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Effective Hamiltonian methods are utilized to model the two-qubit cross-resonance gate for both the ideal two-qubit case and when higher levels are included. Analytic expressions are obtained in the qubit case and the higher-level model is…
It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions…
We present an exact synthesis algorithm for qutrit unitaries in $\mathcal{U}_{3^n}(\mathbb{Z}[1/3,e^{2\pi i/3}])$ over the Clifford$+T$ gate set with at most one ancilla. This extends the already known result of qutrit metaplectic gates…
Physical Gottesman-Kitaev-Preskill (GKP) states are inherently noisy as ideal ones would require infinite energy. While this is typically considered as a deficiency to be actively corrected, this work demonstrates that imperfect GKP…
Multi-qubit entangling interactions arise naturally in several quantum computing platforms and promise advantages over traditional two-qubit gates. In particular, a fixed multi-qubit Ising-type interaction together with single-qubit X-gates…
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…
High-fidelity two-logical-qubit gates are essential for realizing fault-tolerant quantum computation with bosonic codes, yet experimentally reported fidelities have rarely exceeded 90\%. Here, we propose a geometric phase engineering…
Fault-tolerant logical entangling gates are essential for scalable quantum computing, but are limited by the error rates and overheads of physical two-qubit gates and measurements. To address this limitation, we introduce phantom…
In a continuous-variable optical system, the Gottesman-Kitaev-Preskill (GKP) qubit is a promising candidate for fault-tolerant quantum computation. To implement non-Clifford operations on GKP qubits, non-Gaussian operations are required. In…
Three-qubit gates are highly beneficial operations in quantum computing, enabling compact implementations of quantum algorithms and efficient generation of multipartite entangled states. However, realizing such gates with high fidelity…
Bosonic quantum error correction encodes a logical qubit in an oscillator, avoiding the hardware overhead of large qubit arrays. Among such encodings, Gottesman-Kitaev-Preskill (GKP) states are paticularly powerful because their phase-space…
The stable operation of quantum computers will rely on error-correction, in which single quantum bits of information are stored redundantly in the Hilbert space of a larger system. Such encoded qubits are commonly based on arrays of many…
Gottesman, Kitaev and Preskill have proposed a scheme to encode a qubit in a harmonic oscillator, which is called the GKP code. It is designed to be resistant to small shift errors contained in momentum and position quadratures. Thus…
In this paper, we present the experimental realization of multi-qubit gates $% \Lambda_n(not) $ in macroscopic ensemble of three-qubit and four-qubit molecules. Instead of depending heavily on the two-bit universal gate, which served as the…
We study ancilla-free approximation of single-qubit unitaries $U\in {\rm SU}(2)$ by gate sequences over Clifford+$G$, where $G\in\{T,V\}$ or their generalization. Let $p$ denote the characteristic factor of the gate set (e.g., $p=2$ for…
In recent years, squeezed cat codes with resilience to specific types of loss have been proposed as a step toward realizing fault-tolerant optical quantum computers. However, error correction for squeezed cat codes requires a strong…
The composite rotation approach has been used to develop a range of robust quantum logic gates, including single qubit gates and two qubit gates, which are resistant to systematic errors in their implementation. Single qubit gates based on…
Hamiltonian simulation is known to be one of the fundamental building blocks of a variety of quantum algorithms such as its most immediate application, that of simulating many-body systems to extract their physical properties. In this work,…
We study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS=diag(1,1,1,i). The Clifford+CS gate set is universal for quantum computation and its elements can be…
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…