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Yongqi Liang

Publications and source records attributed to Yongqi Liang.

35 records · Page 2Linked to original sources
arXiv2024

Floquet Engineering of Anisotropic Transverse Interactions in Superconducting Qubits

Superconducting transmon qubits have established as a leading candidate for quantum computation, as well as a flexible platform for exploring exotic quantum phases and dynamics. However, physical coupling naturally yields isotropic transverse interactions between qubits, restricting their access to diverse quantum phases that require spatially dependent interactions. Here, we demonstrate the simultaneous realization of both pairing (XX-YY) and hopping (XX+YY) interactions between transmon qubits by Floquet engineering. The coherent superposition of these interactions enables independent control over the XX and YY terms, yielding anisotropic transverse interactions. By aligning the transverse interactions along a 1D chain of six qubits, as calibrated via Aharonov-Bohm interference in synthetic space, we synthesize a transverse field Ising chain model and explore its dynamical phase transition under varying external field. The scalable synthesis of anisotropic transverse interactions paves the way for the implementation of more complex physical systems requiring spatially dependent interactions, enriching the toolbox for engineering quantum phases with superconducting qubits.

quant-ph↗
arXiv2024

M2CS: A Microwave Measurement and Control System for Large-scale Superconducting Quantum Processors

As superconducting quantum computing continues to advance at an unprecedented pace, there is a compelling demand for the innovation of specialized electronic instruments that act as crucial conduits between quantum processors and host computers. Here, we introduce a Microwave Measurement and Control System (M2CS) dedicated for large-scale superconducting quantum processors. M2CS features a compact modular design that balances overall performance, scalability, and flexibility. Electronic tests of M2CS show key metrics comparable to commercial instruments. Benchmark tests on transmon superconducting qubits further show qubit coherence and gate fidelities comparable to state-of-the-art results, confirming M2CS's capability to meet the stringent requirements of quantum experiments run on intermediate-scale quantum processors. The system's compact and scalable design offers significant room for further enhancements that could accommodate the measurement and control requirements of over 1000 qubits, and can also be adopted to other quantum computing platforms such as trapped ions and silicon quantum dots. The M2CS architecture may also be applied to wider range of scenarios, such as microwave kinetic inductance detectors, as well as phased array radar systems.

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arXiv2021

Arithmetic of Châtelet surface bundles revisited

We study arithmetic of the algebraic varieties defined over number fields by applying Lagrange interpolation to fibrations. Assuming the finiteness of the Tate-Shafarevich group of a certain elliptic curve, we show, for Châtelet surface bundles over curves, that the violation of Hasse principle being accounted for by the Brauer-Manin obstruction is not invariant under an arbitrary finite extension of the ground field.

math.AG↗
arXiv2019

Approximation forte sur un produit de variétés abéliennes épointé en des points de torsion

Consider strong approximation for algebraic varieties defined over a number field $k$. Let $S$ be a finite set of places of $k$ containing all archimedean places. Let $E$ be an elliptic curve of positive Mordell-Weil rank and let $A$ be an abelian variety of positive dimension and of finite Mordell-Weil group. For an arbitrary finite set $\mathfrak{T}$ of torsion points of $E\times A$, denote by $X$ its complement. Supposing the finiteness of $Sha(E\times A)$, we prove that $X$ satisfies strong approximation with Brauer-Manin obstruction off $S$ if and only if the projection of $\mathfrak{T}$ to $A$ contains no $k$-rational points.

math.NT↗
arXiv2018

Non-invariance of weak approximation properties under extension of the ground field

For rational points on algebraic varieties defined over a number field $K$, we study the behavior of the property of weak approximation with Brauer-Manin obstruction under extension of the ground field. We construct K-varieties accompanied with a quadratic extension $L/K$ such that the property holds over $K$ (conditional on a conjecture) while fails over $L$. The result is unconditional when $K = \mathbb{Q}$ or $K$ is one of several quadratic number fields. Over $\mathbb{Q}$, we give an explicit example.

math.NT↗
arXiv2018

Arithmetic purity of strong approximation for homogeneous spaces

We prove that any open subset $U$ of a semi-simple simply connected quasi-split linear algebraic group $G$ with ${codim} (G\setminus U, G)\geq 2$ over a number field satisfies strong approximation by establishing a fibration of $G$ over a toric variety. We also prove a similar result of strong approximation with Brauer-Manin obstruction for a partial equivariant smooth compactification of a homogeneous space where all invertible functions are constant and the semi-simple part of the linear algebraic group is quasi-split. Some semi-abelian varieties of any given dimension where the complements of a rational point do not satisfy strong approximation with Brauer-Manin obstruction are given.

