Related papers: Four qubits generated by Clifford gates
Superconducting quantum devices are a leading technology for quantum computation, but they suffer from several challenges. Gate errors, coherence errors and a lack of connectivity all contribute to low fidelity results. In particular,…
Recent work has shown that $n$-qubit quantum states output by circuits with at most $t$ single-qubit non-Clifford gates can be learned to trace distance $\epsilon$ using $\mathsf{poly}(n,2^t,1/\epsilon)$ time and samples. All prior…
In quantum computing and quantum information processing, graph states are a specific type of quantum states which are commonly used in quantum networking and quantum error correction. A recurring problem is finding a transformation from a…
We characterize control of a qutrit implemented in the lowest three energy levels of a capacitively-shunted flux-biased superconducting circuit. Randomized benchmarking over the qutrit Clifford group yields an average fidelity of 98.89…
Using a braid group representation based on the Temperley-Lieb algebra, we construct braid quantum gates that could generate entangled $n$-partite $D$-level qudit states. $D$ different sets of $D^n\times D^n$ unitary representation of the…
We present two classical algorithms for the simulation of universal quantum circuits on $n$ qubits constructed from $c$ instances of Clifford gates and $t$ arbitrary-angle $Z$-rotation gates such as $T$ gates. Our algorithms complement each…
Provided that cavities are initially in a Greenberger-Horne-Zeilinger (GHZ) entangled state, we show that GHZ states of N-group qubits distributed in N cavities can be created via a 3-step operation. The GHZ states of the N-group qubits are…
A quantum computing system is typically represented by a set of non-interacting (local) two-state systems - qubits. Many physical systems can naturally have more accessible states, both local and non-local. We show that the resulting…
We study how much noise can be tolerated by a universal gate set before it loses its quantum-computational power. Specifically we look at circuits with perfect stabilizer operations in addition to imperfect non-stabilizer gates. We prove…
The Clifford algebra over the three-dimensional real linear space includes its linear structure and its exterior algebra, the subspaces spanned by multivectors of the same degree determine a gradation of the Clifford algebra. Through these…
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…
Let $n$ be a positive integer divisible by 8. The Clifford-cyclotomic gate set $\mathcal{G}_n$ consists of the Clifford gates, together with a $z$-rotation of order $n$. It is easy to show that, if a circuit over $\mathcal{G}_n$ represents…
We generalize an efficient exact synthesis algorithm for single-qubit unitaries over the Clifford+T gate set which was presented by Kliuchnikov, Maslov and Mosca. Their algorithm takes as input an exactly synthesizable single-qubit…
The Clifford hierarchy is a set of gates that appears in the theory of fault-tolerant quantum computation, but its precise structure remains elusive. We give a complete characterization of the diagonal gates in the Clifford hierarchy for…
Continuous-variable cluster states allow for fault-tolerant measurement-based quantum computing when used in tandem with the Gottesman-Kitaev-Preskill (GKP) encoding of a qubit into a bosonic mode. For quad-rail-lattice macronode cluster…
We provide a method for compiling approximate multi-controlled single qubit gates into quantum circuits without ancilla qubits. The total number of elementary gates to decompose an n-qubit multi-controlled gate is proportional to 32n, and…
In superconducting architectures, limited connectivity remains a significant challenge for the synthesis and compilation of quantum circuits. We consider models of entanglement-assisted computation where long-range operations are achieved…
We have devised an artificial intelligence algorithm with machine reinforcement learning (Q-learning) to construct remarkable entangled states with 4 qubits. This way, the algorithm is able to generate representative states for some of the…
Qudit-based quantum gates in high-dimensional Hilbert space can provide a viable route towards effectively accelerating the speed of quantum computing and performing complex quantum logic operations. In the paper, we propose a 2-qudit…
Graph states, which include for example Bell states, GHZ states and cluster states, form a well-known class of quantum states with applications ranging from quantum networks to error-correction. Deciding whether two graph states are…