Related papers: Phase space simulation method for quantum computat…
The Wigner function of quantum systems is an effective instrument to construct the approximate classical description of the systems for which the classical approximation is possible. During the last time, the Wigner function formalism is…
The quantum state of a system of qubits can be represented by a Wigner function on a discrete phase space, each axis of the phase space taking values in a finite field. Within this framework, we show that one can make sense of the notion of…
For a quantum computer acting on d-dimensional systems, we analyze the computational power of circuits wherein stabilizer operations are perfect and we allow access to imperfect non-stabilizer states or operations. If the noise rate…
We demonstrate that a tensor product structure could be obtained by introducing pseudorandom phase sequences into classical fields with two orthogonal modes. Using classical fields modulated with pseudorandom phase sequences, we discuss…
Quantum circuit simulation is paramount to the verification and optimization of quantum algorithms, and considerable research efforts have been made towards efficient simulators. While circuits often contain high-level gates such as oracles…
We give a pair of algorithms that efficiently learn a quantum state prepared by Clifford gates and $O(\log n)$ non-Clifford gates. Specifically, for an $n$-qubit state $|\psi\rangle$ prepared with at most $t$ non-Clifford gates, our…
Stabilizer states along with Clifford manipulations (unitary transformations and measurements) thereof -- despite being efficiently simulable on a classical computer -- are an important tool in quantum information processing, with…
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…
A unification of the set of quasiprobability representations using the mathematical theory of frames was recently developed for quantum systems with finite-dimensional Hilbert spaces, in which it was proven that such representations require…
Motivated by their necessity for most fault-tolerant quantum computation schemes, we formulate a resource theory for magic states. We first show that robustness of magic is a well-behaved magic monotone that operationally quantifies the…
In this paper we study reusable magic states. These states are a special subset of the standard magic states. Once distilled, reusable magic states can be used, repeatedly, to apply some unitary U. Given this property, reusable magic states…
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…
This paper builds on the idea of simulating stabiliser circuits through transformations of quadratic form expansions. This is a representation of a quantum state which specifies a formula for the expansion in the standard basis, describing…
We present a quantum-classical hybrid algorithm that simulates electronic structures of periodic systems such as ground states and quasiparticle band structures. By extending the unitary coupled cluster (UCC) theory to describe crystals in…
We present an iterative method to solve the multipartite quantum state estimation problem. We demonstrate convergence for any informationally complete set of generalized quantum measurements in every finite dimension. Our method exhibits…
Polarization quasiprobability distribution defined in the Stokes space shares many important properties with the Wigner function for the position and momentum. Most notably, they both give correct one-dimensional marginal probability…
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…
Efficient simulation of quantum computers relies on understanding and exploiting the properties of quantum states. This is the case for methods such as tensor networks, based on entanglement, and the tableau formalism, which represents…
An important step in building a quantum computer is calibrating experimentally implemented quantum gates to produce operations that are close to ideal unitaries. The calibration step involves estimating the systematic errors in gates and…
We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum…