Narrow Results

Simulation of quantum field theories and fundamental interactions is one of the most challenging tasks in modern particle physics. Classical computers generally fail to reproduce accurate results when it comes to strongly coupled theories such as QCD. Recent developments in quantum technologies open up the possibility of simulating such physical regimes by using quantum computers. In this paper, we study the quantum resource related to the simulability of a quantum theory, i.e. non-stabilizerness for Lattice Gauge Theory (LGT) with discrete symmetry gauge groups. We show that enforcing gauge constraints for ${\mathbb{Z}}_l$ LGTs has no cost in terms of this resource and discuss the relation between non-abelianity of the gauge group with the average non-stabilizerness of the gauge invariant Hilbert space.

Trotter decomposition is the basis of the digital quantum simulation. Asymmetric and symmetric decompositions are used in our GPU demonstration of the digital adiabatic quantum simulations of (2+1)-dimensional quantum ${\mathbb{Z}}_2$ lattice gauge theory. The actual errors in Trotter decompositions are investigated as functions of the coupling parameter and the number of Trotter substeps in each step of the variation of coupling parameter. The relative error of energy is shown to be equal to the Trotter error usually defined in terms of the evolution operators. They are much smaller than the order-of-magnitude estimation. The error in the symmetric decomposition is much smaller than that in the asymmetric decomposition. The features of the Trotter errors obtained here are useful in the experimental implementation of digital quantum simulation and its numerical demonstration.

The internal structure of neutron stars and the physical properties of nuclei depend on the equation of state (EOS) of neutron matter. Dilute neutron matter is a quantum system of spin-1/2 Fermi particles interacting via s-wave scattering. Although a nuclear system and an ultracold atomic system have length scales and energy scales that differ by several orders of magnitude, both systems follow a common universal EOS considering their nondimensional universal interaction parameters. In this study, we determine the EOS of neutron matter in the dilute region, where the influence of the s-wave scattering length is dominant but that of the effective range is small, by utilizing a quantum simulator of ultracold ⁶Li atoms with Feshbach resonance.

We describe a general quantum computational algorithm that simulates the time evolution of an arbitrary nonrelativistic, Coulombic many-body system in three dimensions, considering only spatial degrees of freedom. We use a simple discretized model of Schrödinger evolution in the coordinate representation and discuss detailed constructions of the operators necessary to realize the scheme of Wiesner and Zalka. The algorithm is simulated numerically for small test cases, and its outputs are found to be in good agreement with analytical solutions.

The possibility of approaching quantum simulation of "topological turbulence" is discussed. In the latter, the topological features of turbulent flow are ascribed to a purely group-theoretic and topological view through the group SDiff of volume-preserving diffeomorphisms and the Mapping Class Group for the 2D surfaces that foliate the 3D flow domain. A class of representations of the group of mapping classes for compact boundaryless surfaces is explicitly constructed in terms of the Witt–Virasoro Hopf-coalgebra and implemented in terms of su(1,1). This leads to a complex, nonlinear Hamiltonian naturally associated with the fluid diffeomorphisms that could lend itself to the quantum simulation of turbulence in Fock space.

The Boson sampling problem consists in sampling from the output probability distribution of a bosonic Fock state, after it evolves through a linear interferometer. There is strong evidence that Boson sampling is computationally hard for classical computers, while it can be solved naturally by bosons. This has led it to draw increasing attention as a possible way to provide experimental evidence for the quantum computational supremacy. Nevertheless, the very complexity of the problem makes it hard to exclude the hypothesis that the experimental data are sampled from a different probability distribution. By exploiting integrated quantum photonics, we have carried out a set of three-photon Boson sampling experiments and analyzed the results using a Bayesian approach, showing that it represents a valid alternative to currently used methods. We adopt this approach to provide evidence that the experimental data correspond to genuine three-photon interference, validating the results against fully and partially-distinguishable photon hypotheses.

Recently, the dynamics simulation of light-harvesting complexes as an open quantum system, in the weak and strong coupling regimes, has received much attention. In this paper, we investigate a digital quantum simulation approach of the Fenna–Matthews–Olson (FMO) photosynthetic pigment-protein complex surrounded with a Markovian bath, i.e. memoryless, based on a nuclear magnetic resonance (NMR) quantum computer. For this purpose, we apply the decoupling (recoupling) method, which is turn off (on) the couplings, and also Solovay–Kitaev techniques to decompose Hamiltonian and Lindbladians into efficient elementary gates on an NMR simulator. Finally, we design the quantum circuits for the unitary and nonunitary part due to the system-environment interactions of the open system dynamics.

