Perform Quantum Computation Research Articles

Femtosecond Laser Direct Writing of Integrated Photonic Quantum Chips for Generating Path-Encoded Bell States.

Integrated photonic quantum chip provides a promising platform to perform quantum computation, quantum simulation, quantum metrology and quantum communication. Femtosecond laser direct writing (FLDW) is a potential technique to fabricate various integrated photonic quantum chips in glass. Several quantum logic gates fabricated by FLDW have been reported, such as polarization and path encoded quantum controlled-NOT (CNOT) gates. By combining several single qubit gates and two qubit gates, the quantum circuit can realize different functions, such as generating quantum entangled states and performing quantum computation algorithms. Here we demonstrate the FLDW of integrated photonic quantum chips composed of one Hadamard gate and one CNOT gate for generating all four path-encoded Bell states. The experimental results show that the average fidelity of the reconstructed truth table reaches as high as 98.8 0.3%. Our work is of great importance to be widely applied in many quantum circuits, therefore this technique would offer great potential to fabricate more complex circuits to realize more advanced functions.

GridMol2.0: Implementation and application of linear‐scale quantum mechanics methods and molecular visualization

AbstractGridMol is a “one‐stop” platform for molecular structure building, scientific computing, and molecular visualization aided by a high‐performance computing environment. GridMol version 2.0 introduces two unique features: the first is fragment‐based linear‐scaling quantum chemistry methods, such as molecular fractionation with conjugate caps and fragment molecular orbital methods; the second is that GridMol enables users to visualize molecular geometries along a geometry optimization and an intrinsic reaction coordinate calculation. Compared with version 1.0, fragment‐based linear‐scaling quantum chemistry methods implemented in GridMol version 2.0 can be used as a useful tool for performing quantum calculations for large molecular systems to explore the mechanisms involved in protein‐ligand or targeted drug interactions.

Spin-phonon interaction induces tunnel splitting in single-molecule magnets

Quantum tunneling of the magnetization is a major obstacle to the use of single-molecule magnets (SMMs) as basic constituents of next-generation storage devices. In this context, phonons are often only considered (perturbatively) as disturbances that promote the spin system to traverse the anisotropy barrier. Here, we demonstrate the ability of phonons to induce a tunnel splitting of the ground doublet which then reduces the required bistability due to Landau-Zener tunneling of the magnetization. Harmful are those phonons that modify the spin Hamiltonian so that its rotational symmetry about the field axis is destroyed. In our calculations we treat spins and phonons on the same footing by performing quantum calculations of a Hamiltonian where the single-anisotropy tensors are coupled to harmonic oscillators.

Extending the Frontier of Quantum Computers With Qutrits

We advocate for a fundamentally different way to perform quantum computation by using three-level qutrits instead of qubits. In particular, we substantially reduce the resource requirements of quantum computations by exploiting a third state for temporary variables (ancilla) in quantum circuits. Past work with qutrits has demonstrated only constant factor improvements, owing to the log2(3) binary-to-ternary compression factor. We present a novel technique using qutrits to achieve a logarithmic runtime decomposition of the Generalized Toffoli gate using no ancilla---an exponential improvement over the best qubit-only equivalent. Our approach features a 70x improvement in total two-qudit gate count over the qubit-only decomposition. This results in improvements for important algorithms for arithmetic and QRAM. Simulation results under realistic noise models indicate over 90% mean reliability (fidelity) for our circuit, versus under 30% for the qubit-only baseline. These results suggest that qutrits offer a promising path toward extending the frontier of quantum computers.

Explicit demonstration of initial state construction in artificial neural networks using NetKet and IBM Q experience platform

Quantum neural networks have gained significant interest in recent times for the representation of many-body states and classical simulation of quantum computation. Here, we discuss the methods to generate specific initial states in the Restricted Boltzmann Machines analogous to those used as the initial states while performing quantum computation in quantum computers such as IBM Q. We validate our approach by applying the Pauli X gate to the single-qubit and two-qubit initial states using NetKet and compare the results to that obtained by performing the same task in the IBM quantum computer. We find that using this approach, the RBM neural networks can represent desired quantum states with high accuracy. Thus, this method is promising to mimic quantum computation classically in neural networks by using specific initial states.

