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We propose a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. Once the Ansatz has been decided, the quantum part of the algorithm involves the calculation of two overlap…
Quantum computing has the potential to outperform classical computers and is expected to play an active role in various fields. In quantum machine learning, a quantum computer has been found useful for enhanced feature representation and…
For typical quantum subroutines in the gate-based model of quantum computing, explicit decompositions of circuits in terms of single-qubit and two-qubit entangling gates may exist. However, they often lead to large-depth circuits that are…
Finding solid and practical quantum advantages via noisy quantum devices without error correction is a critical but challenging problem. Conversely, comprehending the fundamental limitations of the state-of-the-art is equally crucial. In…
Demonstrating quantum advantage in machine learning tasks requires navigating a complex landscape of proposed models and algorithms. To bring clarity to this search, we introduce a framework that connects the structure of parametrized…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
Analyzing the impact of noise is of fundamental importance to understand the advantages provided by quantum systems. While the classical simulability of noisy discrete-variable systems is increasingly well understood, noisy bosonic circuits…
We provide an experimental study of the relationship between the action of different classical noises on the dephasing dynamics of a two-level system and the non-Markovianity of the quantum dynamics. The two-level system is encoded in the…
We find a tight upper bound for the classical capacity of quantum thermal noise channels that is within $1/\ln 2$ bits of Holevo's lower bound. This lower bound is achievable using unentangled, classical signal states, namely displaced…
Finding ground states of quantum many-body systems is known to be hard for both classical and quantum computers. As a result, when Nature cools a quantum system in a low-temperature thermal bath, the ground state cannot always be found…
Quantum kernel methods have been widely recognized as one of promising quantum machine learning algorithms that have potential to achieve quantum advantages. In this paper, we theoretically characterize the power of noisy quantum kernels…
Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers due to the extremely high computational cost. Quantum computers promise a solution,…
The biggest challenge that quantum computing and quantum machine learning are currently facing is the presence of noise in quantum devices. As a result, big efforts have been put into correcting or mitigating the induced errors. But, can…
We determine both the quantum and the private capacities of low-noise quantum channels to leading orders in the channel's distance to the perfect channel. It has been an open problem for more than 20 years to determine the capacities of…
A quantum thermodynamic system is described by a Hamiltonian and a list of conserved, non-commuting charges, and a fundamental goal is to determine the minimum energy of the system subject to constraints on the charges. Recently, [Liu et…
We consider situations in which i) Alice wishes to send quantum information to Bob via a noisy quantum channel, ii) Alice has a classical description of the states she wishes to send and iii) Alice can make use of a finite amount of…
Recent work by Bravyi et al. constructs a relation problem that a noisy constant-depth quantum circuit (QNC$^0$) can solve with near certainty (probability $1 - o(1)$), but that any bounded fan-in constant-depth classical circuit (NC$^0$)…
We present a polynomial-time classical algorithm for estimating expectation values of arbitrary observables on typical quantum circuits under any incoherent local noise, including non-unital or dephasing. Although previous research…
Quantum noise or decoherence is a major factor impacting the performance of quantum technologies. On the qubit, an important quantum noise, often relevant in practice, is the thermal noise or generalized amplitude damping noise, describing…
Stabilizer simulation of Clifford quantum circuits - error-correction circuits, Clifford subroutines, etc. - on classical computers has played a central role in our understanding of circuit performance. The stabilizer description, however,…