Related papers: Stabilizer ground states for simulating quantum ma…
Universal quantum computing requires nonstabilizer (magic) quantum states. Quantifying the nonstabilizerness and relating it to other quantum resources is vital for characterizing the complexity of quantum many-body systems. In this work,…
We investigate the entanglement properties of pure quantum states describing $n$ qubits. We characterize all multipartite states which can be maximally entangled to local auxiliary systems using controlled operations. A state has this…
We propose a general method for preparing stabilizer states with reduced two-qubit gate count and depth compared to the state of the art. The method starts from a graph state representation of the stabilizer state and iteratively reduces…
Many-body quantum states, as a matter of fact, are extremely essential to solve certain mathematical problems or simulate quantum systems in measurement-based quantum computation. However, how to verify large scale quantum states, such as…
In this paper we investigate stabilizer quantum error correction codes using controlled phase rotations of strong coherent probe states. We explicitly describe two methods to measure the Pauli operators which generate the stabilizer group…
Preparation of a target quantum many-body state on quantum simulators is one of the significant steps in quantum science and technology. With a small number of qubits, a few quantum states, such as the Greenberger-Horne-Zeilinger state,…
It is a fundamental property of quantum mechanics that information is lost as a result of performing measurements. Indeed, with every quantum measurement one can associate a number -- its POVM norm constant -- that quantifies how much the…
We introduce a graphical representation of stabilizer states and translate the action of Clifford operators on stabilizer states into graph operations on the corresponding stabilizer-state graphs. Our stabilizer graphs are constructed of…
Quantum computing employs controllable interactions to perform sequences of logical gates and entire algorithms on quantum registers. This paradigm has been widely explored, e.g., for simulating dynamics of manybody systems by decomposing…
We start by studying the subgroup structures underlying stabilizer circuits and we use our results to propose a new normal form for stabilizer circuits. This normal form is computed by induction using simple conjugation rules in the…
A set of necessary and sufficient conditions are derived for the equivalence of an arbitrary pure state and a graph state on n qubits under stochastic local operations and classical communication (SLOCC), using the stabilizer formalism.…
Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an $m$-dimensional space of physical parameters, the ground…
We consider the transformation of Hamilton operators under various sets of quantum operations acting simultaneously on all adjacent pairs of particles. We find mappings between Hamilton operators analogous to duality transformations as well…
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 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…
The Wigner function formalism has played a pivotal role in examining the non-classical aspects of quantum states and their classical simulatability. Nevertheless, its application in qubit systems faces limitations due to negativity induced…
We introduce an architecture for neural quantum states for many-body quantum-mechanical systems, based on normalizing flows. The use of normalizing flows enables efficient uncorrelated sampling of configurations from the probability…
Knowledge of the ground state of a homogeneous quantum many-body system can be used to find the exact ground state of a dual inhomogeneous system with a confining potential. For the complete family of parent Hamiltonians with a ground state…
Ground-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert…
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…