Related papers: Phased outcome-complete simulation
Quantum computing will change the way we tackle certain problems. It promises to dramatically speed-up many chemical, financial, and machine-learning applications. However, to capitalize on those promises, complex design flows composed of…
Bravyi and Gosset recently gave classical simulation algorithms for quantum circuits dominated by Clifford operations. These algorithms scale exponentially with the number of T-gate in the circuit, but polynomially in the number of qubits…
Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum error-correcting code. Physical noise sources are efficiently approximated by random insertions of Pauli operators. For a single qubit,…
We present the generalization of the CNC formalism, based on closed and noncontextual sets of Pauli observables, to the setting of odd-prime-dimensional qudits. By introducing new CNC-type phase space point operators, we construct a…
It is important for performance studies in quantum technologies to analyze quantum circuits in the presence of noise. We introduce an error probability tensor, a tool to track generalized Pauli error statistics of qudits within quantum…
Equivalence checking of quantum circuits is an essential element in quantum program compilation, in which a quantum program can be synthesized into different quantum circuits that may vary in the number of qubits, initialization…
Mid-circuit measurements and measurement-controlled gates are supported by an increasing number of quantum hardware platforms and will become more relevant as an essential building block for quantum error correction. However, mid-circuit…
Efficient and effective compilation of quantum circuits remains an important aspect of executing quantum programs. In this paper, we propose a generic compilation framework particularly suitable for limited connectivity, that extends many…
We address the problem of estimating the phase phi given N copies of the phase rotation gate u(phi). We consider, for the first time, the optimization of the general case where the circuit consists of an arbitrary input state, followed by…
We present a method that outputs a sequence of simple unitary operations to prepare a given quantum state that is a generalized coherent state. Our method takes as inputs the expectation values of some relevant observables on the state to…
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…
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 present an algorithm for verifying the local unitary (LU) equivalence of graph and stabilizer states. Our approach reduces the problem to solving a system of linear equations in modular arithmetic. Furthermore, we demonstrate that any LU…
Quantum magic is a necessary resource for quantum computers to be not efficiently simulable by classical computers. Previous results have linked the amount of quantum magic, characterized by the number of $T$ gates or stabilizer rank, to…
We study the complexity of learning quantum states in various models with respect to the stabilizer formalism and obtain the following results: - We prove that $\Omega(n)$ $T$-gates are necessary for any Clifford+$T$ circuit to prepare…
We develop classical simulation algorithms for adaptive quantum circuits that produce states with low levels of ``magic'' (i.e., non-stabilizerness). These algorithms are particularly well-suited to circuits with high rates of Pauli…
We present an algorithm for efficiently simulating a quantum circuit in the graph formalism. In the graph formalism, we represent states as a linear combination of graphs with Clifford operations on their vertices. We show how a…
We start by studying the subgroup structures underlying stabilizer circuits. Then we apply our results to provide two normal forms for stabilizer circuits. These forms are computed by induction using simple conjugation rules in the Clifford…
We propose an extension to the Pauli stabiliser formalism that includes fractional $2\pi/N$ rotations around the $Z$ axis for some integer $N$. The resulting generalised stabiliser formalism - denoted the XP stabiliser formalism - allows…
Variational quantum algorithms have been introduced as a promising class of quantum-classical hybrid algorithms that can already be used with the noisy quantum computing hardware available today by employing parameterized quantum circuits.…