Related papers: Spin-Adapted Fermionic Unitaries: From Lie Algebra…
We discuss here some aspects related to the symmetries of a quantum many-body problem when trying to treat it on a quantum computer. Several features related to symmetry conservation, symmetry breaking, and possible symmetry restoration are…
Simple constructions and protocols are demonstrated to allow the implementation of universal quantum computation on an arbitrarily large quantum system by controlling a fixed number of spins, vastly reducing the engineering requirements in…
Entangled multipartite states are resources for universal quantum computation, but they can also give rise to ensembles of unitary transformations, a topic usually studied in the context of random quantum circuits. Using several graph state…
Topological symmetries, invertible and otherwise, play a fundamental role in the investigation of quantum field theories. Despite their ubiquitous importance across a multitude of disciplines ranging from string theory to condensed matter…
Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure…
Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this paper, we propose quantum algorithms capable of testing whether a Hamiltonian…
Quantum simulators are engineered devices controllably designed to emulate complex and classically intractable quantum systems. A key challenge is to certify whether the simulator truly mimics the Hamiltonian of interest. This certification…
Many coherence transfer experiments in Nuclear Magnetic Resonance Spectroscopy, involving network of coupled spins, use temporary spin-decoupling to produce desired effective Hamiltonians. In this paper, we show that significant time can be…
Various applications of quantum algebraic techniques in nuclear structure physics and in molecular physics are briefly reviewed and a recent application of these techniques to the structure of atomic clusters is discussed in more detail.
The dynamics of physical systems is often constrained to lower dimensional sub-spaces due to the presence of conserved quantities. Here we propose a method to learn and exploit such symmetry constraints building upon Hamiltonian Neural…
We study variational quantum algorithms from the perspective of free fermions. By deriving the explicit structure of the associated Lie algebras, we show that the Quantum Approximate Optimization Algorithm (QAOA) on a one-dimensional…
The ability to simulate a fermionic system on a quantum computer is expected to revolutionize chemical engineering, materials design, nuclear physics, to name a few. Thus, optimizing the simulation circuits is of significance in harnessing…
We explore how to build quantum circuits that compute the lowest energy state corresponding to a given Hamiltonian within a Symmetry subspace by explicitly encoding it into the circuit. We create an explicit unitary and a variationally…
Quantum simulation of non-Abelian gauge theories requires careful handling of gauge redundancy. We address this challenge by presenting universal principles for treating gauge symmetry that apply to any quantum simulation approach,…
In quantum control, quantum speed limits provide fundamental lower bounds on the time that is needed to implement certain unitary transformations. Using Lie algebraic methods, we link these speed limits to symmetries of the control…
Unitary operations are the building blocks of quantum programs. Our task is to design effcient or optimal implementations of these unitary operations by employing the intrinsic physical resources of a given n-qubit system. The most common…
We consider quantum spin chains with a hidden free fermionic structure, distinct from the Jordan-Wigner transformation and its generalizations. We express selected local operators with the hidden fermions. This way we can exactly solve the…
Randomisation is widely used in quantum algorithms to reduce the number of quantum gates and ancillary qubits required. A range of randomised algorithms, including eigenstate property estimation by spectral filters, Hamiltonian simulation,…
This paper studies symmetric constrained linear-quadratic optimal control problems and their parametric solutions. The parametric solution of such a problem is a piecewise-affine feedback law that can be equivalently expressed as a set of…
Conformal field theory, describing systems with scaling symmetry, plays a crucial role throughout physics. We describe a quantum algorithm to simulate the dynamics of conformal field theories, including the action of local conformal…