Quantum computers are able to handle some computing tasks at a much faster speed than traditional supercomputers. However, to implement a universal quantum computer, a huge challenge is, how to protect the qubits encoding information from noise interference? Physicists have found that some exotic quantum phases have long-range entanglement patterns that can be used for quantum error correction, protecting quantum information, and making quantum computing more robust. In two papers published dec. 2 in the journal Science, researchers used programmable quantum processors to simulate quantum phases and measure long-range quantum entanglement patterns within them. Below is a review article by Science about both of these jobs.
Written by | Stephen D. Bartlett
Translated by | Huang Zehao
Review | Liang Jin
Thesis Title:
Realizing topologically ordered states on a quantum processor
Thesis Link:
https://www.science.org/doi/10.1126/science.abi8378
Probing topological spin liquids on a programmable quantum simulator
https://www.science.org/doi/10.1126/science.abi8794
At very low temperatures, some materials may coalesce into exotic phases, where quantum entanglement becomes the dominant feature that governs their behavior. These quantum phases differ from ordinary solids, liquids, gases, and plasmas in exhibiting exotic properties, such as quasiparticle excitations that interfere with each other in unusual ways. From an applied perspective, these quantum phases may play a key role in improving the robustness of quantum storage devices, a key component of quantum computers.
However, although theoretical physicists have predicted the existence of these quantum phases under various conditions, it is extremely difficult to experimentally implement quantum phases with long-range entanglement. Recently, Satzinger et al. [1] and Semeghini et al. [2] have made direct observations of these quantum phases and their key features by using coupled superconducting circuits and atomic arrays, respectively.
1. Singular topological quantum phases
There are many types of quantum phases, two of the most well-known examples of which are superconductors and Bose-Einstein condensation. Since the pattern of long-range entanglement between spins is a fundamental problem in condensed matter physics and has potential applications in quantum information systems, researchers have been focusing on related research. Quantum associations between spins can be long-range and "topological", meaning that under continuous local deformation, this association does not change, so this singular quantum phase is considered to have a "topological order".
Of the quantum phases with topological order, the most studied are those that break the symmetry of time inversion — meaning that if time were reversed, they would behave differently. A key experimental feature of non-temporal inversion symmetric topological phases is that they have robust edge modes, i.e., continuous currents running along the outer edges of the material. One such example is the fractional quantum Hall effect, which led physicists to discover topological insulators and superconductors. Instead, quantum computer designers are more interested in topological phases of time-inverted symmetry because these phases can be used for quantum error correction and protect quantum information from noise, perturbations, and other harmful effects.
Figure 1. Weave quantum topology. The diagram shows an artistic conception of the construction of a topological phase using a quantum processor. The left side represents a quantum circuit that can be controlled to form a specific pattern of long-range entanglement. The long-range entanglement pattern is a sign of the topological quantum phase, represented by wavy lines on the right, some of which form closed loops and some of which have open strings that extend to the edges. | Source: V. ALTOUNIAN/SCIENCE
However, since the topological phase of time symmetry has no edge mode, its long-range entanglement characteristics cannot be detected by traditional methods, and the long-range entanglement characteristics are necessary for its potential for quantum error correction. Due to the fundamental properties of long-range entanglement, we cannot understand the properties of the material by examining local regions, but must probe quantum associations throughout the entire volume. This non-local property of the observation system requires precise control of individual quantum components through entangled interactions and precise measurements. Thanks to state-of-the-art (but still in its infancy) quantum computing devices, this level of control over individual components in complex multi-component quantum systems has only recently become possible.
2. Two experiments: quantum processor programming quantum phases
Satzinger et al. used a prototype quantum processor consisting of a two-dimensional array of 31 coupled superconducting quantum devices. The quantum processor, called Sycamore, made headlines in 2019 when Google claimed "quantum supremacy," meaning that quantum processors are capable of performing certain computational tasks faster than traditional supercomputers.
By executing a short quantum program, Satzinger et al. used plane wood to stitch together the lowest energy states of the toric code[4]. Toric encoding is a typical example of a topologically ordered quantum phase that can be used for quantum error correction. This, along with another short quantum program, makes it possible to measure long-range quantum entanglement.
They also developed other programs to simulate the generation of quasiparticles and conduct quantum interference experiments to verify whether quasiparticles exhibit the expected behavior. The authors also demonstrated that quantum information can be encoded into toric encoding to prevent errors and then read out again. These features illustrate that when extending quantum architectures, toric encoding can be the key to improving quantum error correction.
Figure 2. Sycamore quantum processors. | Source: Erik Lucero, Research Scientist and Lead Production Quantum Hardware
Semeghini et al. report a different experiment with the same goal of creating and exploring the properties of topological order phases associated with toric encoding. Optical tweezers are used in the experiment to arrange 219 atoms on a two-dimensional lattice to form a quantum simulator. By controlling the interactions between adjacent atoms, the lattice is induced into a topologically ordered phase. Like the Sycamore processor, this atomic quantum simulator is programmable.
The researchers ran a program on a quantum processor, monitoring the nature of long-range entanglement between the processor's 219 atoms. Specifically, it is to measure how these spins are connected by quantum correlation, along a winding path to produce long-range entanglement patterns, from which we can get data that directly reflect the topological order of the quantum phase. Semeghini et al. also demonstrated that the encoded information could be read out again, demonstrating how quantum information can be encoded into the system and establishing a path for creating quantum memory.
Figure 3. A quantum spin liquid is a singular quantum phase with topological order with long-range quantum entanglement properties that can be used to implement robust quantum computing. Semeghini et al. used a programmable quantum simulator to probe quantum spin liquids, enabling for the first time a direct measurement of the topological order of quantum spin liquids. | Source: Olena Shmahalo for Quanta Magazine
3. Quantum computing technology as a tool to explore quantum multibody systems
These two experiments show for the first time clear evidence of topologically ordered phases with time-inverse symmetry. None of them are implemented through new materials as usual, but virtually through quantum processors. While quantum processors provide a mechanism for creating long-range entangled quantum states, their most critical contribution is actually to provide a way to measure long-range entanglement patterns that characterize topological order, demonstrating that quantum computing techniques can be a tool for exploring quantum multibody systems.
In order to protect quantum information during computation, it is also necessary to initialize, manipulate, and measure the quantum information in these encodes, which needs to be achieved by using fault-tolerant circuits. To achieve the goal of practical application, the error rate of quantum computing must be further reduced to a level far below the level reached by these two experiments. The key problem is that quantum error correction requires repeating measurements of checksum operators to find errors and updating the logical information by decoding these measurements. This requires not only a powerful quantum processor, but also a highly integrated classical processor and controller.[5]
There are still many challenges to implementing practical quantum processing devices, but the two experiments mark a key advance in quantum computing by demonstrating the use of topological quantum phases for error correction.
bibliography
[1] K. J. Satzinger et al., Science 374, 1237 (2021).
[2] G. Semeghini et al., Science 374, 1242 (2021).
[3] F. Arute et al., Nature 574, 505 (2019).
[4] A. Kitaev, Ann. Phys. 303, 2 (2003).
[5] S. J. Pauka et al., Nat. Electron. 4, 64 (2021).
This article is reproduced with permission from the WeChat public account "Jizhi Club". Programming a quantum phase of matter.
https://www.science.org/doi/10.1126/science.abl8910