A quantum algorithm of SU($N$) Yang–Mills theory is formulated in terms of quantum circuits. It can nonperturbatively calculate the Dyson series and scattering amplitudes with polynomial complexity. The gauge fields in the interaction picture are discretized on the same footing with the lattice fermions in momentum space to avoid the fermion doubling and the gauge symmetry breaking problems. Applying the algorithm to the quantum simulation of quantum chromodynamics, the quark and gluon’s wave functions evolved from the initial states by the interactions can be observed and the information from wave functions can be extracted at any discrete time. This may help us understand the natures of the hadronization which has been an outstanding question of significant implication on high energy phenomenological studies.

A common assumption in an open quantum system is that the noise induced by the environment, due to the interaction between a quantum system and its environment, is responsible for the disappearance of quantum properties. Interestingly, Barreiro et al. [Nature470 (2011) 486] show, experimentally, using an open-system quantum ion traps simulator, an environment state can be engineered and controlled to pump an arbitrary quantum system toward a maximally entangled state and thus can be considered a resource for quantum information processing. Here, we demonstrate this idea to pump an arbitrary maximally mixed state into Greenberger–Horne–Zeilinger (GHZ) state by simulating our quantum circuit using one of the IBM Q processors. Barreiro et al. [Nature470 (2011) 486] offer the circuits for the execution of the GHZ pumping. Nevertheless, those are collected gates that are suitable to the trapped-ions platform, so their circuits implementation on the IBM Q devices would result in large depth circuits and thus requires many gates. Consequently, we suggest a different circuit structure that follows a similar goal, but has been considered the features of the IBM Q platform. Moreover, we run the simulation of our circuit using the QASM simulator and free-web-based interface, IBM Quantum Experience, with and without error mitigation, to investigate the effect of the noise on the preparation of the initial mixed states of the qubits in addition to the population of the target state of the system.

Quantum simulation has become a promising avenue of research that allows one to simulate and gain insight into the models of high energy physics whose experimental realizations are either complicated or inaccessible with current technology. We demonstrate the quantum simulation of such a model, a quantum mechanical system with spatial noncommutativity, which is inspired by the works in noncommutative geometry and noncommutative field theory for a universal quantum computer. We use the novel group theoretical formalism to map the Hamiltonian of such a noncommutative quantum system into the ordinary quantum mechanical Hamiltonian and then carry out the quantum simulation using the Trotter–Suzuki product formula. Furthermore, we distinguish the impact of the noncommutativity parameter on the quantum simulation, especially on the Trotter error, and point out how its sizable value affects the simulation.

In this paper, we examine whether a quantum computer can efficiently simulate time evolution of two Schrödinger particles. We consider particles interacting with each other and with an external potential. In order to solve the Schrödinger equation in the quantum register, we use an algorithm based on the quantum Fourier transform.

Density Matrix Exponentiation is a technique for simulating Hamiltonian dynamics when the Hamiltonian to be simulated is available as a quantum state. In this paper, we present a natural analogue to this technique, for simulating Markovian dynamics governed by the well known Lindblad master equation. For this purpose, we first propose an input model in which a Lindblad operator $L$ is encoded into a quantum state $\psi$. Then, given access to $n$ copies of the state $\psi$, the task is to simulate the corresponding Markovian dynamics for time $t$. We propose a quantum algorithm for this task, called Wave Matrix Lindbladization, and we also investigate its sample complexity. We show that our algorithm uses $n=O(t^2/𝜀)$ samples of $\psi$ to achieve the target dynamics, with an approximation error of $O(𝜀)$.

Motivated by the prospect of the experimental realization of applications like quantum simulation and scalable quantum computation using planar Coulomb crystals, we investigated planar Coulomb crystals with one or multicomponents and analyzed in detail, for the first time, their structure and properties. We also studied the RF-heating of planar crystals and found out in which conditions it can be minimized. These results together with the estimation of the error in the implementation of quantum simulation allowed us to find the experimental requirements for realizing quantum simulation with planar crystals. Trying to fulfill these requirements we designed an RF trap system for the realization of planar Coulomb crystals and quantum simulation.

We investigate the effect of gauge symmetry breaking in an atomic quantum simulator of U(1) lattice gauge theory, finding that a system of cold atoms in an optical lattice with a general set of parameters can be implemented as a simulator of “U(1) lattice gauge-Higgs” model with asymmetric nearest-neighbor Higgs coupling. The gauge-Higgs coupling in the imaginary time direction naturally arises from the violation of the U(1) local gauge invariance of the simulators caused by the deviation from the fine-tuned system parameters. A general method to supply the Higgs coupling in all space-time directions may be realized by coupling atoms in an optical lattice to another particle reservoir filled with the Bose-condensed atoms via laser-induced transitions. Clarification of the dynamics of this gauge-Higgs model sheds some lights upon various unsolved problems including the inflation process of the early universe.