arXiv subjects

Ashley Milsted

Publications and source records attributed to Ashley Milsted.

At least 19 recordsLinked to original sources

arXiv2024

Real-Time Scattering in Ising Field Theory using Matrix Product States

We study scattering in Ising Field Theory (IFT) using matrix product states and the time-dependent variational principle. IFT is a one-parameter family of strongly coupled non-integrable quantum field theories in 1+1 dimensions, interpolating between massive free fermion theory and Zamolodchikov's integrable massive $E_8$ theory. Particles in IFT may scatter either elastically or inelastically. In the post-collision wavefunction, particle tracks from all final-state channels occur in superposition; processes of interest can be isolated by projecting the wavefunction onto definite particle sectors, or by evaluating energy density correlation functions. Using numerical simulations we determine the time delay of elastic scattering and the probability of inelastic particle production as a function of collision energy. We also study the mass and width of the lightest resonance near the $E_8$ point in detail. Close to both the free fermion and $E_8$ theories, our results for both elastic and inelastic scattering are in good agreement with expectations from form-factor perturbation theory. Using numerical computations to go beyond the regime accessible by perturbation theory, we find that the high energy behavior of the two-to-two particle scattering probability in IFT is consistent with a conjecture of Zamolodchikov. Our results demonstrate the efficacy of tensor-network methods for simulating the real-time dynamics of strongly coupled quantum field theories in 1+1 dimensions.

hep-th↗

arXiv2024

Hardware-efficient quantum error correction via concatenated bosonic qubits

In order to solve problems of practical importance, quantum computers will likely need to incorporate quantum error correction, where a logical qubit is redundantly encoded in many noisy physical qubits. The large physical-qubit overhead typically associated with error correction motivates the search for more hardware-efficient approaches. Here, using a microfabricated superconducting quantum circuit, we realize a logical qubit memory formed from the concatenation of encoded bosonic cat qubits with an outer repetition code of distance $d=5$. The bosonic cat qubits are passively protected against bit flips using a stabilizing circuit. Cat-qubit phase-flip errors are corrected by the repetition code which uses ancilla transmons for syndrome measurement. We realize a noise-biased CX gate which ensures bit-flip error suppression is maintained during error correction. We study the performance and scaling of the logical qubit memory, finding that the phase-flip correcting repetition code operates below threshold, with logical phase-flip error decreasing with code distance from $d=3$ to $d=5$. Concurrently, the logical bit-flip error is suppressed with increasing cat-qubit mean photon number. The minimum measured logical error per cycle is on average $1.75(2)\%$ for the distance-3 code sections, and $1.65(3)\%$ for the longer distance-5 code, demonstrating the effectiveness of bit-flip error suppression throughout the error correction cycle. These results, where the intrinsic error suppression of the bosonic encodings allows us to use a hardware-efficient outer error correcting code, indicate that concatenated bosonic codes are a compelling paradigm for reaching fault-tolerant quantum computation.

quant-ph↗

arXiv2024

Loop Series Expansions for Tensor Networks

Belief propagation (BP) can be a useful tool to approximately contract a tensor network, provided that the contributions from any closed loops in the network are sufficiently weak. In this manuscript we describe how a loop series expansion can be applied to systematically improve the accuracy of a BP approximation to a tensor network contraction, in principle converging arbitrarily close to the exact result. More generally, our result provides a framework for expanding a tensor network as a sum of component networks in a hierarchy of increasing complexity. We benchmark this proposal for the contraction of iPEPS, either representing the ground state of an AKLT model or with randomly defined tensors, where it is shown to improve in accuracy over standard BP by several orders of magnitude whilst incurring only a minor increase in computational cost. These results indicate that the proposed series expansions could be a useful tool to accurately evaluate tensor networks in cases that otherwise exceed the limits of established contraction routines.

