Mio Murao | LIP6 - Équipe QI

Mio Murao - A Higher-Order Quantum Algorithm for Learning Singular-Value Moments of Quantum Channels

Wed, 25 Feb 2026 00:00:00 +0000

A Higher-Order Quantum Algorithm for Learning Singular-Value Moments of Quantum Channels

Ce séminaire, donné par Mio Murao, aura lieu le 25 February 2026, à 13:0. Il aura lieu en salle 25-26/105.

Vous trouverez un plan du campus ici.

Résumé

Efficiently learning properties of quantum objects is a widely anticipated application of quantum computers. We develop quantum learning algorithms, based on higher-order quantum computation, that take an unknown quantum channel as input. In this framework, a quantum computer acquires quantum data through black-box queries and computes target properties coherently, without reconstructing a full classical description of the channel. We present a new fully quantum algorithm for estimating the singular-value moments of an unknown quantum channel by introducing a block-encoding scheme for its Liouville representation accessed via a black box. This algorithm can be viewed as implementing a measurement device powered by quantum computation. Reference : R. Niwa, Z. M. Rossi, P. Taranto and M. Murao, arXiv 2506.24112

Higher-order quantum computing with known input states

Mon, 15 Dec 2025 00:00:00 +0000

88 pages, 27 figures. A concise overview of the main results is provided in the Sec. 2 (Summary of main results) for a quick read

Exponential separation in quantum query complexity of the quantum switch with respect to simulations with standard quantum circuits

Wed, 10 Dec 2025 00:00:00 +0000

Quantum theory is consistent with a computational model permitting black-box operations to be applied in an indefinite causal order, going beyond the standard circuit model of computation. The quantum switch – the simplest such example – has been shown to provide numerous information-processing advantages. Here, we prove that the action of the quantum switch on two $n$-qubit quantum channels cannot be simulated deterministically and exactly by any causally ordered quantum circuit that uses $M$ calls to one channel and one call to the other, if $M \leq \max(2, 2^n-1)$. This demonstrates an exponential separation in quantum query complexity of indefinite causal order compared to standard quantum circuits.

Simulating the quantum switch with quantum circuits is computationally hard

Thu, 20 Nov 2025 00:00:00 +0000

Higher-order transformations acting on input quantum channels in an indefinite causal order—such as the quantum switch—cannot be described by quantum circuits using the same number of calls to the input channels. A natural question is whether they can be simulated, i.e., whether their action can be exactly and deterministically reproduced by a quantum circuit with more calls to the input channels. Here, we prove that the quantum switch acting on two n-qubit channels cannot be simulated by any quantum circuit using k calls to one channel and one to the other, if k < 2^n. This establishes an exponential separation in quantum query complexity between processes with indefinite causal order and quantum circuits. Moreover, even with one extra call to both input channels, such a simulation remains impossible. We further demonstrate the robustness of this separation by extending the result to probabilistic and approximate simulations scenarios.

Higher-Order Quantum Operations

Mon, 17 Mar 2025 00:00:00 +0000

An operational description of quantum phenomena concerns developing models that describe experimentally observed behaviour. $\textit{Higher-order quantum operations}\unicode{x2014}$quantum operations that transform quantum operations$\unicode{x2014}$are fundamental to modern quantum theory, extending beyond basic state preparations, evolutions, and measurements described by the Born rule. These operations naturally emerge in quantum circuit architectures, correlated open dynamics, and investigations of quantum causality, to name but a few fields of application. This Review Article provides both a pedagogical introduction to the framework of higher-order quantum operations and a comprehensive survey of current literature, illustrated through physical examples. We conclude by identifying open problems and future research directions in this rapidly evolving field.

Can the quantum switch be deterministically simulated?

