Related papers: Simulation and reversal of n-qubit Hamiltonians us…
Parity-time ($PT$)-symmetric Hamiltonians exhibit non-unitary dynamical evolution while maintaining real spectra, and offer unique approaches to quantum sensing and entanglement generation. Here we present a method for simulating the…
The quantum circuit model is the de-facto way of designing quantum algorithms. Yet any level of abstraction away from the underlying hardware incurs overhead. In the era of near-term, noisy, intermediate-scale quantum (NISQ) hardware with…
The efficient implementation of matrix arithmetic operations underpins the speedups of many quantum algorithms. We develop a suite of methods to perform matrix arithmetics -- with the result encoded in the off-diagonal blocks of a…
Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and…
Quantum simulation provides a powerful route for exploring many-body phenomena beyond the capabilities of classical computation. Existing approaches typically proceed in the forward direction: a model Hamiltonian is specified, implemented…
Quantum simulation can help us study poorly understood topics such as high-temperature superconductivity and drug design. However, existing quantum simulation algorithms for current quantum computers often have drawbacks that impede their…
We develop randomized quantum algorithms to simulate quantum collision models, also known as repeated interaction schemes, which provide a rich framework to model various open-system dynamics. The underlying technique involves composing…
We have developed a concrete quantum simulation scheme and experimentally simulated a pairing model on an NMR quantum computer. The design of our experiment includes choosing an appropriate initial state in order to make our scheme scalable…
Extensions of average Hamiltonian theory to quantum computation permit the design of arbitrary Hamiltonians, allowing rotations throughout a large Hilbert space. In this way, the kinematics and dynamics of any quantum system may be…
With a focus on universal quantum computing for quantum simulation, and through the example of lattice gauge theories, we introduce rather general quantum algorithms that can efficiently simulate certain classes of interactions consisting…
We present a hybrid quantum-classical algorithm to simulate thermal states of a classical Hamiltonians on a quantum computer. Our scheme employs a sequence of locally controlled rotations, building up the desired state by adding qubits one…
Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value…
Unknown unitary inversion is a fundamental primitive in quantum computing and physics. Although recent work has demonstrated that quantum algorithms can invert arbitrary unknown unitaries without accessing their classical descriptions,…
We propose an iterative algorithm to simulate the dynamics generated by any $n$-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator $U$ (unitary) into a product of different time-step unitaries. The…
The well-known algorithm for quantum phase estimation requires that the considered unitary is available as a conditional transformation depending on the quantum state of an ancilla register. We present an algorithm converting an unknown…
Since quantum feedback is based on classically accessible measurement results, it can provide fundamental insights into the dynamics of quantum systems by making available classical information on the evolution of system properties and on…
Parity-time ($PT$) symmetric Hamiltonians are generally non-Hermitian and give rise to exotic behaviour in quantum systems at exceptional points, where eigenvectors coalesce. The recent realisation of $PT$-symmetric Hamiltonians in quantum…
We show that an n-th root of the Walsh-Hadamard transform (obtained from the Hadamard gate and a cyclic permutation of the qubits), together with two diagonal matrices, namely a local qubit-flip (for a fixed but arbitrary qubit) and a…
Quantum machine learning models are designed for performing learning tasks. Some quantum classifier models are proposed to assign classes of inputs based on fidelity measurements. Quantum Hadamard test is a well-known quantum algorithm for…
We propose a quantum inverse iteration algorithm which can be used to estimate the ground state properties of a programmable quantum device. The method relies on the inverse power iteration technique, where the sequential application of the…