quant-ph↗

arXiv2023

Demonstrating a long-coherence dual-rail erasure qubit using tunable transmons

Quantum error correction with erasure qubits promises significant advantages over standard error correction due to favorable thresholds for erasure errors. To realize this advantage in practice requires a qubit for which nearly all errors are such erasure errors, and the ability to check for erasure errors without dephasing the qubit. We demonstrate that a "dual-rail qubit" consisting of a pair of resonantly coupled transmons can form a highly coherent erasure qubit, where transmon $T_1$ errors are converted into erasure errors and residual dephasing is strongly suppressed, leading to millisecond-scale coherence within the qubit subspace. We show that single-qubit gates are limited primarily by erasure errors, with erasure probability $p_\text{erasure} = 2.19(2)\times 10^{-3}$ per gate while the residual errors are $\sim 40$ times lower. We further demonstrate mid-circuit detection of erasure errors while introducing $< 0.1\%$ dephasing error per check. Finally, we show that the suppression of transmon noise allows this dual-rail qubit to preserve high coherence over a broad tunable operating range, offering an improved capacity to avoid frequency collisions. This work establishes transmon-based dual-rail qubits as an attractive building block for hardware-efficient quantum error correction.

quant-ph↗

arXiv2022

A generalized multi-scale entanglement renormalization ansatz: more accurate conformal data from a critical lattice model

The multi-scale entanglement renormalization ansatz (MERA) provides a natural description of the ground state of a quantum critical Hamiltonian on the lattice. From an optimized MERA, one can extract the scaling dimensions of the underlying conformal field theory. However, extracting conformal data from the ascending superoperator derived from MERA seems to have a limited range of accuracy, even after increasing the bond dimension. Here, we propose an alternative ansatz based on an increasing number of disentangling layers. This leads to generalized versions of MERA that improve the extraction of scaling dimensions, as tested in the Gaussian MERA setting for the critical Ising model.

cond-mat.str-el↗

arXiv2020

Collisions of false-vacuum bubble walls in a quantum spin chain

We simulate, using nonperturbative methods, the real-time dynamics of small bubbles of "false vacuum" in a quantum spin chain near criticality, where the low-energy physics is described by a relativistic (1+1)-dimensional quantum field theory. We consider bubbles whose walls are kink and antikink quasiparticle excitations, so that wall collisions are kink-antikink scattering events. To construct these bubbles in the presence of strong correlations, we extend a recently proposed matrix product state (MPS) ansatz for quasiparticle wavepackets. We simulate dynamics within a window of about 1000 spins embedded in an infinite chain at energies of up to about 5 times the mass gap. By choosing the wavepacket width and the bubble size appropriately, we avoid strong lattice effects and observe relativistic kink-antikink collisions. We use the MPS quasiparticle ansatz to detect scattering outcomes. (i) In the Ising model, with transverse and longitudinal fields, we do not observe particle production despite nonintegrability (supporting recent observations of nonthermalizing states in this model). (ii) Switching on an additional interaction, we see production of confined and unconfined particle pairs. We characterize the amount of entanglement generated as a function of energy and time and conclude that our classical simulation methods will ultimately fail as these increase. We anticipate that kink-antikink scattering in 1+1 dimensions will be an instructive benchmark problem for future quantum computers and analog quantum simulators.

quant-ph↗

arXiv2020

Quantum Yang-Mills theory: an overview of a programme

We present an overview of a programme to understand the low-energy physics of quantum Yang-Mills theory from a quantum-information perspective. Our setting is that of the hamiltonian formulation of pure Yang-Mills theory in the temporal gauge on the lattice. Firstly, inspired by recent constructions for $\mathbb{Z}/2\mathbb{Z}$ lattice gauge theory, in particular, Kitaev's toric code, we describe the gauge-invariant sector of hilbert space by introducing a primitive quantum gate: the quantum parallel transporter. We then develop a nonabelian generalisation of laplace interpolation to present an ansatz for the ground state of pure Yang-Mills theory which interpolates between the weak- and strong-coupling RG fixed points. The resulting state acquires the structure of a tensor network, namely, a multiscale entanglement renormalisation ansatz, and allows for the efficient computation of local observables and Wilson loops. Various refinements of the tensor network are discussed leading to several generalisations. Finally, the continuum limit of our ansatz as the lattice regulator is removed is then described. This paper is intended as an abstract for an ongoing programme: there are still many open problems.

quant-ph↗

arXiv2019

Probabilistic Simulation of Quantum Circuits with the Transformer

The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our ability to emulate quantum circuits. Here we present an exact formulation of quantum dynamics via factorized generalized measurements which maps quantum states to probability distributions with the advantage that local unitary dynamics and quantum channels map to local quasi-stochastic matrices. This representation provides a general framework for using state-of-the-art probabilistic models in machine learning for the simulation of quantum many-body dynamics. Using this framework, we have developed a practical algorithm to simulate quantum circuits with the Transformer, a powerful ansatz responsible for the most recent breakthroughs in natural language processing. We demonstrate our approach by simulating circuits which build GHZ and linear graph states of up to 60 qubits, as well as a variational quantum eigensolver circuit for preparing the ground state of the transverse field Ising model on six qubits. Our methodology constitutes a modern machine learning approach to the simulation of quantum physics with applicability both to quantum circuits as well as other quantum many-body systems.