Spinor Bose-Einstein condensate interferometer within the undepleted pump approximation: Role of the initial state

Most interferometers operate with photons or dilute, non-condensed cold atom clouds in which collisions are strongly suppressed. Spinor Bose-Einstein condensates (BECs) provide an alternative route toward realizing three-mode interferometers; in this realization, spin-changing collisions provide a resource that generates mode entanglement. Working in the regime where the pump mode, i.e., the m=0 hyperfine state, has a much larger population than the side or probe modes (m=+1 and m=-1 hyperfine states), f=1 spinor BECs approximate SU(1,1) interferometers. We derive analytical expressions within the undepleted pump approximation for the phase sensitivity of such an SU(1,1) interferometer for two classes of initial states: pure Fock states and coherent spin states. The interferometer performance is analyzed for initial states without seeding, with single-sided seeding, and with double-sided seeding. The validity regime of the undepleted pump approximation is assessed by performing quantum calculations for the full spin Hamiltonian. Our analytical results and the associated dynamics are expected to guide experiments as well as numerical studies that explore regimes where the undepleted pump approximation makes quantitatively or qualitatively incorrect predictions.

Quantum-Inspired Acromyrmex Evolutionary Algorithm

Obtaining efficient optimisation algorithms has become the focus of much research interest since current developing trends in machine learning, traffic management, and other cutting-edge applications require complex optimised models containing a huge number of parameters. At present, computers based on the classical Turing-machine are inefficient when intent to solve optimisation tasks in complex and wicked problems. As a solution, quantum computers that should satisfy the Deutsch-Church-Turing principle have been proposed but this technology is still at an early stage. quantum-inspired algorithms (QIA) have emerged trying to fill-up an existing gap between the theoretical advances in quantum computation and real quantum computers. QIA use classical computers to simulate some physical phenomena such as superposition and entanglement to perform quantum computations. This paper proposes the quantum-inspired Acromyrmex evolutionary algorithm (QIAEA) as a highly efficient global optimisation method for complex systems. We present comparative statistical analyses that demonstrate how this nature-inspired proposal outperforms existing outstanding quantum-inspired evolutionary algorithms when testing benchmark functions.

Scalable fermionic error correction in Majorana surface codes

We study the error correcting properties of Majorana Surface Codes (MSC), topological quantum codes constructed out of interacting Majorana fermions, which can be used to store quantum information and perform quantum computation. These quantum memories suffer from purely "fermionic" errors, such as quasiparticle poisoning (QP), that have no analog in conventional platforms with bosonic qubits. In physical realizations where QP dominates, we show that errors can be corrected provided that the poisoning rate is below a threshold of $\sim11\%$. When QP is highly suppressed and fermionic bilinear ("bosonic") errors become dominant, we find an error threshold of $\sim16\%$, which is much higher than the threshold for spin-based topological memories like the Surface code or the Color code. In addition, we derive new lattice gauge theories to account for measurement errors. These results, together with the inherent error suppression provided by the superconducting gap in physical realizations of the MSC, makes this a strong candidate for a robust topological quantum memory.

Theoretical Aspects of the Cross Effect Enhancement of Nuclear Polarization under Static Dynamic Nuclear Polarization Conditions.

In this study, we perform quantum calculations of the spin dynamics of a small spin system that includes nine coupled electrons and one nucleus placed in an external magnetic field and exposed to microwave irradiation. This is an extension of a previous work in which we have demonstrated on a system of 11 coupled electron spins the dynamics of the electron polarizations composing the electron paramagnetic resonance (EPR) line during static dynamic nuclear polarization (DNP) experiments. There we have shown that the electron polarizations are determined by a spectral diffusion process, induced by the dipolar interaction and cross-relaxation. Additionally, we showed that a distinction had to be made between strong and weak dipolar-coupled systems relative to the inhomogeneity of the EPR line with only the first behaving according to the thermal mixing DNP (with two electron spin temperatures) description. The EPR spectra in the weak and strong dipolar interaction cases show different types of spectral features. In the extended spin system, we again make a distinction between weak and strong electron-electron interactions and show that the DNP spectra for the two cases are different in nature but that the DNP spectra can be derived in all cases from the EPR line shapes using the indirect cross effect.

