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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…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…
Efficiently characterising quantum systems, verifying operations of quantum devices and validating underpinning physical models, are central challenges for the development of quantum technologies and for our continued understanding of…
The dynamics of a quantum system can be simulated using a quantum computer by breaking down the unitary into a quantum circuit of one and two qubit gates. The most established methods are the Trotter-Suzuki decompositions, for which…
Circulant matrices are an important family of operators, which have a wide range of applications in science and engineering related fields. They are in general non-sparse and non-unitary. In this paper, we present efficient quantum circuits…
Unitary evolutions of a qubit are traditionally represented geometrically as rotations of the Bloch sphere, but the composition of such evolutions is handled algebraically through matrix multiplication [of SU(2) or SO(3) matrices].…
We study time evolution of a subsystem's density matrix under unitary evolution, generated by a sufficiently complex, say quantum chaotic, Hamiltonian, modeled by a random matrix. We exactly calculate all coherences, purity and…
Classical simulations of quantum circuits are vital for assessing potential quantum advantage and benchmarking devices, yet they require sophisticated methods to avoid the exponential growth of resources. Tensor network approaches, in…
We present a quantum algorithm for the dynamical simulation of time-dependent Hamiltonians. Our method involves expanding the interaction-picture Hamiltonian as a sum of generalized permutations, which leads to an integral-free Dyson series…
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…
Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…
Electronic structure simulation is an anticipated application for quantum computers. Due to high-dimensional quantum entanglement in strongly correlated systems, the quantum resources required to perform such simulations are far beyond the…
Quantum unitary synthesis addresses the problem of translating abstract quantum algorithms into sequences of hardware-executable quantum gates. Solving this task exactly is infeasible in general due to the exponential growth of the…
Density matrices evolved according the von Neumann equation are commonly used to simulate the dynamics of driven quantum systems. However, computational methods using density matrices are often too slow to explore the large parameter spaces…
The variational quantum imaginary time evolution (VarQITE) algorithm is a near-term method to prepare the ground state and Gibbs state of Hamiltonians. Finding an appropriate parameterization of the quantum circuit is crucial to the success…
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of…
We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of…
In this note we develop quantum circuits for exactly simulating the thermal properties of the quantum XY/Ising chain. These circuits are applicable to the simplest integrable lattice models for which the exact momentum-space…
In this paper, we investigate the simulation of continuous-time quantum walks on specific classes of graphs, for which it is possible to fast-forward the time-evolution operator to achieve constant-time simulation complexity and to perform…
Simulating quantum dynamics is one of the central applications of quantum computing. For Hamiltonians written as a sum of many terms, deterministic Trotter--Suzuki product formulas can require applying a large number of term-wise evolutions…