cond-mat.str-el↗

arXiv2019

TensorNetwork on TensorFlow: Entanglement Renormalization for quantum critical lattice models

We use TensorNetwork [C. Roberts et al., arXiv: 1905.01330], a recently developed API for performing tensor network contractions using accelerated backends such as TensorFlow, to implement an optimization algorithm for the Multi-scale Entanglement Renormalization Ansatz (MERA). We use the MERA to approximate the ground state wave function of the infinite, one-dimensional transverse field Ising model at criticality, and extract conformal data from the optimized ansatz. Comparing run times of the optimization on CPUs vs. GPU, we report a very significant speed-up, up to a factor of 200, of the optimization algorithm when run on a GPU.

physics.comp-ph↗

arXiv2019

TensorNetwork: A Library for Physics and Machine Learning

TensorNetwork is an open source library for implementing tensor network algorithms. Tensor networks are sparse data structures originally designed for simulating quantum many-body physics, but are currently also applied in a number of other research areas, including machine learning. We demonstrate the use of the API with applications both physics and machine learning, with details appearing in companion papers.

physics.comp-ph↗

arXiv2019

TensorNetwork on TensorFlow: A Spin Chain Application Using Tree Tensor Networks

TensorNetwork is an open source library for implementing tensor network algorithms in TensorFlow. We describe a tree tensor network (TTN) algorithm for approximating the ground state of either a periodic quantum spin chain (1D) or a lattice model on a thin torus (2D), and implement the algorithm using TensorNetwork. We use a standard energy minimization procedure over a TTN ansatz with bond dimension $χ$, with a computational cost that scales as $O(χ^4)$. Using bond dimension $χ\in [32,256]$ we compare the use of CPUs with GPUs and observe significant computational speed-ups, up to a factor of $100$, using a GPU and the TensorNetwork library.

cond-mat.str-el↗

arXiv2019

Conformal data and renormalization group flow in critical quantum spin chains using periodic uniform matrix product states

We establish that a Bloch-state ansatz based on periodic uniform Matrix Product States (puMPS), originally designed to capture single-quasiparticle excitations in gapped systems, is in fact capable of accurately approximating all low-energy eigenstates of critical quantum spin chains on the circle. When combined with the methods of [Milsted, Vidal, Phys. Rev. B 96 245105] based on the Koo-Saleur formula, puMPS Bloch states can then be used to identify each low-energy eigenstate of a chain made of up to hundreds of spins with its corresponding scaling operator in the emergent conformal field theory (CFT). This enables the following two tasks, that we demonstrate using the quantum Ising model and a recently proposed generalization thereof due to O'Brien and Fendley [Phys. Rev. Lett. 120, 206403]. (i) From the spectrum of low energies and momenta we extract conformal data (specifying the emergent CFT) with unprecedented numerical accuracy. (ii) By changing the lattice size, we investigate nonperturbatively the RG flow of the low-energy spectrum between two CFTs. In our example, where the flow is from the Tri-Critical Ising CFT to the Ising CFT, we obtain excellent agreement with an analytical result [Klassen and Melzer, Nucl. Phys. B 370 511] conjectured to describe the flow of the first spectral gap directly in the continuum.

cond-mat.str-el↗

arXiv2019

Conformal fields and operator product expansion in critical quantum spin chains

We propose a variational method for identifying lattice operators in a critical quantum spin chain with scaling operators in the underlying conformal field theory (CFT). In particular, this allows us to build a lattice version of the primary operators of the CFT, from which we can numerically estimate the operator product expansion coefficients $C_{αβγ}^{\textrm{ CFT}}$. We demonstrate the approach with the critical Ising quantum spin chain.

