Mehdi Mhalla
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View article: Classical and Quantum Query Complexity of Boolean Functions under Indefinite Causal Order
Classical and Quantum Query Complexity of Boolean Functions under Indefinite Causal Order Open
Computational models typically assume that operations are applied in a fixed sequential order. In recent years several works have looked at relaxing this assumption, considering computations without any fixed causal structure and showing t…
View article: Quantum query complexity of Boolean functions under indefinite causal order
Quantum query complexity of Boolean functions under indefinite causal order Open
The standard model of quantum circuits assumes operations are applied in a fixed sequential “causal” order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant at…
View article: Factory-based fault-tolerant preparation of quantum polar codes encoding one logical qubit
Factory-based fault-tolerant preparation of quantum polar codes encoding one logical qubit Open
International audience
View article: A blindness property of the Min-Sum decoding for the toric code
A blindness property of the Min-Sum decoding for the toric code Open
Kitaev's toric code is one of the most prominent models for fault-tolerant quantum computation, currently regarded as the leading solution for connectivity constrained quantum technologies. Significant effort has been recently devoted to i…
View article: Improving social welfare in non-cooperative games with different types of quantum resources
Improving social welfare in non-cooperative games with different types of quantum resources Open
We investigate what quantum advantages can be obtained in multipartite non-cooperative games by studying how different types of quantum resources can lead to new Nash equilibria and improve social welfare — a measure of the quality of an e…
View article: Check-Agnosia based Post-Processor for Message-Passing Decoding of Quantum LDPC Codes
Check-Agnosia based Post-Processor for Message-Passing Decoding of Quantum LDPC Codes Open
The inherent degeneracy of quantum low-density parity-check codes poses a challenge to their decoding, as it significantly degrades the error-correction performance of classical message-passing decoders. To improve their performance, a pos…
View article: Vertex-Minor Universal Graphs for Generating Entangled Quantum Subsystems
Vertex-Minor Universal Graphs for Generating Entangled Quantum Subsystems Open
We study the notion of k-stabilizer universal quantum state, that is, an n-qubit quantum state, such that it is possible to induce any stabilizer state on any k qubits, by using only local operations and classical communications. These sta…
View article: Check-Agnosia based Post-Processor for Message-Passing Decoding of Quantum LDPC Codes
Check-Agnosia based Post-Processor for Message-Passing Decoding of Quantum LDPC Codes Open
The inherent degeneracy of quantum low-density parity-check codes poses a challenge to their decoding, as it significantly degrades the error-correction performance of classical message-passing decoders. To improve their performance, a pos…
View article: Fault-tolerant preparation of quantum polar codes encoding one logical qubit
Fault-tolerant preparation of quantum polar codes encoding one logical qubit Open
International audience
View article: Small k-pairable states
Small k-pairable states Open
A $k$-pairable $n$-qubit state is a resource state that allows Local Operations and Classical Communication (LOCC) protocols to generate EPR-pairs among any $k$-disjoint pairs of the $n$ qubits. Bravyi et al. introduced a family of $k$-pai…
View article: Improved Rate Fault-Tolerant Preparation of Q<sub>1</sub> Code-States
Improved Rate Fault-Tolerant Preparation of Q<sub>1</sub> Code-States Open
International audience
View article: Layered Decoding of Quantum LDPC Codes
Layered Decoding of Quantum LDPC Codes Open
International audience
View article: Layered Decoding of Quantum LDPC Codes
Layered Decoding of Quantum LDPC Codes Open
We address the problem of performing message-passing-based decoding of quantum LDPC codes under hardware latency limitations. We propose a novel way to do layered decoding that suits quantum constraints and outperforms flooded scheduling, …
View article: Factory-based Fault-tolerant Preparation of Quantum Polar Codes Encoding One logical Qubit
Factory-based Fault-tolerant Preparation of Quantum Polar Codes Encoding One logical Qubit Open
A fault-tolerant way to prepare logical code-states of Q1 codes, i.e., quantum polar codes encoding one qubit, has been recently proposed. The fault tolerance therein is guaranteed by an error detection gadget, where if an error is detecte…
View article: Quantum Query Complexity of Boolean Functions under Indefinite Causal Order
Quantum Query Complexity of Boolean Functions under Indefinite Causal Order Open
