A Double-field Computation Model to Simulate Physical Systems

Philip Baback Alipour, Thomas Aaron Gulliver

Quantum field theory (QFTh) simulators simulate physical systems using quantum circuits that process quantum information (qubits) via single field (SF) and/or quantum double field (QDF) transformation. This review presents models that classify states against pairwise particle states | i j 〉 , given their state transition (ST) probability P | i j 〉 . A quantum AI (QAI) program, weighs and compares the field's distance between entangled states as qubits from their scalar field of radius R ≥ | r i j | . These states distribute across 〈 R 〉 with expected probability 〈 P distribute 〉 and measurement outcome 〈 M ( P distribute ) 〉 = P | i j 〉 . A quantum-classical hybrid model of processors via QAI, classifies and predicts states by decoding qubits into classical bits. For example, a QDF as a quantum field computation model (QFCM) in IBM-QE, performs the doubling of P | i j 〉 for a strong state prediction outcome. QFCMs are compared to achieve a universal QFCM (UQFCM). This model is novel in making strong event predictions by simulating systems on any scale using QAI. Its expected measurement fidelity is 〈 M ( F ) 〉 ≥ 7 / 5 in classifying states to select 7 optimal QFCMs to predict 〈 M 〉 's on QFTh observables. This includes QFCMs' commonality of 〈 M 〉 against QFCMs limitations in predicting system events. Common measurement results of QFCMs include their expected success probability 〈 P success 〉 over STs occurring in the system. Consistent results with high F 's, are averaged over STs as 〈 P distribute 〉 yielding 〈 P success 〉 ≥ 2 / 3 performed by an SF or QDF of certain QFCMs. A combination of QFCMs with this fidelity level predicts error rates (uncertainties) in measurements, by which a P | i j 〉 = 〈 P success 〉 < ∼ 1 is weighed as a QAI output to a QFCM user. The user then decides which QFCMs perform a more efficient system simulation as a reliable solution. A UQFCM is useful in predicting system states by preserving and recovering information for intelligent decision support systems in applied, physical, legal and decision sciences, including industry 4.0 systems.

Richard P. Feynman

David M. Ceperley

Daiwei Zhu, Sonika Johri, Norbert M. Linke +6 more

Finite-temperature phases of many-body quantum systems are fundamental to phenomena ranging from condensed-matter physics to cosmology, yet they are generally difficult to simulate. Using an ion trap quantum computer and protocols motivated by the quantum approximate optimization algorithm (QAOA), we generate nontrivial thermal quantum states of the transverse-field Ising model (TFIM) by preparing thermofield double states at a variety of temperatures. We also prepare the critical state of the TFIM at zero temperature using quantum-classical hybrid optimization. The entanglement structure of thermofield double and critical states plays a key role in the study of black holes, and our work simulates such nontrivial structures on a quantum computer. Moreover, we find that the variational quantum circuits exhibit noise thresholds above which the lowest-depth QAOA circuits provide the best results.

Andrzej Posiewnik

Gavin K. Brennen, M. Aguado, J. I. Cirac

We demonstrate how to build a simulation of two-dimensional (2D) physical theories describing topologically ordered systems whose excitations are in one-to-one correspondence with irreducible representations of a Hopf algebra, D( G ), the quantum double of a finite group G . Our simulation uses a digital sequence of operations in a spin lattice model originally due to Kitaev to prepare a ground 'vacuum' state and to create, braid and fuse anyonic excitations. The simulation works with or without the presence of a background Hamiltonian though only in the latter case is the system topologically protected. We describe a physical realization of a simulation of the simplest non-Abelian model, D( S 3 ), using trapped neutral atoms in a 2D optical lattice and provide a sequence of steps to perform universal quantum computation with anyons. The use of ancillary spin degrees of freedom figures prominently in our construction and provides a novel technique to prepare and probe these systems.