Quantum computing practical This study disproves IBM!
Quantum computing has reached the point where it has an advantage over classical computers on several technologies and platforms, and just this month, an IBM team even bypassed quantum noise, demonstrated for the first time that a quantum computer can produce accurate results on Eagle (127 quantum bits), and beat a supercomputer on the time evolution problem of the two-dimensional transverse field Ising model --demonstrating the practical capabilities of quantum computers.
It was certainly a huge experimental achievement: the (claimed) state-of-the-art 127Q quantum chip, Eagle, earned IBM a lot of attention; however, a preprint article just published in the arXiv knocks it back to cold, hard reality.
"Efficient tensor network simulation of IBM's kicked Ising experiment"
Link to the paper:
https://arxiv.org/abs/2306.14887
This time, scientists at New York University and the Flatiron Institute have simulated the Eagle chip on digital computation with tensor networks and found that the tensor network simulation is faster and better than the pure quantum chip solution for the classical kicked ising problem, better.
The quantum bit layout of the Eagle quantum processor and the tensor network structure used in the experimental simulations.
For classical verifiable systems, the experimental tensor network can simulate the dynamics of the two-dimensional transverse field Ising model; the above figure shows the comparison of the simulation results with the Eagle quantum processor and other tensor network methods.
For the non-classical verifiable system, the above simulation results are compared with the Eagle quantum processor and other tensor network methods.
This experiment shows that the simulation of 127 quantum bits of the Ising model on a heavy-hexagon lattice (HHL) simulated with a quantum processor can be performed accurately with a tensor network, and, with minimal computational resources.
An important insight from the results is that there can be many complementary avenues for classical simulations of quantum many-body systems, especially for those with physical structure. The experimental team also emphasized that the tensor network approach is not limited to one- and two-dimensional systems, and that higher-dimensional, non-planar systems can actually become more like mean fields, making the tensor network approach work well again.
Of course, the significance of this result does not stop at overturning previous IBM scientific data; the team believes that this work opens up new directions: highly flexible and computationally inexpensive tensor network methods can be used to benchmark new quantum processor designs and can better delineate which multi-body quantum systems might become difficult for classical computing techniques.
In short, they also bring new ideas for the development of quantum simulations.
Many of the most promising short-term applications of quantum computers fall within the realm of quantum simulation: modeling the quantum properties of microscopic particles directly relevant to modern materials science, high-energy physics and quantum chemistry.
"In recent years, there have been many exciting advances in the field of analog and digital quantum simulation, and quantum simulation is one of the most promising areas of quantum information processing, both in terms of algorithm development, which is already quite mature." Professor Andrew Daley of the Department of Physics at the University of Strathclyde has praised quantum simulation technology in this way.
The development of this technology will also affect several important real-world applications, such as the development of materials for batteries, industrial catalysis or nitrogen fixation. Just as aerodynamics can be studied by simulation on digital computers or in wind tunnels, quantum simulations can be performed not only on future fault-tolerant digital quantum computers, but are now also already possible with special-purpose analog quantum simulators.
Overview of the Quantum Simulator. Understanding the physical properties of real and promising materials (depicted as a magnet that floats on top of a superconductor when this magnet is cold enough) often requires theoretical models that simplify the material to be manageable. Such models can treat the material as a rigid lattice of interacting particles (depicted in blue and red), but even these models may be too complex to compute accurately. These computational tasks can be mapped to a programmable quantum simulator, using both digital and analog means to deal with these problems. The problem can be solved on a fault-tolerant digital quantum computer (shown as a circuit on the far right, where lines correspond to individual quantum bits and boxes represent operations between quantum bits), or a scale model of the problem can be built in an analogous quantum simulator (depicted on the right as an array of atoms, with blue and red representing different species that are "trapped " in a lattice of light represented in gray). A series of programmable quantum simulators is under development, with the hope of increasing the programmability of the simulation devices and combining them with variational numerical algorithms. With the insights gleaned from quantum simulators, we can build better models or gain new understanding of simulated materials.
In general, simulating many-body quantum dynamics on a classical computer faces several challenges.
This is because a system can take on a large number of configurations that grow exponentially with the number of its constituent particles (e.g., doubling with each additional constituent building block). This makes it a challenging task to store such states on even the most powerful supercomputers available once the system grows beyond a very small size (typically 50 quantum spins). To simulate a quantum system on a classical computer, science in a sense needs to compress or sample from this exponentially large space - for all known methods, the time cost of computation grows exponentially with the size of the system.
