Quantum simulation of negative hydrogen ion using variational quantum eigensolver on IBM quantum computer

Abstract

The negative hydrogen ion is the first three body quantum problem whose ground state energy is theoretically calculated using the "Chandrasekhar Wavefunction" that accounts for the electronelectron correlation 1 . The best value of ground state energy is obtained by photodetachment experiment using lasers in the laboratory. Solving multi-body systems is a daunting task in quantum mechanics as it includes choosing a trial wavefunction and the calculation of integrals for the system that becomes almost impossible for systems with three or more particles. This difficulty can be addressed by quantum computers. They have emerged as a tool to address different electronic structure problems with remarkable efficiency. Here, we show the quantum simulation of H − ion to calculate it's ground state energy in IBM quantum computer. We observe that the quantum computer is efficient in preparing the correlated wavefunction of H − and shows it as a bound entity as the ground state energy is found to be lower than that of Hydrogen atom. We use a recently developed algorithm known as "Variational Quantum Eigensolver" 2,3 and implement it in IBM's 5-qubit quantum chips "ibmqx2" and "ibmqx4". An optimization routine is performed on a classical computer by running quantum chemistry program and codes in QISKit to converge the energy to the minimum. We also present a comparison of different optimization routines and encoding methods used to converge the energy value to the minimum. The circuit is parametrized by 12 arbitrary angles and is thus used to create different trial wavefuntions by varying the parameters. The technique can be used to solve various many body problems 4 with great efficiency.

Implementation of the Projective Quantum Eigensolver on a Quantum Computer

“…96,101−108 Of particular interest to this paper are those VQE computations that report the effectiveness of d i ff e r e n t e r r o r m i t i g a t i o n schemes, 56,59,60,63,64,69,73,75,79,82,83,85,88,93,94,103,105 or that are p e r f o r m e d o n I B M d e v ices. 41,54,55,[58][59][60]62,65,67,69,73,74,76,78,79,82,85,[87][88][89]92,93,95,[97][98][99][100][101][102][103][104][105]107 Since our computations will utilize IBM devices and performance is device-specific, …”

“…In the literature, the closest reference points are VQE computations, as hardware results on PQE have not yet been reported. Some papers have reported VQE ground-state energies or properties. ,,− Other studies have used VQE as an ingredient of methods to compute excited-state energies and properties, ,,,,,,,,− linear response properties, , molecular dynamics, and vibrational eigenstates, , while yet more studies have used VQE as an active space solver for a dynamical correlation or embedding method. ,− Of particular interest to this paper are those VQE computations that report the effectiveness of different error mitigation schemes, ,,,,,,,,,,,,,,,, or that are performed on IBM devices. ,,,− ,,…”

“… 96 , 101 − 108 Of particular interest to this paper are those VQE computations that report the effectiveness of different error mitigation schemes, 56 , 59 , 60 , 63 , 64 , 69 , 73 , 75 , 79 , 82 , 83 , 85 , 88 , 93 , 94 , 103 , 105 or that are performed on IBM devices. 41 , 54 , 55 , 58 − 60 , 62 , 65 , 67 , 69 , 73 , 74 , 76 , 78 , 79 , 82 , 85 , 87 − 89 , 92 , 93 , 95 , 97 − 105 , 107 Since our computations will utilize IBM devices and performance is device-specific, 76 , 93 , 109 comparisons with results from similar hardware are more apt.…”

Assessing the Precision of Quantum Simulation of Many-Body Effects in Atomic Systems Using the Variational Quantum Eigensolver Algorithm

“…Moreover, energies of a whole host of molecular systems, such as H 2 O [21], H 2 [13,20] (also see Ref. [22] for an excited state treatment using an extended version of the variational quantum eigensolver), HeH + [17,23], LiH, BeH 2 [20], and H 4 [24], have been calculated, but atomic systems have received little attention, except for one work on H − , which is a relatively simple system [25], despitefinding many applications [26][27][28][29][30][31][32]. Atomic systems, in our view, merit separate study, since they have been and are still being used in testing new physics, such as parity violation [28,30,33,34] and electric dipole moments of quarks [35,36].…”

Solving diner’s dilemma game, circuit implementation and verification on the IBM quantum simulator

“…IBM Q gives access to a superconducting-qubit based operating system that is globally access to a wide class of researchers and has found significant applications in a user-friendly interface [23]. A number of experiments in the field of quantum simulations [26,27,28,29,30,31,32] developing quantum algorithms [33,34,35,36,37,38,39,40,41], testing of quantum information theoret- ical tasks [42,43,44,45,46,47], quantum cryptography [48,49,50,51], quantum error correction [52,53,54,55,56], quantum applications [57,58,59,60], quantum games [61,62], quantum chemistry [63], quantum teleportation [64,65,66], quantum neural network [67], quantum machine learning [68,69], quantum walk [70], quantum robotics…”