Sun, 06 Oct 2024 00:00:00 +0000

Higher-order transformations that act on a certain number of input quantum channels in an indefinite causal order - such as the quantum switch - cannot be described by standard quantum circuits that use the same number of calls of the input quantum channels. However, the question remains whether they can be simulated, i.e., whether their action on their input channels can be deterministically reproduced, for all arbitrary inputs, by a quantum circuit that uses a larger number of calls of the input channels. Here, we prove that when only one extra call of each input channel is available, the quantum switch cannot be simulated by any quantum circuit. We demonstrate that this result is robust by showing that, even when probabilistic and approximate simulations are considered, higher-order transformations that are close to the quantum switch can be at best simulated with a probability strictly less than one. This result stands in stark contrast with the known fact that, when the quantum switch acts exclusively on unitary channels, its action can be simulated.

Exponential separation in quantum query complexity of the quantum switch with respect to simulations with standard quantum circuits

Sun, 06 Oct 2024 00:00:00 +0000

Multicopy quantum state teleportation with application to storage and retrieval of quantum programs

Sat, 21 Sep 2024 00:00:00 +0000

This work considers a teleportation task for Alice and Bob in a scenario where Bob cannot perform corrections. In particular, we analyse the task of \textit{multicopy state teleportation}, where Alice has $k$ identical copies of an arbitrary unknown $d$-dimensional qudit state $\vert\psi\rangle$ to teleport a single copy of $\vert\psi\rangle$ to Bob using a maximally entangled two-qudit state shared between Alice and Bob without Bob’s correction. Alice may perform a joint measurement on her half of the entangled state and the $k$ copies of $\vert\psi\rangle$. We prove that the maximal probability of success for teleporting the exact state $\vert\psi\rangle$ to Bob is $p(d,k)=\frac{k}{d(k-1+d)}$ and present an explicit protocol to attain this performance. Then, by utilising $k$ copies of an arbitrary target state $\vert\psi\rangle$, we show how the multicopy state teleportation protocol can be employed to enhance the success probability of storage and retrieval of quantum programs, which aims to universally retrieve the action of an arbitrary quantum channel that is stored in a state. Our proofs make use of group representation theory methods, which may find applications beyond the problems addressed in this work.

The quantum switch is uniquely defined by its action on unitary operations

Tue, 07 Nov 2023 00:00:00 +0000

The quantum switch is a quantum process that creates a coherent control between different unitary operations, which is often described as a quantum process which transforms a pair of unitary operations ( U 1 , U 2 ) into a controlled unitary operation that coherently applies them in different orders as |0><0| \otimes U_1U_2 + |1><1| \otimes U_2U_1 . This description, however, does not directly define its action on non-unitary operations. The action of the quantum switch on non-unitary operations is then chosen to be a ``natural’’ extension of its action on unitary operations. In general, the action of a process on non-unitary operations is not uniquely determined by its action on unitary operations. It may be that there could be a set of inequivalent extensions of the quantum switch for non-unitary operations. We prove, however, that the natural extension is the only possibility for the quantum switch for the 2-slot case. In other words, contrary to the general case, the action of the quantum switch on non-unitary operations (as a linear and completely CP preserving supermap) is completely determined by its action on unitary operations. We also discuss the general problem of when the complete description of a quantum process is uniquely determined by its action on unitary operations and identify a set of single-slot processes which are completely defined by their action on unitary operations.

Characterising the Hierarchy of Multi-time Quantum Processes with Classical Memory

Fri, 21 Jul 2023 00:00:00 +0000

Memory is the fundamental form of temporal complexity: when present but uncontrollable, it manifests as non-Markovian noise; conversely, if controllable, memory can be a powerful resource for information processing. Memory effects arise from/are transmitted via interactions between a system and its environment; as such, they can be either classical or quantum in nature. From a practical standpoint, quantum processes with classical memory promise near-term applicability: they are more powerful than their memoryless counterpart, yet at the same time can be controlled over significant timeframes without being spoiled by decoherence. However, despite practical and foundational value, apart from simple two-time scenarios, the distinction between quantum and classical memory remains unexplored. We first analyse various physically-motivated candidates regarding a suitable definition for classical memory that lead to remarkably distinct phenomena in the multi-time setting. Subsequently, we systematically characterise the hierarchy of multi-time memory effects in quantum mechanics, many levels of which collapse in the two-time setting, thereby making our results genuinely multi-time phenomena.