We propose an efficient protocol for digital quantum simulation of quantum chemistry problems and enhanced digital-analog quantum simulation of transport phenomena in biomolecules with superconducting circuits. Along these lines, we optimally digitize fermionic models of molecular structure with single-qubit and two-qubit gates, by means of Trotter-Suzuki decomposition and Jordan-Wigner transformation. Furthermore, we address the modelling of system-environment interactions of biomolecules involving bosonic degrees of freedom with a digital-analog approach. Finally, we consider gate-truncated quantum algorithms to allow the study of environmental effects.
We propose an efficient protocol for digital quantum simulation of quantum chemistry problems and enhanced digital-analog quantum simulation of transport phenomena in biomolecules with superconducting circuits. Along these lines, we optimally digitize fermionic models of molecular structure with single-qubit and two-qubit gates, by means of Trotter-Suzuki decomposition and Jordan-Wigner transformation. Furthermore, we address the modelling of system-environment interactions of biomolecules involving bosonic degrees of freedom with a digital-analog approach. Finally, we consider gate-truncated quantum algorithms to allow the study of environmental effects.
We propose a digital-analog quantum simulation of generalized Dicke models with superconducting circuits, including Fermi- Bose condensates, biased and pulsed Dicke models, for all regimes of light-matter coupling. We encode these classes of problems in a set of superconducting qubits coupled with a bosonic mode implemented by a transmission line resonator. Via digital-analog techniques, an efficient quantum simulation can be performed in state-of-the-art circuit quantum electrodynamics platforms, by suitable decomposition into analog qubit-bosonic blocks and collective single-qubit pulses through digital steps. Moreover, just a single global analog block would be needed during the whole protocol in most of the cases, superimposed with fast periodic pulses to rotate and detune the qubits. Therefore, a large number of digital steps may be attained with this approach, providing a reduced digital error. Additionally, the number of gates per digital step does not grow with the number of qubits, rendering the simulation efficient. This strategy paves the way for the scalable digital-analog quantum simulation of many-body dynamics involving bosonic modes and spin degrees of freedom with superconducting circuits.
Abstract We propose a digital-analog quantum algorithm for simulating the Hubbard-Holstein model, describing strongly-correlated fermion-boson interactions, in a suitable architecture with superconducting circuits. It comprises a linear chain of qubits connected by resonators, emulating electron-electron (e-e) and electron-phonon (e-p) interactions, as well as fermion tunneling. Our approach is adequate for a digital-analog quantum computing (DAQC) of fermion-boson models including those described by the Hubbard-Holstein model. We show the reduction in the circuit depth of the DAQC algorithm, a sequence of digital steps and analog blocks, outperforming the purely digital approach. We exemplify the quantum simulation of a half-filling two-site Hubbard-Holstein model. In such example we obtain fidelities larger than 0.98, showing that our proposal is suitable to study the dynamical behavior of solid-state systems. Our proposal opens the door to computing complex systems for chemistry, materials, and high-energy physics.
We propose a method for the efficient quantum simulation of fermionic systems with superconducting circuits. It consists in the suitable use of Jordan-Wigner mapping, Trotter decomposition, and multiqubit gates, be with the use of a quantum bus or direct capacitive couplings. We apply our method to the paradigmatic cases of 1D and 2D Fermi-Hubbard models, involving couplings with nearest and next-nearest neighbours. Furthermore, we propose an optimal architecture for this model and discuss the benchmarking of the simulations in realistic circuit quantum electrodynamics setups.
We present several improvements to the standard Trotter-Suzuki based algorithms used in the simulation of quantum chemistry on a quantum computer. First, we modify how Jordan-Wigner transformations are implemented to reduce their cost from linear or logarithmic in the number of orbitals to a constant. Our modification does not require additional ancilla qubits. Then, we demonstrate how many operations can be parallelized, leading to a further linear decrease in the parallel depth of the circuit, at the cost of a small constant factor increase in number of qubits required. Thirdly, we modify the term order in the Trotter-Suzuki decomposition, significantly reducing the error at given Trotter-Suzuki timestep. A final improvement modifies the Hamiltonian to reduce errors introduced by the non-zero Trotter-Suzuki timestep. All of these techniques are validated using numerical simulation and detailed gate counts are given for realistic molecules.
We present several improvements to the standard Trotter-Suzuki based algorithms used in the simulation of quantum chemistry on a quantum computer. First, we modify how Jordan-Wigner transformations are implemented to reduce their cost from linear or logarithmic in the number of orbitals to a constant. Our modification does not require additional ancilla qubits. Then, we demonstrate how many operations can be parallelized, leading to a further linear decrease in the parallel depth of the circuit, at the cost of a small constant factor increase in number of qubits required. Thirdly, we modify the term order in the Trotter-Suzuki decomposition, significantly reducing the error at given Trotter-Suzuki timestep. A final improvement modifies the Hamiltonian to reduce errors introduced by the non-zero Trotter-Suzuki timestep. All of these techniques are validated using numerical simulation and detailed gate counts are given for realistic molecules.
Quantum simulation, as a practical application of noisy quantum computing, has aided the study of exotic quantum matters and the implementation of algorithms that outperform classical approaches. Superconducting qubits, one of the most promising candidates for realizing universal quantum computing, possess state-of-the-art features like easy integration of qubits, long coherence time, and high-fidelity single- and two-qubit gates. These characteristics have enabled applications of digital quantum simulation in the fields of physics, chemistry, and computer science. In this review, we first present the basic concepts of superconducting qubits, quantum gates, and digital quantum simulations. We also explore recent progress in digital quantum simulations using superconducting qubits, especially in relation to quantum chemistry, quantum matters, combinatorial optimization, and quantum machine learning. Finally, we address the current challenges of digital quantum simulation with superconducting qubits, and provide a perspective on the future of the field.