Publications

Order by: publication date number of citations

• Parameter-parallel distributed variational quantum algorithm

  Yun-Fei Niu, Shuo Zhang, Chen Ding, Wan-Su Bao, He-Liang Huang

  SciPost Phys. 14, 132 (2023) · published 26 May 2023 | Toggle abstract · pdf

  Variational quantum algorithms (VQAs) have emerged as a promising near-term technique to explore practical quantum advantage on noisy intermediate-scale quantum (NISQ) devices. However, the inefficient parameter training process due to the incompatibility with backpropagation and the cost of a large number of measurements, posing a great challenge to the large-scale development of VQAs. Here, we propose a parameter-parallel distributed variational quantum algorithm (PPD-VQA), to accelerate the training process by parameter-parallel training with multiple quantum processors. To maintain the high performance of PPD-VQA in the realistic noise scenarios, a alternate training strategy is proposed to alleviate the acceleration attenuation caused by noise differences among multiple quantum processors, which is an unavoidable common problem of distributed VQA. Besides, the gradient compression is also employed to overcome the potential communication bottlenecks. The achieved results suggest that the PPD-VQA could provide a practical solution for coordinating multiple quantum processors to handle large-scale real-word applications.

  7 citations

• An exact method for bosonizing the Fermi surface in arbitrary dimensions

  Takamori Park, Leon Balents

  SciPost Phys. 16, 069 (2024) · published 8 March 2024 | Toggle abstract · pdf

  Inspired by the recent work by Delacretaz et. al. [Phys. Rev. Res. 4, 033131 (2022)], we rigorously derive an exact and simple method to bosonize a non-interacting fermionic system with a Fermi surface starting from a microscopic Hamiltonian. In the long-wavelength limit, we show that the derived bosonized action is exactly equivalent to the action obtained by Delacretaz et. al. In addition, we propose diagrammatic rules to evaluate correlation functions using our bosonized theory and demonstrate these rules by calculating the three- and four-point density correlation functions. We also consider a general density-density interaction and show that the simplest approximation in our bosonic theory is identical to RPA results.

  7 citations

• Learning Coulomb Diamonds in Large Quantum Dot Arrays

  Oswin Krause, Anasua Chatterjee, Ferdinand Kuemmeth, Evert van Nieuwenburg

  SciPost Phys. 13, 084 (2022) · published 5 October 2022 | Toggle abstract · pdf

  We introduce an algorithm that is able to find the facets of Coulomb diamonds in quantum dot arrays. We simulate these arrays using the constant-interaction model, and rely only on one-dimensional raster scans (rays) to learn a model of the device using regularized maximum likelihood estimation. This allows us to determine, for a given charge state of the device, which transitions exist and what the compensated gate voltages for these are. For smaller devices the simulator can also be used to compute the exact boundaries of the Coulomb diamonds, which we use to assess that our algorithm correctly finds the vast majority of transitions with high precision.

  7 citations

• Complexity is not enough for randomness

  Shiyong Guo, Martin Sasieta, Brian Swingle

  SciPost Phys. 17, 151 (2024) · published 4 December 2024 | Toggle abstract · pdf

  We study the dynamical generation of randomness in Brownian systems as a function of the degree of locality of the Hamiltonian. We first express the trace distance to a unitary design for these systems in terms of an effective equilibrium thermal partition function, and provide a set of conditions that guarantee a linear time to design. We relate the trace distance to design to spectral properties of the time-evolution operator. We apply these considerations to the Brownian $p$-SYK model as a function of the degree of locality $p$. We show that the time to design is linear, with a slope proportional to $1/p$. We corroborate that when $p$ is of order the system size this reproduces the behavior of a completely non-local Brownian model of random matrices. For the random matrix model, we reinterpret these results from the point of view of classical Brownian motion in the unitary manifold. Therefore, we find that the generation of randomness typically persists for exponentially long times in the system size, even for systems governed by highly non-local time-dependent Hamiltonians. We conjecture this to be a general property: there is no efficient way to generate approximate Haar random unitaries dynamically, unless a large degree of fine-tuning is present in the ensemble of time-dependent Hamiltonians. We contrast the slow generation of randomness to the growth of quantum complexity of the time-evolution operator. Using known bounds on circuit complexity for unitary designs, we obtain a lower bound determining that complexity grows at least linearly in time for Brownian systems. We argue that these bounds on circuit complexity are far from tight and that complexity grows at a much faster rate, at least for non-local systems.

  7 citations

• Why space could be quantised on a different scale to matter

  Matthew J. Lake

  SciPost Phys. Proc. 4, 014 (2021) · published 13 August 2021 | Toggle abstract · pdf

  The scale of quantum mechanical effects in matter is set by Planck's constant, $\hbar$. This represents the quantisation scale for material objects. In this article, we present a simple argument why the quantisation scale for space, and hence for gravity, may not be equal to $\hbar$. Indeed, assuming a single quantisation scale for both matter and geometry leads to the `worst prediction in physics', namely, the huge difference between the observed and predicted vacuum energies. Conversely, assuming a different quantum of action for geometry, $\beta \ll \hbar$, allows us to recover the observed density of the Universe. Thus, by measuring its present-day expansion, we may in principle determine, empirically, the scale at which the geometric degrees of freedom should be quantised.

