Andrew S. Darmawan

The development of robust architectures capable of large-scale fault-tolerant quantum computation should consider both their quantum error-correcting codes, and the underlying physical qubits upon which they are built, in tandem. Following this design principle we demonstrate remarkable error correction performance by concatenating the XZZX surface code with Kerr-cat qubits. We contrast several variants of fault-tolerant systems undergoing different circuit noise models that reflect the physics

The surface code is a many-body quantum system, and simulating it in generic conditions is computationally hard. While the surface code is believed to have a high threshold, the numerical simulations used to establish this threshold are based on simplified noise models. We present a tensor-network algorithm for simulating error correction with the surface code under arbitrary local noise. We use this algorithm to study the threshold and the subthreshold behavior of the amplitude damping and syst

The long-studied Hubbard model is one of the simplest models of copper-oxide superconductors. However, the connection between the model and the experimental phase diagram is still under debate, in particular regarding the existence and extent of the $d$-wave superconducting phase. Recent rapid progress in improving the accuracy of numerical solvers has opened a way to answer this question reliably. Here, we study the hole-doping concentration ($\ensuremath{\delta}$) dependence of the Hubbard mod

Measurement-based quantum computing, a powerful alternative to the standard circuit model, proceeds using only local adaptive measurements on a highly entangled resource state of many spins on a graph or lattice. Along with the canonical cluster state, the valence-bond solid ground state on a chain of spin-1 particles, studied by Affleck, Kennedy, Lieb, and Tasaki (AKLT), is such a resource state. We propose a simulation of this AKLT state using linear optics, wherein we can make use of the high

Recent work [M. J. Gullans , ] has shown that quantum error correcting codes defined by random Clifford encoding circuits can achieve a nonzero encoding rate in correcting errors even if the random circuits on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>n</a:mi></a:math> qubits, embedded in one spatial dimension (1D), have a logarithmic depth <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>d</b:mi><b:mo>=</b:mo><b:mi>O</b:mi><b:mo>(</b:mo><b:mo form="prefix">log

We study the spectral properties of a family of quantum antiferromagnets on two-dimensional (2D) lattices. This family of models is obtained by a deformation of the well-studied 2D quantum antiferromagnetic model of Affleck, Kennedy, Lieb, and Tasaki (AKLT); they are described by two-body, frustration-free Hamiltonians on a three-colorable lattice of spins. Although the existence of a spectral gap in the 2D AKLT model remains an open question, we rigorously prove the existence of a gap for a sub

This is a comprehensive study on how knowledge of the physical noise model affects the performance of surface-code decoders in quantum error correction. While noise generally requires many parameters to describe completely, the author finds that to achieve near-optimal decoding, it is only necessary to adapt the decoder to a small number of critical parameters.

The development of robust architectures capable of large-scale fault-tolerant quantum computation should consider both their quantum error-correcting codes and the underlying physical qubits upon which they are built, in tandem. Following this design principle, we demonstrate remarkable error-correction performance by concatenating the XZZX surface code with Kerr-cat qubits. We contrast several variants of fault-tolerant systems undergoing different circuit-noise models that reflect the physics

Abstract Leakage errors, in which a qubit is excited to a level outside the qubit subspace, represent a significant obstacle in the development of robust quantum computers. We present a computationally efficient simulation methodology for studying leakage errors in quantum error correcting codes (QECCs) using tensor network methods, specifically matrix product states. Our approach enables the simulation of various leakage processes, including thermal noise and coherent errors, without approximat

Recent work [M. J. Gullans et al., Physical Review X, 11(3):031066 (2021)] has shown that quantum error correcting codes defined by random Clifford encoding circuits can achieve a non-zero encoding rate in correcting errors even if the random circuits on $n$ qubits, embedded in one spatial dimension (1D), have a logarithmic depth $d=\mathcal{O}(\log{n})$. However, this was demonstrated only for a simple erasure noise model. In this work, we discover that this desired property indeed holds for th

Information obtained from noise characterization of a quantum device can be used in classical decoding algorithms to improve the performance of quantum error-correcting codes. Focusing on the surface code under local (i.e. single-qubit) noise, we present a simple method to determine the maximum extent to which adapting a surface-code decoder to a noise feature can lead to a performance improvement. Our method is based on a tensor-network decoding algorithm, which uses the syndrome information as

Universal quantum computation can be realised by measuring individual particles in a specially entangled state of many particles, called a universal resource state. This model of quantum computation, called measurement-based quantum computation (MBQC), provides a framework for studying the intrinsic computational power of physical systems. In this thesis I will investigate how universal resource states may arise naturally as ground states of interacting spin systems. In particular, I will descri

In this report I will describe my scientific activities at the Yukawa Institute for Theoretical Physics as an Advanced Future Studies Researcher since my arrival in June 2018.