Searcharxiv⌕ Search

arXiv subjects

Terry Farrelly

Publications and source records attributed to Terry Farrelly.

At least 19 recordsLinked to original sources
arXiv2026

Macromux: scalable postselection for high-threshold fault-tolerant quantum computation

We introduce a new resource-efficient scheme for fault-tolerant quantum computation known as `macroscale multiplexing' (or simply `Macromux'), that utilizes scalable postselection to significantly improve the threshold of a given fault-tolerant protocol against both Pauli and erasure errors. Macromux is a hierarchical method for postselecting on constant-size space-time windows of a fault tolerant protocol, requiring only constant additional overheads. The method can be straightforwardly implemented for any fault-tolerant protocol and in any architecture that has access to routing and memory, such as linear-optical fusion-based architectures. We construct fault-tolerant protocols that, to our knowledge, have the highest thresholds in the literature; we perform simulations of fusion-based schemes based on the surface code, showing a maximum possible increase in Pauli thresholds of up to a factor of $\sim6$ (from $1.0\%$ to $5.9\%$). Our schemes are highly-resource efficient, and can for example, double the loss thresholds of some photonic fusion-based protocols using as little as $3 \times$ overhead.

quant-ph↗
arXiv2024

Tensor-network decoders for process tensor descriptions of non-Markovian noise

Quantum error correction (QEC) is essential for fault-tolerant quantum computation. Often in QEC errors are assumed to be independent and identically distributed and can be discretised to a random Pauli error during the execution of a quantum circuit. In real devices, however, the noise profile is much more complex and contains non-trivial spatiotemporal correlations, such as cross-talk, non-Markovianity, and their mixtures. Here, we examine the performance of two paradigmatic QEC codes in the presence of complex noise by using process tensors to represent spatiotemporal correlations beyond iid errors. This integration is an instance of the recently proposed \textit{strategic code}, which combines QEC with process tensors. In particular, we construct the maximum likelihood (ML) decoder for a quantum error correction code with a process tensor. To understand the computational overhead and implications of this approach, we implement our framework numerically for small code instances and evaluate its performance. We also propose a method to evaluate the performance of strategic codes and construct the ML decoder with an efficient tensor network approximation. Our results highlight the possible detrimental effects of correlated noise and potential pathways for designing decoders that account for such effects.

quant-ph↗
arXiv2023

Fault-tolerant complexes

Fault-tolerant complexes describe surface-code fault-tolerant protocols from a single geometric object. We first introduce fusion complexes that define a general family of fusion-based quantum computing (FBQC) fault-tolerant quantum protocols based on surface codes. We show that any 3-dimensional cell complex where each edge has four incident faces gives a valid fusion complex. This construction enables an automated search for fault tolerance schemes, allowing us to identify 627 examples within a moderate search time. We implement this using the open-source software tool Gavrog and present threshold results for a variety of schemes, finding fusion networks with higher erasure and Pauli thresholds than those existing in the literature. We then define more general structures we call fault-tolerant complexes that provide a homological description of fault tolerance from a large family of low-level error models, which include circuit-based computation, floquet-based computation, and FBQC with multi-qubit measurements. This extends the applicability of homological descriptions of fault tolerance, and enables the generation of many new schemes which have not been previously identified. We also define families of fault-tolerant complexes for color codes and 3d single-shot subsystem codes, which enables similar constructive methods, and we present several new examples of each.

quant-ph↗
arXiv2023

Optimization of Tensor Network Codes with Reinforcement Learning

Tensor network codes enable structured construction and manipulation of stabilizer codes out of small seed codes. Here, we apply reinforcement learning to tensor network code geometries and demonstrate how optimal stabilizer codes can be found. Using the projective simulation framework, our reinforcement learning agent consistently finds the best possible codes given an environment and set of allowed actions, including for codes with more than one logical qubit. The agent also consistently outperforms a random search, for example finding an optimal code with a $10\%$ frequency after 1000 trials, vs a theoretical $0.16\%$ from random search, an improvement by a factor of 65.

quant-ph↗
arXiv2022

Does causal dynamics imply local interactions?