math.AG↗
arXiv2015

Approximation faible pour les 0-cycles sur un produit de variétés rationnellement connexes

Consider weak approximation for 0-cycles on a smooth proper variety defined over a number field, it is conjectured to be controlled by its Brauer group. Let $X$ be a Châtelet surface or a smooth compactification of a homogeneous space of a connected linear algebraic group with connected stabilizer. Let $Y$ be a rationally connected variety. We prove that weak approximation for 0-cycles on the product $X\times Y$ is controlled by its Brauer group if it is the case for $Y$ after every finite extension of the base field. We do not suppose the existence of 0-cycles of degree $1$ neither on $X$ nor on $Y$.

math.NT↗
arXiv2014

Local-global principle for 0-cycles on fibrations over rationally connected bases

We study the Brauer-Manin obstruction to the Hasse principle and to weak approximation for 0-cycles on algebraic varieties that possess a fibration structure. The exactness of the local-to-global sequence $(E)$ of Chow groups of 0-cycles was known only for a fibration whose base is either a curve or the projective space. In the present paper, we prove the exactness of $(E)$ for fibrations whose bases are Châtelet surfaces or projective models of homogeneous spaces of connected linear algebraic groups with connected stabilizers. We require that either all fibres are split and most fibres satisfy weak approximation for 0-cycles, or the generic fibre has a 0-cycle of degree $1$ and $(E)$ is exact for most fibres.

math.NT↗
arXiv2013

Towards the Brauer-Manin obstruction on varieties fibred over the projective line

Recently Dasheng Wei proved that the Brauer-Manin obstruction is the only obstruction to the Hasse principle for 0-cycles of degree 1 on some fibrations over the projective line defined by bi-cyclic normic equations. In the present paper, we prove the exactness of the global-to-local sequence for Chow groups of 0-cycles of such varieties, which signifies that the Brauer-Manin obstruction is also the only obstruction to weak approximation for 0-cycles of arbitrary degree. Our main theorem also generalizes several existing results.

math.AG↗
arXiv2013

Local-global principle for certain biquadratic normic bundles

Let $X$ be a proper smooth variety having an affine open subset defined by the normic equation $N_{k(\sqrt{a},\sqrt{b})/k}({x})=Q(t_{1},...,t_{m})^{2}$ over a number field $k$. We prove that : (1) the failure of the local-global principle for zero-cycles is controlled by the Brauer group of $X$; (2) the analogue for rational points is also valid assuming Schinzel's hypothesis.

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arXiv2012

The local-global exact sequence for Chow groups of zero-cycles

A local-global sequence for Chow groups of zero-cycles involving Brauer groups has been conjectured to be exact for all proper smooth algebraic varieties. We apply existing methods to construct several new families of varieties verifying the exact sequence. The examples are explicit, they are normic bundles over the projective space.

math.NT↗
arXiv2012

Astuce de Salberger et zéro-cycles sur certaines fibrations

We prove that the Brauer-Manin obstruction is the only obstruction to the Hasse principle and to the weak approximation for zero-cycles on certain fibrations over a smooth curve or over the projective space. The principal novelty is that the arithmetic hypotheses are supposed only on the fibres over a generalized Hilbertian subset.

math.AG↗
arXiv2011

Arithmetic of 0-cycles on varieties defined over number fields

Let $X$ be a rationally connected algebraic variety, defined over a number field $k$. We find a relation between the arithmetic of rational points on $X$ and the arithmetic of zero-cycles. More precisely, we consider the following statements: (1) the Brauer-Manin obstruction is the only obstruction to weak approximation for $K$-rational points on $X_K$ for all finite extensions $K/k$; (2) the Brauer-Manin obstruction is the only obstruction to weak approximation in some sense that we define for zero-cycles of degree 1 on $X_K$ for all finite extensions $K/k$; (3) a certain sequence of local-global type for Chow groups of 0-cycles on $X_K$ is exact for all finite extensions $K/k$. We prove that (1) implies (2), and that (2) and (3) are equivalent. We also prove a similar implication for the Hasse principle. As an application, we prove the exactness of the sequence mentioned above for smooth compactifications of certain homogeneous spaces of linear algebraic groups.

math.AG↗
arXiv2011

Principe local-global pour les zéro-cycles sur certaines fibrations au-dessus d'une courbe : I

Let $X$ be a smooth projective variety over a number field, fibered over a curve, with geometrically integral fibers. We prove that, supposing the finiteness of $\sha(Jac(C))$, if the fibers over a generalised Hilbertian subset satisfy the Hasse principle (resp. weak approximation), then the Brauer-Manin obstruction coming from the base curve is the only obstruction to the Hasse principle (resp. to weak approximation) for zero-cycles of degree 1 on $X$.

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