The standard model of quantum circuits assumes operations are applied in a fixed sequential "causal" order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant at…
View article: A formalization of the CHSH inequality and Tsirelson's upper-bound in Isabelle/HOL
A formalization of the CHSH inequality and Tsirelson's upper-bound in Isabelle/HOL Open
We present a formalization of several fundamental notions and results from Quantum Information theory, including density matrices and projective measurements, along with the proof that the local hidden-variable hypothesis advocated by Eins…
View article: A Strict Constrained Superposition Calculus for Graphs
A Strict Constrained Superposition Calculus for Graphs Open
We propose a superposition-based proof procedure to reason on equational first order formulas defined over graphs. First, we introduce the considered graphs that are directed labeled graphs with lists of roots standing for pins or interfac…
View article: Improving social welfare in non-cooperative games with different types of quantum resources
Improving social welfare in non-cooperative games with different types of quantum resources Open
We investigate what quantum advantages can be obtained in multipartite non-cooperative games by studying how different types of quantum resources can lead to new Nash equilibria and improve social welfare -- a measure of the quality of an …
View article: Stabilizer Inactivation for Message-Passing Decoding of Quantum LDPC Codes
Stabilizer Inactivation for Message-Passing Decoding of Quantum LDPC Codes Open
International audience
View article: Fault-Tolerant Preparation of Quantum Polar Codes Encoding One Logical Qubit
Fault-Tolerant Preparation of Quantum Polar Codes Encoding One Logical Qubit Open
This paper explores a new approach to fault-tolerant quantum computing (FTQC), relying on quantum polar codes. We consider quantum polar codes of Calderbank-Shor-Steane type, encoding one logical qubit, which we refer to as $\mathcal{Q}_1$…
View article: Shadow Pauli Flow: Characterising Determinism in MBQCs involving Pauli Measurements
Shadow Pauli Flow: Characterising Determinism in MBQCs involving Pauli Measurements Open
We introduce a new characterisation of determinism in Measurement-Based Quantum Computing (MBQC). The one-way model consists in performing local measurements over a large entangled state represented by a graph. The ability to perform an ov…
View article: Stabilizer Inactivation for Message-Passing Decoding of Quantum LDPC Codes
Stabilizer Inactivation for Message-Passing Decoding of Quantum LDPC Codes Open
We propose a post-processing method for message-passing (MP) decoding of CSS quantum LDPC codes, called stabilizer-inactivation (SI). It relies on inactivating a set of qubits, supporting a check in the dual code, and then running the MP d…
View article: Quantum Polarization of Qudit Channels
Quantum Polarization of Qudit Channels Open
We provide a generalization of quantum polar codes to quantum channels with qudit-input, achieving the symmetric coherent information of the channel. Our scheme relies on a channel combining and splitting construction, where a two-qudit un…
View article: Multilevel polarization for quantum Channels
Multilevel polarization for quantum Channels Open
Recently, a purely quantum version of polar codes has been proposed in~\cite{DGMS19} based on a quantum channel combining and splitting procedure, where a randomly chosen two-qubit Clifford unitary acts as a channel combining operation. He…
View article: A Superposition-Based Calculus for Quantum Diagrammatic Reasoning and Beyond
A Superposition-Based Calculus for Quantum Diagrammatic Reasoning and Beyond Open
We introduce a class of rooted graphs which allows one to encode various kinds of classical or quantum circuits. We then follow a set-theoretic approach to define rewrite systems over the considered graphs and propose a new complete Superp…
View article: Quantum projective measurements and the CHSH inequality in Isabelle/HOL
Quantum projective measurements and the CHSH inequality in Isabelle/HOL Open
We present a formalization in Isabelle/HOL of quantum projective measurements, a class of measurements involving orthogonal projectors that is frequently used in quantum computing. We also formalize the CHSH inequality, a result that holds…
View article: Polarization of Quantum Channels Using Clifford-Based Channel Combining
Polarization of Quantum Channels Using Clifford-Based Channel Combining Open
International audience
View article: Coherent control and distinguishability of quantum channels via PBS-diagrams
Coherent control and distinguishability of quantum channels via PBS-diagrams Open
We introduce a graphical language for coherent control of general quantum channels inspired by practical quantum optical setups involving polarising beam splitters (PBS). As standard completely positive trace preserving maps are known not …