Related papers: Quon Classical Simulation: Unifying Cliffords, Mat…
We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modelled classically. This question is useful for providing upper bounds on fault tolerant thresholds, and for understanding…
Concordant computation is a circuit-based model of quantum computation for mixed states, that assumes that all correlations within the register are discord-free (i.e. the correlations are essentially classical) at every step of the…
We employ quantum circuit learning to simulate quantum field theories (QFTs). Typically, when simulating QFTs with quantum computers, we encounter significant challenges due to the technical limitations of quantum devices when implementing…
We introduce an enhanced technique for strong classical simulation of quantum circuits which combines the `sum-of-stabilisers' method with an automated simplification strategy based on the ZX-calculus. Recently it was shown that quantum…
In recent years, the number of hybrid algorithms that combine quantum and classical computations has been continuously increasing. These two approaches to computing can mutually enhance each others' performances thus bringing the promise of…
The Clifford hierarchy is a foundational concept for universal quantum computation (UQC). It was introduced to show that UQC can be realized via quantum teleportation, given access to certain standard resources. While the full structure of…
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…
Efficiently simulating quantum circuits on classical computers is a fundamental challenge in quantum computing. This paper presents a novel theoretical approach that achieves substantial speedups over existing simulators for a wide class of…
Hamiltonian simulation is a key quantum algorithm for modeling complex systems. To implement a Hamiltonian simulation, it is typically decomposed into a list of Pauli strings, each corresponds to an RZ rotation gate with many Clifford…
Classical simulations of quantum circuits are essential for verifying and benchmarking quantum algorithms, particularly for large circuits, where computational demands increase exponentially with the number of qubits. Among available…
We study the computational power of unitary Clifford circuits with solely magic state inputs (CM circuits), supplemented by classical efficient computation. We show that CM circuits are hard to classically simulate up to multiplicative…
Recent advancements have highlighted the limitations of current quantum systems, particularly the restricted number of qubits available on near-term quantum devices. This constraint greatly inhibits the range of applications that can…
It is well known that a quantum circuit on $N$ qubits composed of Clifford gates with the addition of $k$ non Clifford gates can be simulated on a classical computer by an algorithm scaling as $\text{poly}(N)\exp(k)$[1]. We show that, for a…
We present elementary mappings between classical lattice models and quantum circuits. These mappings provide a general framework to obtain efficiently simulable quantum gate sets from exactly solvable classical models. For example, we…
Parallel operations in conventional computing have proven to be an essential tool for efficient and practical computation, and the story is not different for quantum computing. Indeed, there exists a large body of works that study…
In the recent years, numerous research advancements have extended the limit of classical simulation of quantum algorithms. Although, most of the state-of-the-art classical simulators are only limited to binary quantum systems, which…
We develop and analyze a method for simulating quantum circuits on classical computers by representing quantum states as rooted tree tensor networks. Our algorithm first determines a suitable, fixed tree structure adapted to the expected…
Classical simulation is essential in quantum algorithm development and quantum device verification. With the increasing complexity and diversity of quantum circuit structures, existing classical simulation algorithms need to be improved and…
The scarcity of qubits is a major obstacle to the practical usage of quantum computers in the near future. To circumvent this problem, various circuit knitting techniques have been developed to partition large quantum circuits into…
We propose to represent both $n$--qubits and quantum gates acting on them as elements in the complex Clifford algebra defined on a complex vector space of dimension $2n.$ In this framework, the Dirac formalism can be realized in…