Computing on quantum shared secrets for general quantum access structures

Quantum secret sharing is a method for sharing a secret quantum state among a number of individuals such that certain authorized subsets of participants can recover the secret shared state by collaboration and other subsets cannot. In this paper, we first propose a method for sharing a quantum secret in a basic $(2,3)$ threshold scheme, only by using qubits and the 7-qubit CSS code. Based on this $(2,3)$ scheme, we propose a new $(n, n)$ scheme and we also construct a quantum secret sharing scheme for any quantum access structure by induction. Secondly, based on the techniques of performing quantum computation on 7-qubit CSS codes, we introduce a method that authorized subsets can perform universal quantum computation on this shared state, without the need for recovering it. This generalizes recent attempts for doing quantum computation on $(n, n)$ threshold schemes.

Structural Instability of Driven Josephson Circuits Prevented by an Inductive Shunt

Superconducting circuits are a versatile platform to implement a multitude of Hamiltonians which perform quantum computation, simulation and sensing tasks. A key ingredient for realizing a desired Hamiltonian is the irradiation of the circuit by a strong drive. These strong drives provide an in-situ control of couplings, which cannot be obtained by near-equilibrium Hamiltonians. However, as shown in this paper, out-of-equilibrium systems are easily plagued by complex dynamics leading to instabilities. Predicting and preventing these instabilities is crucial, both from a fundamental and application perspective. We propose an inductively shunted transmon as the elementary circuit optimized for strong parametric drives. Developing a novel numerical approach that avoids the built-in limitations of perturbative analysis, we demonstrate that adding the inductive shunt significantly extends the range of pump powers over which the circuit behaves in a stable manner.

Effect of Giant Resonances on Fluctuations of Electromagnetic Fields in Heavy Ion Collisions

We perform quantum calculations of fluctuations of the electromagnetic fields in $AA$ collisions at RHIC and LHC energies. Calculations are performed with the help of the fluctuation-dissipation theorem accounting for the giant dipole and quadrupole resonances. We find that in the quantum picture the field fluctuations are much smaller than that predicted by the classical Monte-Carlo simulation with the Woods-Saxon nuclear density used in previous analyses.

A simple protocol for fault tolerant verification of quantum computation

With experimental quantum computing technologies now in their infancy, the search for efficient means of testing the correctness of these quantum computations is becoming more pressing. An approach to the verification of quantum computation within the framework of interactive proofs has been fruitful for addressing this problem. Specifically, an untrusted agent (prover) alleging to perform quantum computations can have his claims verified by another agent (verifier) who only has access to classical computation and a small quantum device for preparing or measuring single qubits. However, when this quantum device is prone to errors, verification becomes challenging and often existing protocols address this by adding extra assumptions, such as requiring the noise in the device to be uncorrelated with the noise on the prover’s devices. In this paper, we present a simple protocol for verifying quantum computations, in the presence of noisy devices, with no extra assumptions. This protocol is based on post hoc techniques for verification, which allow for the prover to know the desired quantum computation and its input. We also perform a simulation of the protocol, for a one-qubit computation, and find the error thresholds when using the qubit repetition code as well as the Steane code.

The boundaries and twist defects of the color code and their applications to topological quantum computation

The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The contributions of this work are threefold. First of all, we build upon the abstract theory of boundaries and domain walls of topological phases of matter to comprehensively catalog the objects realizable in color codes. Together with our classification we also provide lattice representations of these objects which include three new types of boundaries as well as a generating set for all 72 color code twist defects. Our work thus provides an explicit toy model that will help to better understand the abstract theory of domain walls. Secondly, we discover a number of interesting new applications of the cataloged objects for quantum information protocols. These include improved methods for performing quantum computations by code deformation, a new four-qubit error-detecting code, as well as families of new quantum error-correcting codes we call stellated color codes, which encode logical qubits at the same distance as the next best color code, but using approximately half the number of physical qubits. To the best of our knowledge, our new topological codes have the highest encoding rate of local stabilizer codes with bounded-weight stabilizers in two dimensions. Finally, we show how the boundaries and twist defects of the color code are represented by multiple copies of other phases. Indeed, in addition to the well studied comparison between the color code and two copies of the surface code, we also compare the color code to two copies of the three-fermion model. In particular, we find that this analogy offers a very clear lens through which we can view the symmetries of the color code which gives rise to its multitude of domain walls.

