A resource theory of quantum measurements - Guff, Thomas; McMahon, Nathan; Sanders, Yuval R.; Gilchrist, Alexei (Journal of Physics A: Mathematical and Theoretical, 2021)
Resource theories are broad frameworks that capture how useful objects are in performing specific tasks. In this paperwe devise a formal resource theory quantum measurements, focusing on the ability of a measurement to acquire information. The objects of the theory are equivalence classes of positive operatorvalued measures, and the free transformations are changes to a measurement device that can only deteriorate its ability to report information about a physical system. We show that catalysis and purification, protocols that are possible in other resource theories, are impossible in our resource theory for quantum measurements. Standard measures of information gain are shown to be resource monotones, and the resource theory is applied to the task of quantum state discrimination.
CRIS-Team Scopus Importer:2021-05-14
Keywords: Catalysis; Measurement; Quantum; Quantum information; Resource; State discrimination; Theory

Decoding holographic codes with an integer optimization decoder - Harris, Robert J.; Coupe, Elliot; Mcmahon, Nathan A.; Brennen, Gavin K.; Stace, Thomas M. (Physical Review A, 2020)
We develop a most likely error Pauli error decoding algorithm for stabilizer codes based on general purpose integer optimization. Using this decoder we analyze the performance of holographic codes against Pauli errors and find numerical evidence for thresholds against Pauli errors for bulk qubits. We compare the performance of holographic code families of various code rates and find phenomenological Pauli error thresholds ranging from 7% to 16%, depending on the code rate. Additionally we give numerical evidence that specific distance measures of the codes we consider scale polynomially with number of physical qubits.
CRIS-Team WoS Importer:2021-01-15

Error-tolerant quantum convolutional neural networks for symmetry-protected topological phases - Zapletal, Petr; McMahon, Nathan; Hartmann, Michael (Physical Review Research, 2024)
The analysis of noisy quantum states prepared on current quantum computers is getting beyond the capabilities of classical computing. Quantum neural networks based on parametrized quantum circuits, measurements and feed-forward can process large amounts of quantum data to reduce measurement and computational costs of detecting nonlocal quantum correlations. The tolerance of errors due to decoherence and gate infidelities is a key requirement for the application of quantum neural networks on near-term quantum computers. Here we construct quantum convolutional neural networks (QCNNs) that can, in the presence of incoherent errors, recognize different symmetry-protected topological phases of generalized cluster-Ising Hamiltonians from one another as well as from topologically trivial phases. Using matrix product state simulations, we show that the QCNN output is robust against symmetry-breaking errors below a threshold error probability and against symmetry-preserving errors provided the error channel is invertible. This is in contrast to string order parameters and the output of previously designed QCNNs, which vanish in the presence of any symmetry-breaking errors. To facilitate the implementation of the QCNNs on near-term quantum computers, the QCNN circuits can be shortened from logarithmic to constant depth in system size by performing a large part of the computation in classical postprocessing. These constant-depth QCNNs reduce sample complexity exponentially with system size in comparison to the direct sampling using local Pauli measurements.
CRIS-Team Scopus Importer:2024-08-09

Parallel decoding of multiple logical qubits in tensor-network codes - Farrelly, Terry; Milicevic, Nicholas; Harris, Robert J.; Mcmahon, Nathan A.; Stace, Thomas M. (Physical Review A, 2022)
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. Holographic codes are interesting examples of tensor-network codes, so we first test out this parallel decoding strategy on the max-rate holographic Steane (heptagon) code. For holographic codes with a constant number of logical qubits, the 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. We then calculate the bulk threshold (the threshold for logical qubits a fixed distance from the code center) under depolarizing noise for the max-rate holographic Steane code to be 9.4%. We also introduce some further holographic error-correcting codes and calculate their thresholds under depolarizing noise. One example is based on an 11-qubit code due to Gottesman, which has asymptotic rate 0.114 and threshold 13.8%. Another code we consider is an asymptotically zero-rate holographic code, which performs extremely well under dephasing noise in the X, Y, or Z basis with a threshold of 50%.
CRIS-Team WoS Importer:2022-06-24

Realizing quantum convolutional neural networks on a superconducting quantum processor to recognize quantum phases - Herrmann, Johannes; Llima, Sergi Masot; Remm, Ants; Zapletal, Petr; McMahon, Nathan; Scarato, Colin; Swiadek, Francois; Andersen, Christian Kraglund; Hellings, Christoph; Krinner, Sebastian; Lacroix, Nathan; Lazar, Stefania; et al. (Nature Communications, 2022)
Quantum neural networks could help analysing the output of quantum computers and quantum simulators of growing complexity. Here, the authors use a 7-qubit superconducting quantum processor to show how a quantum convolutional neural network can correctly recognise the phase of a quantum many-body state.
CRIS-Team WoS Importer:2022-07-29

Tensor-Network Codes - Farrelly, Terry; Harris, Robert J.; McMahon, Nathan; Stace, Thomas M. (Physical Review Letters, 2021)
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 show that, for holographic codes, the exact tensor-network decoder (with no bond-dimension truncation) has polynomial complexity in the number of physical qubits, even for locally correlated noise, making this the first efficient decoder for holographic codes against Pauli noise and, also, a rare example of a decoder that is both efficient and exact.
CRIS-Team WoS Importer:2021-08-06