We consider quantum systems with causal dynamics in discrete spacetimes, also known as quantum cellular automata (QCA). Due to time-discreteness this type of dynamics is not characterized by a Hamiltonian but by a one-time-step unitary. This can be written as the exponential of a Hamiltonian but in a highly non-unique way. We ask if any of the Hamiltonians generating a QCA unitary is local in some sense, and we obtain two very different answers. On one hand, we present an example of QCA for which all generating Hamiltonians are fully non-local, in the sense that interactions do not decay with the distance. We expect this result to have relevant consequences for the classification of topological phases in Floquet systems, given that this relies on the effective Hamiltonian. On the other hand, we show that all one-dimensional quasi-free fermionic QCAs have quasi-local generating Hamiltonians, with interactions decaying exponentially in the massive case and algebraically in the critical case. We also prove that some integrable systems do not have local, quasi-local nor low-weight constants of motion; a result that challenges the standard definition of integrability.

quant-ph↗
arXiv2021

Local tensor-network codes

Tensor-network codes enable the construction of large stabilizer codes out of tensors describing smaller stabilizer codes. An application of tensor-network codes was an efficient and exact decoder for holographic codes. Here, we show how to write some topological codes, including the surface code and colour code, as simple tensor-network codes. We also show how to calculate distances of stabilizer codes by contracting a tensor network. The algorithm actually gives more information, including a histogram of all logical coset weights. We prove that this method is efficient in the case of holographic codes. Using our tensor-network distance calculator, we find a modification of the rotated surface code that has the same distance but fewer minimum-weight logical operators by injecting the non-CSS five-qubit code tensor into the tensor network. This corresponds to an improvement in successful error correction of up to 2% against depolarizing noise (in the perfect-measurement setting), but comes at the cost of introducing four higher-weight stabilizers. Our general construction lets us pick a network geometry (e.g., a Euclidean lattice in the case of the surface code), and, using only a small set of seed codes (constituent tensors), build extensive codes with the potential for optimisation.

quant-ph↗
arXiv2020

Parallel decoding of multiple logical qubits in tensor-network codes

We consider tensor-network stabilizer codes and show that their tensor-network decoder has the property that independent logical qubits can be decoded in parallel. As long as the error rate is below threshold, we show that this parallel decoder is essentially optimal. As an application, we verify this for the max-rate holographic Steane (heptagon) code. For holographic codes this tensor-network decoder was shown to be efficient with complexity polynomial in n, the number of physical qubits. Here we show that, by using the parallel decoding scheme, the complexity is also linear in k, the number of logical qubits. Because the tensor-network contraction is computationally efficient, this allows us to exactly contract tensor networks corresponding to codes with up to half a million qubits. Finally, we calculate the bulk threshold (the threshold for logical qubits a fixed distance from the code centre) under depolarizing noise for the max-rate holographic Steane code to be 9.4%.

quant-ph↗
arXiv2020

A review of Quantum Cellular Automata

Discretizing spacetime is often a natural step towards modelling physical systems. For quantum systems, if we also demand a strict bound on the speed of information propagation, we get quantum cellular automata (QCAs). These originally arose as an alternative paradigm for quantum computation, though more recently they have found application in understanding topological phases of matter and have been proposed as models of periodically driven (Floquet) quantum systems, where QCA methods were used to classify their phases. QCAs have also been used as a natural discretization of quantum field theory, and some interesting examples of QCAs have been introduced that become interacting quantum field theories in the continuum limit. This review discusses all of these applications, as well as some other interesting results on the structure of quantum cellular automata, including the tensor-network unitary approach, the index theory and higher dimensional classifications of QCAs.

quant-ph↗
arXiv2020

Tensor-network codes

Inspired by holographic codes and tensor-network decoders, we introduce tensor-network stabilizer codes which come with a natural tensor-network decoder. These codes can correspond to any geometry, but, as a special case, we generalize holographic codes beyond those constructed from perfect or block-perfect isometries, and we give an example that corresponds to neither. Using the tensor-network decoder, we find a threshold of 18.8% for this code under depolarizing noise. We also show that for holographic codes the exact tensor-network decoder (with no bond-dimension truncation) is efficient with a complexity that is polynomial in the number of physical qubits, even for locally correlated noise.