In contrast, through direct implementation on quantum hardware, quantum simulators avoid the exponential scaling that can occur in memory, and the time costs associated with manipulation or sampling.
Quantum device architectures for simulation. The ecosystem of quantum device architectures for simulation includes photonic networks, trapped ions, superconducting RF cavities, neutral atoms in optical lattice or tweezer arrays, superconducting circuits as well as molecular arrays, defects in solid-state crystals, semiconductor technology with embedded atomic spins, quantum annealers, coherent Ising machines with Floquet dynamics, Bose-Einstein condensates, and optical cavities.
In the analogous quantum simulator, the system is able to implement a specific class of models and is designed to implement a selected model with well-calibrated parameters. Scientists can then find the lowest energy states, for example, starting with a simple, well-controlled Hamiltonian and a well-defined initial state of the system, and then very slowly mixing to more complex Hamiltonians.
The limitations of the analogous quantum simulator can be summarized in two parts:
- First, we only have access to models that can directly implement Hamiltonian quantities in the analog simulator;
- Second, without error correction, these systems are in general vulnerable to calibration errors (including incompletely implemented Hamiltonian quantities and parameter calibration), as well as decoherence and noise.
The ultimate limit of analogous quantum simulations is then set by the decoherence timescale, which provides an upper limit on the timescale at which we can controllably observe coherent quantum dynamics; but this is typically well beyond the timescale available in classical computation, allowing for the realization of practical quantum advantages.
Many of the algorithms used on classical computers can also be used on fault-tolerant digital quantum computers and vice versa. This includes a range of adaptable methods for computing the lowest energy states, as well as time-evolutionary methods: including those based on the Suzuki-Trotter decomposition of time evolution. The great advantage of digital quantum simulators is that any desired Hamiltonian quantity of the system can be implemented, which provides the opportunity to study a wide range of models, for engineering design.
The problem is that, in practice, algorithms for computing time evolution require long computations on large fault-tolerant quantum computers. As with other fault-tolerant quantum computations, this is accompanied by an error correction overhead based on gate fidelity, a huge overhead in terms of the number of quantum bits required to implement quantum error correction, and running time.
Summary of the state of the art in quantum system simulation
The conclusion that can be drawn is that the current simulation system can already operate in the regime of quantum dominance. However, is it beyond the capabilities of classical simulations?IBM has tried to respond to this challenge, but it seems too early to cover the bases.
The next step will be to verify that quantum devices are a priori by direct comparison with classical computing.
In summary, solving quantum problems in quantum many-body physics has a long history and many practical applications: both directly for quantum systems in physics, chemistry, and materials science, and for computation in other fields. These problems are both intractable and relevant - and important - beyond testing quantum hardware, so they are excellent candidates for demonstrating practical quantum advantages.
While there is no formal complexity to demonstrate that the time cost of classical algorithms must scale exponentially, the same is true for most difficult problems in classical computing (including factorization and NP-complete problems); however, decades of progress and understanding emphasize that this is a difficult problem for which general solutions will likely not be found.
Analog and digital quantum simulators provide answers to some of these challenges, avoiding the exponential expansion of memory resources; and, at least for time evolution from known states, the time cost of computation.
It is indisputable that today's analogous quantum simulators have already had a tremendous impact on basic science. There is further excitement about the range of models and the future availability of scalable and fault-tolerant digital quantum simulations, with cautious optimism about the time scales for implementing the necessary hardware.
In the history of computing, classical analog and digital computing have coexisted for more than half a century, with a gradual transition to digital computing. In a Nature review co-authored by researchers at the University of Strathclyde, the Max Planck Institute for Quantum Optics, the University of Munich, the Munich Center for Quantum Science and Technology, the University of Innsbruck, the Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, and Microsoft, the researchers had assessed the near- and medium-term possibilities of quantum simulation:
[1] https://arxiv.org/abs/2306.14887
[2]https://www.nature.com/articles/s41586-022-04940-6
[3]https://www.nature.com/articles/s42254-023-00599-8
[4]https://phys.org/news/2022-07-roadmap-future-quantum-simulation.html