  7 citations

• Shot noise distinguishes Majorana fermions from vortices injected in the edge mode of a chiral p-wave superconductor

  C. W. J. Beenakker, D. O. Oriekhov

  SciPost Phys. 9, 080 (2020) · published 23 November 2020 | Toggle abstract · pdf

  The chiral edge modes of a topological superconductor support two types of excitations: fermionic quasiparticles known as Majorana fermions and $\pi$-phase domain walls known as edge vortices. Edge vortices are injected pairwise into counter-propagating edge modes by a flux bias or voltage bias applied to a Josephson junction. An unpaired edge mode carries zero electrical current on average, but there are time-dependent current fluctuations. We calculate the shot noise power produced by a sequence of edge vortices and find that it increases logarithmically with their spacing - even if the spacing is much larger than the core size so the vortices do not overlap. This nonlocality produces an anomalous V log V increase of the shot noise in a voltage-biased geometry, which serves as a distinguishing feature in comparison with the linear-in-V Majorana fermion shot noise.

  7 citations

• Positivity, low twist dominance and CSDR for CFTs

  Agnese Bissi, Aninda Sinha

  SciPost Phys. 14, 083 (2023) · published 25 April 2023 | Toggle abstract · pdf

  We consider a crossing symmetric dispersion relation (CSDR) for CFT four point correlation with identical scalar operators, which is manifestly symmetric under the cross-ratios $u,v$ interchange. This representation has several features in common with the CSDR for quantum field theories. It enables a study of the expansion of the correlation function around $u=v=1/4$, which is used in the numerical conformal bootstrap program. We elucidate several remarkable features of the dispersive representation using the four point correlation function of $\Phi_{1,2}$ operators in 2d minimal models as a test-bed. When the dimension of the external scalar operator ($\Delta_\sigma$) is less than $\frac{1}{2}$, the CSDR gets contribution from only a single tower of global primary operators with the second tower being projected out. We find that there is a notion of low twist dominance (LTD) which, as a function of $\Delta_\sigma$, is maximized near the 2d Ising model as well as the non-unitary Yang-Lee model. The CSDR and LTD further explain positivity of the Taylor expansion coefficients of the correlation function around the crossing symmetric point and lead to universal predictions for specific ratios of these coefficients. These results carry over to the epsilon expansion in $4-\epsilon$ dimensions. We also conduct a preliminary investigation of geometric function theory ideas, namely the Bieberbach-Rogosinski bounds.

  7 citations

• A comment on instantons and their fermion zero modes in adjoint QCD_2

  Andrei Smilga

  SciPost Phys. 10, 152 (2021) · published 22 June 2021 | Toggle abstract · pdf

  The adjoint 2-dimensional $QCD$ with the gauge group $SU(N)/Z_N$ admits topologically nontrivial gauge field configurations associated with nontrivial $\pi_1[SU(N)/Z_N] = Z_N$. The topological sectors are labelled by an integer $k=0,\ldots, N-1$. However, in contrast to $QED_2$ and $QCD_4$, this topology is not associated with an integral invariant like the magnetic flux or Pontryagin index. These instantons may admit fermion zero modes, but there is always an equal number of left-handed and right-handed modes, so that the Atiyah-Singer theorem, which determines in other cases the number of the modes, does not apply. The mod. 2 argument suggests that, for a generic gauge field configuration, there is either a single doublet of such zero modes or no modes whatsoever. However, the known solution of the Dirac problem for a wide class of gauge field configurations indicates the presence of $k(N-k)$ zero mode doublets in the topological sector $k$. In this note, we demonstrate in an explicit way that these modes are not robust under a generic enough deformation of the gauge background and confirm thereby the mod. 2 conjecture. The implications for the physics of this theory (screening vs. confinement issue) are briefly discussed.

  7 citations

• Higher-point integrands in $\mathcal{N} = 4$ super Yang-Mills theory

  Till Bargheer, Thiago Fleury, Vasco Gonçalves

  SciPost Phys. 15, 059 (2023) · published 10 August 2023 | Toggle abstract · pdf

  We compute the integrands of five-, six-, and seven-point correlation functions of twenty-prime operators with general polarizations at the two-loop order in $\mathcal{N}=4$ super Yang-Mills theory. In addition, we compute the integrand of the five-point function at three-loop order. Using the operator product expansion, we extract the two-loop four-point function of one Konishi operator and three twenty-prime operators. Two methods were used for computing the integrands. The first method is based on constructing an ansatz, and then numerically fitting for the coefficients using the twistor-space reformulation of $\mathcal{N}=4$ super Yang-Mills theory. The second method is based on the OPE decomposition. Only very few correlator integrands for more than four points were known before. Our results can be used to test conjectures, and to make progresses on the integrability-based hexagonalization approach for correlation functions.

  7 citations

• Random quench predicts universal properties of amorphous solids

  Masanari Shimada, Eric De Giuli

  SciPost Phys. 12, 090 (2022) · published 11 March 2022 | Toggle abstract · pdf

  Amorphous solids display numerous universal features in their mechanics, structure, and response. Current models assume heterogeneity in mesoscale elastic properties, but require fine-tuning in order to quantitatively explain vibrational properties. A complete model should derive the magnitude and character of elastic heterogeneity from an initially structureless medium, through a model of the quenching process during which the temperature is rapidly lowered and the solid is formed. Here we propose a field-theoretic model of a quench, and compute structural, mechanical, and vibrational observables in arbitrary dimension $d$. This allows us to relate the properties of the amorphous solid to those of the initial medium, and to those of the quench. We show that previous mean-field results are subsumed by our analysis and unify spatial fluctuations of elastic moduli, long-range correlations of inherent state stress, universal vibrational anomalies, and localized modes into one picture.

  7 citations