quant-ph↗
arXiv2020

Discretizing quantum field theories for quantum simulation

To date, all proposed quantum algorithms for simulating quantum field theory (QFT) simulate (continuous-time) Hamiltonian lattice QFT as a stepping stone. Two overlooked issues are how large we can take the timestep in these simulations while getting the right physics and whether we can go beyond the standard recipe that relies on Hamiltonian lattice QFT. The first issue is crucial in practice for, e.g., trapped-ion experiments which actually have a lower bound on the possible ratio of timestep to lattice spacing. To this end, we show that a timestep equal to or going to zero faster than the spatial lattice spacing is necessary for quantum simulations of QFT, but far more importantly a timestep equal to the lattice spacing is actually sufficient. To do this, first for $ϕ^4$ theory, we give a quantum circuit exactly equivalent to the real-time path integral from the discrete-time Lagrangian formulation of lattice QFT. Next we give another circuit with no lattice QFT analogue, but, by using Feynman rules applied to the circuit, we see that it also reproduces the correct continuum behaviour. Finally, we look at non-abelian gauge fields, showing that the discrete-time lattice QFT path-integral is exactly equivalent to a finite-depth local circuit. All of these circuits have an analogue of a lightcone on the lattice and therefore are examples of quantum cellular automata. Aside from the potential practical benefit of these circuits, this all suggests that the path-integral approach to lattice QFT need not be overlooked in quantum simulations of physics and has a simple quantum information interpretation.

quant-ph↗
arXiv2020

A quantum cellular automaton for one-dimensional QED

We propose a discrete spacetime formulation of quantum electrodynamics in one-dimension (a.k.a the Schwinger model) in terms of quantum cellular automata, i.e. translationally invariant circuits of local quantum gates. These have exact gauge covariance and a maximum speed of information propagation. In this picture, the interacting quantum field theory is defined as a "convergent" sequence of quantum cellular automata, parameterized by the spacetime lattice spacing---encompassing the notions of continuum limit and renormalization, and at the same time providing a quantum simulation algorithm for the dynamics.

quant-ph↗
arXiv2019

Equilibration towards generalized Gibbs ensembles in non-interacting theories

Even after almost a century, the foundations of quantum statistical mechanics are still not completely understood. In this work, we provide a precise account on these foundations for a class of systems of paradigmatic importance that appear frequently as mean-field models in condensed matter physics, namely non-interacting lattice models of fermions (with straightforward extension to bosons). We demonstrate that already the translation invariance of the Hamiltonian governing the dynamics and a finite correlation length of the possibly non-Gaussian initial state provide sufficient structure to make mathematically precise statements about the equilibration of the system towards a generalized Gibbs ensemble, even for highly non-translation invariant initial states far from ground states of non-interacting models. Whenever these are given, the system will equilibrate rapidly according to a power-law in time as long as there are no long-wavelength dislocations in the initial second moments that would render the system resilient to relaxation. Our proof technique is rooted in the machinery of Kusmin-Landau bounds. Subsequently, we numerically illustrate our analytical findings by discussing quench scenarios with an initial state corresponding to an Anderson insulator observing power-law equilibration. We discuss the implications of the results for the understanding of current quantum simulators, both in how one can understand the behaviour of equilibration in time, as well as concerning perspectives for realizing distinct instances of generalized Gibbs ensembles in optical lattice-based architectures.

quant-ph↗
arXiv2019

Uncertainty from Heisenberg to Today

We explore the different meanings of "quantum uncertainty" contained in Heisenberg's seminal paper from 1927, and also some of the precise definitions that were explored later. We recount the controversy about "Anschaulichkeit", visualizability of the theory, which Heisenberg claims to resolve. Moreover, we consider Heisenberg's programme of operational analysis of concepts, in which he sees himself as following Einstein. Heisenberg's work is marked by the tensions between semiclassical arguments and the emerging modern quantum theory, between intuition and rigour, and between shaky arguments and overarching claims. Nevertheless, the main message can be taken into the new quantum theory, and can be brought into the form of general theorems. They come in two kinds, not distinguished by Heisenberg. These are, on one hand, constraints on preparations, like the usual textbook uncertainty relation, and, on the other, constraints on joint measurability, including trade-offs between accuracy and disturbance.

