Related papers: Asymptotically Optimal Quantum Circuits for d-leve…

Given a quantum gate implementing a $d$-dimensional unitary operation $U_d$, without any specific description but $d$, and permitted to use $k$ times, we present a universal probabilistic heralded quantum circuit that implements the exact…

We describe in detail how to perform universal fault-tolerant quantum computation on a 2-D color code, making use of only nearest neighbor interactions. Three defects (holes) in the code are used to represent logical qubits. Triple defect…

We analyze and compare the optimality of approximate and probabilistic universal programmable quantum processors. We define several characteristics how to quantify the optimality and we study in detail performance of three types of…

We extend our previous results on local asymptotic normality (LAN) for qubits, to quantum systems of arbitrary finite dimension $d$. LAN means that the quantum statistical model consisting of $n$ identically prepared $d$-dimensional systems…

Surface codes describe quantum memory stored as a global property of interacting spins on a surface. The state space is fixed by a complete set of quasi-local stabilizer operators and the code dimension depends on the first homology group…

In classical statistics, a well known paradigm consists in establishing asymptotic equivalence between an experiment of i.i.d. observations and a Gaussian shift experiment, with the aim of obtaining optimal estimators in the former…

We develop qutrit circuit models for discrete-time three-state quantum walks on Cayley graphs corresponding to Dihedral groups $D_N$ and the additive groups of integers modulo any positive integer $N$. The proposed circuits comprise of…

Cat-state qubits (qubits encoded with cat states) have recently drawn intensive attention due to their enhanced life times with quantum error correction. We here propose a method to implement a universal controlled-phase gate of two…

We present a comprehensive and self-contained simplified review of the quantum computing scheme of Phys. Rev. Lett. 98, 190504 (2007), which features a 2-D nearest neighbor coupled lattice of qubits, a threshold error rate approaching 1%,…

Gerjuoy [Phys. Rev. A 67, 052308 (2003)] has derived a closed- form lower bound for the entanglement of formation of a mixed qubit-qudit system (qudit system has d levels with d>=3. In this paper, inspired by Gerjuoy's method, we propose a…

We construct a fault-tolerant quantum error-correcting protocol based on a qubit encoded in a large spin qudit using a spin-cat code, analogous to the continuous variable cat encoding. With this, we can correct the dominant error sources,…

The vast and complicated large-qubit state space forbids us to comprehensively capture the dynamics of modern quantum computers via classical simulations or quantum tomography. Recent progress in quantum learning theory prompts a crucial…

We present a way for implementing an n-qubit controlled-rotation gate with three-level superconducting qubit systems in cavity QED. The two logical states of a qubit are represented by the two lowest levels of each system while a…

The quantum Schur transform maps the computational basis of a system of $n$ qudits onto a \textit{Schur basis}, which spans the minimal invariant subspaces of the representations of the unitary and the symmetric groups acting on the state…

Interconnecting well-functioning, scalable stationary qubits and photonic qubits could substantially advance quantum communication applications and serve to link future quantum processors. Here, we present two protocols for transferring the…

Gottesman, Kitaev and Preskill have formulated a way of encoding a qubit into an oscillator such that the qubit is protected against small shifts (translations) in phase space. The idea underlying this encoding is that error processes of…

We investigate the emergence of quantum complexity and chaos in doped Clifford circuits acting on qudits of odd prime dimension $d$. Using doped Clifford Weingarten calculus and a replica tensor network formalism, we derive exact results…

We consider a model of two interacting always-on, exchange-only qubits for which controlled phase ($CPHASE$), controlled NOT ($CNOT$), quantum Fourier transform ($QFT$) and $SWAP$ operations can be implemented only in a few electrical…

Building a quantum computer is a daunting challenge since it requires good control but also good isolation from the environment to minimize decoherence. It is therefore important to realize quantum gates efficiently, using as few operations…

A qudit ($d$-level quantum systems) has a large Hilbert space and thus can be used to achieve many quantum information and communication tasks. Here, we propose a method to transfer arbitrary $d$-dimensional quantum states (known or…