Related papers: Fast simulation of planar Clifford circuits
Efficiently implementing Clifford circuits is crucial for quantum error correction and quantum algorithms. Linear reversible circuits, equivalent to circuits composed of CNOT gates, have important applications in classical computing. In…
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…
We present a quantum algorithm for sampling random spanning trees from a weighted graph in $\widetilde{O}(\sqrt{mn})$ time, where $n$ and $m$ denote the number of vertices and edges, respectively. Our algorithm has sublinear runtime for…
Efficiently learning expectation values of a quantum state using classical shadow tomography has become a fundamental task in quantum information theory. In a classical shadows protocol, one measures a state in a chosen basis W after it has…
Accurately estimating observables on noisy quantum devices remains a central challenge for near-term quantum algorithms. While quantum error mitigation techniques can reduce noise-induced bias, they often rely on unverifiable assumptions…
Outcome probability estimation via classical methods is an important task for validating quantum computing devices. Outcome probabilities of any quantum circuit can be estimated using Monte Carlo sampling, where the amount of negativity…
Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…
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…
We investigate the problem of evaluating the output probabilities of Clifford circuits with nonstabilizer product input states. First, we consider the case when the input state is mixed, and give an efficient classical algorithm to…
In this work we improve the runtime of recent classical algorithms for strong simulation of quantum circuits composed of Clifford and T gates. The improvement is obtained by establishing a new upper bound on the stabilizer rank of $m$…
We present a discussion of the generalized Clifford group over non-cyclic finite abelian groups. These Clifford groups appear naturally in the theory of topological error correction and abelian anyon models. We demonstrate a generalized…
(Abridged abstract.) In this thesis we introduce new models of quantum computation to study the emergence of quantum speed-up in quantum computer algorithms. Our first contribution is a formalism of restricted quantum operations, named…
Recent studies have highlighted the combination of tensor network methods and the stabilizer formalism as a very effective framework for simulating quantum many-body systems, encompassing areas from ground state to time evolution…
We investigate for which resource states an efficient classical simulation of measurement based quantum computation is possible. We show that the Schmidt--rank width, a measure recently introduced to assess universality of resource states,…
Variational quantum algorithms are considered to be appealing applications of near-term quantum computers. However, it has been unclear whether they can outperform classical algorithms or not. To reveal their limitations, we must seek a…
Stabilizer simulation can efficiently simulate an important class of quantum circuits consisting exclusively of Clifford gates. However, all existing extensions of this simulation to arbitrary quantum circuits including non-Clifford gates…
Classical simulations of quantum systems are notoriously difficult computational problems, with conventional state vector and tensor network methods restricted to quantum systems that feature only a small number of qudits. The recently…
We develop a new approach for distributed distance computation in planar graphs that is based on a variant of the metric compression problem recently introduced by Abboud et al. [SODA'18]. One of our key technical contributions is in…
Output probability distributions of several sub-universal quantum computing models cannot be classically efficiently sampled unless some unlikely consequences occur in classical complexity theory, such as the collapse of the polynomial-time…
In a recent work a quantum error mitigation protocol was applied to the expectation values obtained from circuits on the IBM Eagle quantum processor with up $127$ - qubits with up to $60 \; - \; \mbox{CNOT}$ layers. To benchmark the…