physics.hist-ph↗
arXiv2019

Efficient Learning for Deep Quantum Neural Networks

Neural networks enjoy widespread success in both research and industry and, with the imminent advent of quantum technology, it is now a crucial challenge to design quantum neural networks for fully quantum learning tasks. Here we propose the use of quantum neurons as a building block for quantum feed-forward neural networks capable of universal quantum computation. We describe the efficient training of these networks using the fidelity as a cost function and provide both classical and efficient quantum implementations. Our method allows for fast optimisation with reduced memory requirements: the number of qudits required scales with only the width, allowing the optimisation of deep networks. We benchmark our proposal for the quantum task of learning an unknown unitary and find remarkable generalisation behaviour and a striking robustness to noisy training data.

quant-ph↗
arXiv2018

Discrete-time quantum walks as fermions of lattice gauge theory

It is shown that discrete-time quantum walks can be used to digitize, i.e., to time discretize fermionic models of continuous-time lattice gauge theory. The resulting discrete-time dynamics is thus not only manifestly unitary, but also ultralocal, i.e. the particle's speed is upper bounded, as in standard relativistic quantum field theories. The lattice chiral symmetry of staggered fermions, which corresponds to a translational invariance, is lost after the requirement of ultralocality of the evolution; this fact is an instance of Meyer's 1996 no-go lemma stating that no non-trivial one-dimensional scalar quantum cellular automaton can be translationally invariant [1]. All results are presented in a single-particle framework and for a (1+1)-dimensional spacetime.

quant-ph↗
arXiv2017

Energy cost of entanglement extraction in complex quantum systems

What is the energy cost of extracting entanglement from complex quantum systems? In other words, given a state of a quantum system, how much energy does it cost to extract m EPR pairs? This is an important question, particularly for quantum field theories where the vacuum is generally highly entangled. Here we build a theory to understand the energy cost of entanglement extraction. First, we apply it to a toy model, and then we define the entanglement temperature, which relates the energy cost to the amount of extracted entanglement. Next, we give a physical argument to find the energy cost of entanglement extraction in some condensed matter and quantum field systems. The energy cost for those quantum field theories depends on the spatial dimension, and in one dimension, for example, it grows exponentially with the number of EPR pairs extracted. Next, we outline some approaches for bounding the energy cost of extracting entanglement in general quantum systems. Finally, we look at the antiferromagnetic Heisenberg and transverse field Ising models numerically to calculate the entanglement temperature using matrix product states.

quant-ph↗
arXiv2017

Insights from Quantum Information into Fundamental Physics

This thesis is split into two parts, which are united in the sense that they involve applying ideas from quantum information to fundamental physics. The first part is focused on examining discrete-time models in quantum computation (discrete-time quantum walks and quantum cellular automata) as discretized models of relativistic systems. One of the results here is a theorem demonstrating that a large class of discrete-time quantum walks have relativistic dynamics in the continuum limit. Additionally, the problem of fermion doubling for these models is investigated, and it is seen that the problem can be circumvented in two dimensional space. This was already known for one dimensional systems. Another result involves taking the limits of causal free field theories in discrete spacetime to recover continuum field theories, something that is not straightforward because of the nontrivial nature of the vacuum in quantum field theory. Additionally, it is shown that general systems of fermions evolving causally in discrete spacetime can be represented by quantum cellular automata, which makes them efficiently simulable by quantum computers. A related result is that quantum cellular automata composed of fermions are equivalent to regular quantum cellular automata. In the second part of this thesis, the focus is on the foundations of statistical physics. The main result of this part is a general bound on the time it takes a quantum system to effectively reach equilibrium. The discussion also includes a practical definition of equilibration that takes our measurement capabilities into account. Finally, the nature of the equilibrium state is also discussed, with a focus on initial state independence, which relates to the important question of when the equilibrium state is a Gibbs state.

quant-ph↗