Related papers: Strict Hierarchy for Quantum Channel Certification…

Quantum circuit equivalence checking asks whether two circuits implement the same unitary. It guarantees compiler correctness and safe optimization, yet most existing approaches scale exponentially with the number of qubits or the circuit…

We propose a quantum soft-covering problem for a given general quantum channel and one of its output states, which consists in finding the minimum rank of an input state needed to approximate the given channel output. We then prove a…

Given the ability to apply an unknown quantum channel acting on a $d$-dimensional system, we develop a quantum algorithm for transforming its singular values. The spectrum of a quantum channel as a superoperator is naturally tied to its…

We introduce a notion of the quantum query complexity of a certificate structure. This is a formalisation of a well-known observation that many quantum query algorithms only require the knowledge of the disposition of possible certificates…

We analyze the quantum capacity of a unital quantum channel, using ideas from the proof of near-optimality of Petz recovery map [Barnum and Knill 2000] and give an upper bound on the quantum capacity in terms of regularized output $2$-norm…

We generalise some well-known graph parameters to operator systems by considering their underlying quantum channels. In particular, we introduce the quantum complexity as the dimension of the smallest co-domain Hilbert space a quantum…

Tradeoffs between the information rate and fidelity of quantum error-correcting codes are discussed. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a general completely…

The purpose of this work is to extend the result of previous papers quant-ph/9611023, quant-ph/9703013 to quantum channels with additive constraints onto the input signal, by showing that the capacity of such channel is equal to the…

We initiate the study of parameterized complexity of $\textsf{QMA}$ problems in terms of the number of non-Clifford gates in the problem description. We show that for the problem of parameterized quantum circuit satisfiability, there exists…

In this work, we analyze the local certification of unitary quantum channels, which is a natural extension of quantum hypothesis testing. A particular case of a quantum channel operating on two systems corresponding to product states at the…

We give asymptotically converging semidefinite programming hierarchies of outer bounds on bilinear programs of the form $\mathrm{Tr}\big[M(X\otimes Y)\big]$, maximized with respect to semidefinite constraints on $X$ and $Y$. Applied to the…

In this report we study certification of quantum measurements, which can be viewed as the extension of quantum hypotheses testing. This extension involves also the study of the input state and the measurement procedure. Here, we will be…

We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize quantum…

What is the ultimate performance for discriminating two arbitrary quantum channels acting on a finite-dimensional Hilbert space? Here we address this basic question by deriving a general and fundamental lower bound. More precisely, we…

We show that it is possible for the so-called weak locking capacity of a quantum channel [Guha et al., PRX 4:011016, 2014] to be much larger than its private capacity. Both reflect different ways of capturing the notion of reliable…

The minimum accuracy heuristic evaluates quantum feature maps without requiring full quantum support vector machine (QSVM) training. However, the original formulation is computationally expensive, restricted to balanced datasets, and lacks…

Security proofs in quantum cryptography rely on conditional entropies. In a many-round protocol, their estimation is a challenging task; one must account for the most general attacks by an eavesdropper, including those that are not…

The ability to characterise and discern quantum channels is a crucial aspect of noisy quantum technologies. In this work, we explore the problem of distinguishing quantum channels when limited to sub-exponential resources, framed as von…

We prove a new lower bound for the unitary synthesis problem in the so-called 1.5-query setting. Our analysis establishes that any attempt to implement arbitrary n-qubit unitaries via limited oracle access requires resources that exceed the…

Deep neural networks (DNNs) enable high performance across domains but remain vulnerable to adversarial perturbations, limiting their use in safety-critical settings. Here, we introduce two quantum-optimization-based models for robust…