Topological quantum computation based on chiral Majorana fermions

The chiral Majorana fermion is a massless self-conjugate fermion which can arise as the edge state of certain 2D topological matters. It has been theoretically predicted and experimentally observed in a hybrid device of a quantum anomalous Hall insulator and a conventional superconductor. Its closely related cousin, the Majorana zero mode in the bulk of the corresponding topological matter, is known to be applicable in topological quantum computations. Here we show that the propagation of chiral Majorana fermions leads to the same unitary transformation as that in the braiding of Majorana zero modes and propose a platform to perform quantum computation with chiral Majorana fermions. A Corbino ring junction of the hybrid device can use quantum coherent chiral Majorana fermions to implement the Hadamard gate and the phase gate, and the junction conductance yields a natural readout for the qubit state.

QUANTUM-INSPIRED ARTIFICIL NEURAL NETWORKS AND EVOLUTIONARY ALGORITHMS METHODS APPLIED TO MODELING OF THE POLISH ELECTRIC POWER EXCHANGE USING THE DAY-AHEAD MARKET DATA

The paper presents selected results of research on the use of artificial intelligence methods, which are inspired by quantum computing solutions for modelling of electric power exchange systems. Methods used in the modelling of quantum data acquisition, quantization and dequantization of information as well as the methods of performing quantum computations were emphasized. Furthermore, we have analysed the results obtained for the neural model and for the evolutionary algorithm inspired by the quantum computer science. Eventually, the model was verified on the example of the neural model of the Electric Power Exchange (EPE).

Introduction to topological quantum computation with non-Abelian anyons

Topological quantum computers promise a fault tolerant means to perform quantum computation. Topological quantum computers use particles with exotic exchange statistics called non-Abelian anyons, and the simplest anyon model which allows for universal quantum computation by particle exchange or braiding alone is the Fibonacci anyon model. One classically hard problem that can be solved efficiently using quantum computation is finding the value of the Jones polynomial of knots at roots of unity. We aim to provide a pedagogical, self-contained, review of topological quantum computation with Fibonacci anyons, from the braiding statistics and matrices to the layout of such a computer and the compiling of braids to perform specific operations. Then we use a simulation of a topological quantum computer to explicitly demonstrate a quantum computation using Fibonacci anyons, evaluating the Jones polynomial of a selection of simple knots. In addition to simulating a modular circuit-style quantum algorithm, we also show how the magnitude of the Jones polynomial at specific points could be obtained exactly using Fibonacci or Ising anyons. Such an exact algorithm seems ideally suited for a proof of concept demonstration of a topological quantum computer.

Lattice surgery on the Raussendorf lattice

Lattice surgery is a method to perform quantum computation fault-tolerantly by using operations on boundary qubits between different patches of the planar code. This technique allows for universal planar code computation without eliminating the intrinsic two-dimensional nearest-neighbor properties of the surface code that eases physical hardware implementations. Lattice surgery approaches to algorithmic compilation and optimization have been demonstrated to be more resource efficient for resource-intensive components of a fault-tolerant algorithm, and consequently may be preferable over braid-based logic. Lattice surgery can be extended to the Raussendorf lattice, providing a measurement-based approach to the surface code. In this paper we describe how lattice surgery can be performed on the Raussendorf lattice and therefore give a viable alternative to computation using braiding in measurement-based implementations of topological codes.

Multiscale Modeling Approach to Identify Glassy Electrolytes for Sodium Ion Batteries

