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Variational Quantum Algorithms are promising candidates for near-term quantum computing, yet they face scalability challenges due to barren plateaus, where gradients vanish exponentially relative to system size. Recent conjectures suggest…
Variational quantum algorithms are believed to be promising for solving computationally hard problems and are often comprised of repeated layers of quantum gates. An example thereof is the quantum approximate optimization algorithm (QAOA),…
We investigate the emergence of quantum complexity and chaos in doped Clifford circuits acting on qudits of odd prime dimension $d$. Using doped Clifford Weingarten calculus and a replica tensor network formalism, we derive exact results…
A general quantum circuit can be simulated classically in exponential time. If it has a planar layout, then a tensor-network contraction algorithm due to Markov and Shi has a runtime exponential in the square root of its size, or more…
We study the implementation of fault-tolerant logical Clifford gates on stabilizer quantum error correcting codes based on their symmetries. Our approach is to map the stabilizer code to a binary linear code, compute its automorphism group,…
Scaling of variational quantum algorithms to large problem sizes requires efficient optimization of random parameterized quantum circuits. For such circuits with uncorrelated parameters, the presence of exponentially vanishing gradients in…
The variational quantum algorithm (VQA) with a parametrized quantum circuit is widely applicable to near-term quantum computing, but its fundamental issues that limit optimization performance have been reported in the literature. For…
Solving optimisation problems is a promising near-term application of quantum computers. Quantum variational algorithms leverage quantum superposition and entanglement to optimise over exponentially large solution spaces using an…
Sampling from the output distribution of chaotic quantum evolutions, and of pseudo-random universal quantum circuits in particular, has been proposed as a prominent milestone for near-term quantum supremacy. The same paper notes that…
Classical simulation of noisy quantum circuits is essential for understanding quantum computing experiments. It enables scalable error characterization, analysis of how noise impacts quantum algorithms, and optimized implementations of…
To successfully perform quantum computations, it is often necessary to first accurately characterize the noise in the underlying hardware. However, it is well known that fundamental limitations prevent the unique identification of the…
With rapid advances in quantum hardware, a central question is whether quantum devices with or without full error correction can outperform classical computers on practically relevant problems. Variational Quantum Algorithms (VQAs) have…
Variational quantum algorithms (VQAs) hold great potentials for near-term applications and are promising to achieve quantum advantage on practical tasks. However, VQAs suffer from severe barren plateau problem as well as have a large…
Shor's algorithm for the prime factorization of numbers provides an exponential speedup over the best known classical algorithms. However, nontrivial practical applications have remained out of reach due to experimental limitations. The…
The conventional circuit paradigm, utilizing a limited number of gates to construct arbitrary quantum circuits, is hindered by significant noise overhead. For instance, the standard gate paradigm employs two CNOT gates for the partial…
The promise of quantum computing to address complex problems requiring high computational resources has long been hindered by the intrinsic and demanding requirements of quantum hardware development. Nonetheless, the current state of…
Classical data encoding is usually treated as a black-box in the oracle-based quantum algorithms. On the other hand, their constructions are crucial for practical algorithm implementations. Here, we open the black-boxes of data encoding and…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
In this research, we create a scalable version of the quantum Fourier transform-based arithmetic circuit to perform addition and subtraction operations on N n-bit unsigned integers encoded in quantum registers, and it is compatible with…
The Quantum Alternating Operator Ansatz (QAOA+) is one of the Variational Quantum Algorithm (VQA) specifically developed to tackle combinatorial optimization problems by exploring the feasible space in search of a target solution. For…