arXiv subjects

Michael Vasmer

Publications and source records attributed to Michael Vasmer.

24 records · Page 2Linked to original sources

arXiv2021

Universal Fault-Tolerant Quantum Computing with Stabiliser Codes

The quantum logic gates used in the design of a quantum computer should be both universal, meaning arbitrary quantum computations can be performed, and fault-tolerant, meaning the gates keep errors from cascading out of control. A number of no-go theorems constrain the ways in which a set of fault-tolerant logic gates can be universal. These theorems are very restrictive, and conventional wisdom holds that a universal fault-tolerant logic gate set cannot be implemented natively, requiring us to use costly distillation procedures for quantum computation. Here, we present a general framework for universal fault-tolerant logic with stabiliser codes, together with a no-go theorem that reveals the very broad conditions constraining such gate sets. Our theorem applies to a wide range of stabiliser code families, including concatenated codes and conventional topological stabiliser codes such as the surface code. The broad applicability of our no-go theorem provides a new perspective on how the constraints on universal fault-tolerant gate sets can be overcome. In particular, we show how non-unitary implementations of logic gates provide a general approach to circumvent the no-go theorem, and we present a rich landscape of constructions for logic gate sets that are both universal and fault-tolerant. That is, rather than restricting what is possible, our no-go theorem provides a signpost to guide us to new, efficient architectures for fault-tolerant quantum computing.

quant-ph↗

arXiv2021

Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer

Photonics is the platform of choice to build a modular, easy-to-network quantum computer operating at room temperature. However, no concrete architecture has been presented so far that exploits both the advantages of qubits encoded into states of light and the modern tools for their generation. Here we propose such a design for a scalable and fault-tolerant photonic quantum computer informed by the latest developments in theory and technology. Central to our architecture is the generation and manipulation of three-dimensional hybrid resource states comprising both bosonic qubits and squeezed vacuum states. The proposal enables exploiting state-of-the-art procedures for the non-deterministic generation of bosonic qubits combined with the strengths of continuous-variable quantum computation, namely the implementation of Clifford gates using easy-to-generate squeezed states. Moreover, the architecture is based on two-dimensional integrated photonic chips used to produce a qubit cluster state in one temporal and two spatial dimensions. By reducing the experimental challenges as compared to existing architectures and by enabling room-temperature quantum computation, our design opens the door to scalable fabrication and operation, which may allow photonics to leap-frog other platforms on the path to a quantum computer with millions of qubits.

quant-ph↗

arXiv2021

Cellular automaton decoders for topological quantum codes with noisy measurements and beyond

We propose an error correction procedure based on a cellular automaton, the sweep rule, which is applicable to a broad range of codes beyond topological quantum codes. For simplicity, however, we focus on the three-dimensional (3D) toric code on the rhombic dodecahedral lattice with boundaries and prove that the resulting local decoder has a non-zero error threshold. We also numerically benchmark the performance of the decoder in the setting with measurement errors using various noise models. We find that this error correction procedure is remarkably robust against measurement errors and is also essentially insensitive to the details of the lattice and noise model. Our work constitutes a step towards finding simple and high-performance decoding strategies for a wide range of quantum low-density parity-check codes.

quant-ph↗

arXiv2020

Single-shot error correction of three-dimensional homological product codes

Single-shot error correction corrects data noise using only a single round of noisy measurements on the data qubits, removing the need for intensive measurement repetition. We introduce a general concept of confinement for quantum codes, which roughly stipulates qubit errors cannot grow without triggering more measurement syndromes. We prove confinement is sufficient for single-shot decoding of adversarial errors and linear confinement is sufficient for single-shot decoding of local stochastic errors. Further to this, we prove that all three-dimensional homological product codes exhibit confinement in their $X$-components and are therefore single-shot for adversarial phase-flip noise. For local stochastic phase-flip noise, we numerically explore these codes and again find evidence of single-shot protection. Our Monte Carlo simulations indicate sustainable thresholds of $3.08(4)\%$ and $2.90(2)\%$ for 3D surface and toric codes respectively, the highest observed single-shot thresholds to date. To demonstrate single-shot error correction beyond the class of topological codes, we also run simulations on a randomly constructed 3D homological product code.

quant-ph↗

arXiv2019

Machine learning logical gates for quantum error correction

Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure which generates logical operations given known encoding and correcting procedures. Our technique is to use variational circuits for learning both the logical gates and the physical operations implementing them. This procedure can be implemented on near-term quantum computers via quantum process tomography. It enables automatic discovery of logical gates from analytically designed error correcting codes and can be extended to error correcting codes found by numerical optimizations. We test the procedure by simulation on classical computers on small quantum codes of four qubits to fifteen qubits and show that it finds most logical gates known in the current literature. Additionally, it generates logical gates not found in the current literature for the [[5,1,2]] code, the [[6,3,2]] code, and the [[8,3,2]] code.

quant-ph↗

arXiv2019

Three-dimensional surface codes: Transversal gates and fault-tolerant architectures

One of the leading quantum computing architectures is based on the two-dimensional (2D) surface code. This code has many advantageous properties such as a high error threshold and a planar layout of physical qubits where each physical qubit need only interact with its nearest neighbours. However, the transversal logical gates available in 2D surface codes are limited. This means that an additional (resource intensive) procedure known as magic state distillation is required to do universal quantum computing with 2D surface codes. Here, we examine three-dimensional (3D) surface codes in the context of quantum computation. We introduce a picture for visualizing 3D surface codes which is useful for analysing stacks of three 3D surface codes. We use this picture to prove that the $CZ$ and $CCZ$ gates are transversal in 3D surface codes. We also generalize the techniques of 2D surface code lattice surgery to 3D surface codes. We combine these results and propose two quantum computing architectures based on 3D surface codes. Magic state distillation is not required in either of our architectures. Finally, we show that a stack of three 3D surface codes can be transformed into a single 3D color code (another type of quantum error-correcting code) using code concatenation.

quant-ph↗