Sodium is an earth-abundant element, which makes sodium-ion batteries a promising technology for grid-scale energy storage applications. Conventional liquid electrolytes pose safety concerns due to poor stability, which has led to an extensive research to explore solid-state electrolytes. Developing novel solid electrolytes with ionic conductivity comparable to that of liquid electrolytes has been a major challenge over the past decade. Sulfide glasses have been reported to possess excellent ionic conductivity making them potential electrolytes for high performance sodium ion batteries. Optimizing electrolyte compositions through series of fabrication and experimental characterization cycles is not an economical approach. Atomistic simulations provide an economical route to analyze wide range of compositions and get crucial insights into ion transport in these glasses. With this motivation, we have analyzed the local structure of sulfide glasses and its subsequent impact on the ionic conductivity. We have employed ab initio molecular dynamics (MD) simulations that perform quantum calculations on the fly while solving equations of motions at each MD step to accurately capture the complex chemistry in sodium thiophosphate glasses. We modeled a range of sodium thiophosphate glasses with composition x Na2S – (1-x) P2S5 (x = 0, 0.33, 0.5, 0.6, 0.67, 0.75). The glasses were formed using melt-quench technique and the calculated density of the glasses from simulations matched well (within 5%) with the experimentally measured value. We characterized the local structure of these glasses by calculating the radial pair distribution functions (RDF’s) from ab initio MD and compared it to those obtained through X-ray scattering experiments to validate the model. The FTIR and NMR characterization of these glasses help in identifying the different structural units dominating the local structure at a composition. We calculated the relative fractions of each of these structural units present in the different glasses and correlated the results to change in composition. The dominant structural units influence the ion transport in these glassy electrolytes. These atomistic simulations thereby allow us to predict the trend in ionic conductivity with composition. Our calculations indicate that an optimal room temperature ionic conductivity of ~ 10-6 S/cm is obtained at 75 Na2S – 25 P2S5 composition. A relatively high ionic conductivity (~ 10-5 S/cm) can be achieved at slightly elevated temperatures of around 60 °C, making these sodium thiophosphate glasses promising electrolytes for solid-state sodium ion batteries. Our calculations provide crucial insights into ion transport that can help develop solid electrolytes with high ionic conductivity. We developed a kinetic Monte Carlo (kMC) model to scale up our calculations. Crucial inputs such as Na+ ions distribution and migration energies obtained from ab initio MD are the key inputs to this kMC model. This kMC model is able to predict the ionic conductivity of these glasses in agreement with experimental values. A separate Monte Carlo based model was developed to determine the charge-discharge plots for the entire battery employing these solid-state electrolytes. This novel multiscale approach of coupling atomistic simulations with Monte Carlo model provides an economical route for developing novel electrolytes for sodium ion batteries.

Na+ Ion Transport in x Na2s – (1-x) P2S5 thiophosphate Glasses: An Ab Initio Molecular Dynamics Study

Sodium is an earth abundant element, which makes sodium ion batteries a promising technology for grid-scale energy storage applications. Due to safety concerns with liquid electrolytes, extensive research has been carried out over the past decade to develop new solid-state electrolytes. However, developing solid-state electrolytes with relatively high ionic conductivity at room temperatures is a major challenge. Sulfide glasses have been reported to possess excellent ionic conductivity making them potential electrolytes for high performance sodium ion batteries. With an aim to develop novel electrolyte for high performance sodium ion batteries, our present work focuses on analyzing the local structure of sulfide glasses and its subsequent impact on transport properties through atomistic simulations, in conjunction with experimental characterization. As model systems, we studied x Na2S – (1-x) P2S5 glasses. The polarization and resonance effect of the P=S bonds in the glass complicates the parametrization of interatomic potentials necessary for classical MD simulations. Therefore, we employed ab initio MD simulations that perform quantum calculations on the fly while solving equations of motions at each MD step to accurately capture the complex chemistry. As model systems for our calculations, we considered a range of electrolytes with composition x Na2S – (1-x) P2S5 (x = 0, 0.33, 0.5, 0.6, 0.67, 0.75). The glasses were formed using melt-quench technique and the density of the glasses matched well (within 5%) with the experimentally measured value. We analyzed the local structure of these glasses by calculating the radial pair distribution functions (RDF’s) from ab initio MD and compared it to those obtained through X-ray scattering experiments to validate the model. The FTIR and NMR characterization of these glasses show presence of different structural units that effectively control the ionic conductivity of these glasses. We calculated the fractions of each of these functional units present in the glasses from ab initio MD. At 75% Na2S, all the sulfur present in the structure is non-bridging due to presence of purely [PS4]3- groups in the glass. At concentration lower than 75% Na2S, other structural units containing bridging sulfur such as [P2S7]4- dominate the local structure. On the other hand, at concentrations above 75% Na2S, additional structural units corresponding to [PS3]3- and polysulfides are observed along with [PS4]3- due to excess Na2S content. Increase in concentration of polysulfides leads to lower ionic conductivity. As a result, optimal ionic conductivity of these glasses is observed at 75 Na2S – 25 P2S5 composition. The calculated ionic conductivity of these glasses at room temperature was ~ 10-6 S/cm, which matches well in terms of order of magnitude with experimentally measured values. A relatively high ionic conductivity (~ 10-5 S/cm) can be achieved at slightly elevated temperatures of around 60 °C, making these sodium thiophosphate glasses promising electrolytes for solid-state sodium ion batteries.