Related papers: The stabilizer ground state and applications to qu…
In quantum error-correcting code (QECC), many quantum operations and measurements are necessary to correct errors in logical qubits. In the stabilizer formalism, which is widely used in QECC, generators $G_i (i=1,2,..)$ consist of multiples…
The classification of stabilizer states under local Clifford (LC) equivalence is of particular importance in quantum error-correction and measurement-based quantum computation. Two stabilizer states are called LC equivalent if there exists…
We consider the optimal approximation of certain quantum states of a harmonic oscillator with the superposition of a finite number of coherent states in phase space placed either on an ellipse or on a certain lattice. These scenarios are…
Simulating Clifford and near-Clifford circuits using the extended stabilizer formalism has become increasingly popular, particularly in quantum error correction. Compared to the state-vector approach, the extended stabilizer formalism can…
When preparing a pure state with a quantum circuit, there is an unavoidable approximation error due to the compilation error in fault-tolerant implementation. A recently proposed approach called probabilistic state synthesis, where the…
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…
As quantum systems expand in size and complexity, manual qubit characterization and gate optimization will be a non-scalable and time-consuming venture. Physical qubits have to be carefully calibrated because quantum processors are very…
Many experiments in quantum information aim at creating graph states. Quantifying the purity of an experimentally achieved graph state could in principle be accomplished using full-state tomography. This method requires a number of…
The exponential scaling of the wave function is a fundamental property of quantum systems with far reaching implications in our ability to process quantum information. A problem where these are particularly relevant is quantum state…
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 $m$…
One of the goals in quantum simulation is to adiabatically generate the ground state of a complicated Hamiltonian by starting with the ground state of a simple Hamiltonian and slowly evolving the system to the complicated one. If the…
The preparation of quantum states, especially cooling, is a fundamental technology for nanoscale devices. The past decade has seen important results related to both the limits of state transformation and the limits to their efficiency --…
Compressible models extend the domain of simulable systems in quantum computers, but little is known about their precise limits of applicability. Using the theory of compressible matchgate circuits, we identify a class of quadratic…
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…
Lattice models, also known as generalized Ising models or cluster expansions, are widely used in many areas of science and are routinely applied to alloy thermodynamics, solid-solid phase transitions, magnetic and thermal properties of…
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 consider the problem of reconstructing global quantum states from local data. Because the reconstruction problem has many solutions in general, we consider the reconstructed state of maximum global entropy consistent with the local data.…
Trace distance and infidelity (induced by square root fidelity), as basic measures of the closeness of quantum states, are commonly used in quantum state discrimination, certification, and tomography. However, the sample complexity for…
We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the…
The use of combinatorial optimization algorithms has contributed substantially to the major progress that has occurred in recent years in the understanding of the physics of disordered systems, such as the random-field Ising model. While…