, it is limited by cyclic and mutative evolution path,…