cond-mat.str-el↗

arXiv2018

Geometric interpretation of the multi-scale entanglement renormalization ansatz

The multi-scale entanglement renormalization ansatz (MERA) is a tensor network representation for ground states of critical quantum spin chains, with a network that extends in an additional dimension corresponding to scale. Over the years several authors have conjectured, both in the context of holography and cosmology, that MERA realizes a discrete version of some geometry. However, while one proposal argued that the tensor network should be interpreted as representing the hyperbolic plane, another proposal instead equated MERA to de Sitter spacetime. In this \letter we show, using the framework of path integral geometry [A. Milsted, G. Vidal, arXiv:1807.02501], that MERA on the real line (and finite circle) can be given a rigorous interpretation as a two-dimensional geometry, namely a light sheet (respectively, a light cone). Accordingly, MERA describes neither the hyperbolic plane nor de Sitter spacetime. However, we also propose euclidean and lorentzian generalizations of MERA that correspond to a path integral on these two geometries.

hep-th↗

arXiv2018

Tensor networks as path integral geometry

In the context of a quantum critical spin chain whose low energy physics corresponds to a conformal field theory (CFT), it was recently demonstrated [A. Milsted G. Vidal, arXiv:1805.12524] that certain classes of tensor networks used for numerically describing the ground state of the spin chain can also be used to implement (discrete, approximate versions of) conformal transformations on the lattice. In the continuum, the same conformal transformations can be implemented through a CFT path integral on some curved spacetime. Based on this observation, in this paper we propose to interpret the tensor networks themselves as a path integrals on curved spacetime. This perspective assigns (a discrete, approximate version of) a geometry to the tensor network, namely that of the underlying curved spacetime.

cond-mat.str-el↗

arXiv2018

Tensor networks as conformal transformations

Tensor networks are often used to accurately represent ground states of quantum spin chains. Two popular choices of such tensor network representations can be seen to implement linear maps that correspond, respectively, to euclidean time evolution and to global scale transformations. In this paper, by exploiting the local structure of the tensor networks, we explain how to also implement local or non-uniform versions of both euclidean time evolution and scale transformations. We demonstrate our proposal with a critical quantum spin chain on a finite circle, where the low energy physics is described by a conformal field theory (CFT), and where non-uniform euclidean time evolution and local scale transformations are conformal transformations acting on the Hilbert space of the CFT. We numerically show, for the critical quantum Ising chain, that the proposed tensor networks indeed transform the low energy states of the periodic spin chain in the same way as the corresponding conformal transformations do in the CFT.

cond-mat.str-el↗

arXiv2017

Extraction of conformal data in critical quantum spin chains using the Koo-Saleur formula

We study the emergence of two-dimensional conformal symmetry in critical quantum spin chains on the finite circle. Our goal is to characterize the conformal field theory (CFT) describing the universality class of the corresponding quantum phase transition. As a means to this end, we propose and demonstrate automated procedures which, using only the lattice Hamiltonian $H = \sum_j h_j$ as an input, systematically identify the low-energy eigenstates corresponding to Virasoro primary and quasiprimary operators, and assign the remaining low-energy eigenstates to conformal towers. The energies and momenta of the primary operator states are needed to determine the primary operator scaling dimensions and conformal spins -- an essential part of the conformal data that specifies the CFT. Our techniques use the action, on the low-energy eigenstates of $H$, of the Fourier modes $H_n$ of the Hamiltonian density $h_j$. The $H_n$ were introduced as lattice representations of the Virasoro generators by Koo and Saleur [Nucl. Phys. B 426, 459 (1994)]. In this paper we demonstrate that these operators can be used to extract conformal data in a nonintegrable quantum spin chain.

cond-mat.str-el↗

arXiv2016

Matrix product states and the nonabelian rotor model

We use uniform matrix product states (MPS) to study the (1+1)D $O(2)$ and $O(4)$ rotor models, which are equivalent to the Kogut-Susskind formulation of matter-free nonabelian lattice gauge theory on a "hawaiian earring" graph for $U(1)$ and $SU(2)$, respectively. Applying tangent space methods to obtain ground states and determine the mass gap and the $β$ function, we find excellent agreement with known results, locating the BKT transition for $O(2)$ and successfully entering the asymptotic weak-coupling regime for $O(4)$. To obtain a finite local Hilbert space, we truncate in the space of generalized Fourier modes of the gauge group, comparing the effects of different cutoff values. We find that higher modes become important in the crossover and weak-coupling regimes of the nonabelian theory, where entanglement also suddenly increases. This could have important consequences for TNS studies of Yang-Mills on higher dimensional graphs.

hep-lat↗