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Posted by Charles Neill and Zhang Jiang, Senior Research Scientists, Google Quantum AI

In fall of 2019, we demonstrated that the Sycamore quantum processor could outperform the most powerful classical computers when applied to a tailor-made problem. The next challenge is to extend this result to solve practical problems in materials science, chemistry and physics. But going beyond the capabilities of classical computers for these problems is challenging and will require new insights to achieve state-of-the-art accuracy. Generally, the difficulty in performing quantum simulations of such physical problems is rooted in the wave nature of quantum particles, where deviations in the initial setup, interference from the environment, or small errors in the calculations can lead to large deviations in the computational result.

In two upcoming publications, we outline a blueprint for achieving record levels of precision for the task of simulating quantum materials. In the first work, we consider one-dimensional systems, like thin wires, and demonstrate how to accurately compute electronic properties, such as current and conductance. In the second work, we show how to map the Fermi-Hubbard model, which describes interacting electrons, to a quantum processor in order to simulate important physical properties. These works take a significant step towards realizing our long-term goal of simulating more complex systems with practical applications, like batteries and pharmaceuticals.

A bottom view of one of the quantum dilution refrigerators during maintenance. During the operation, the microwave wires that are floating in this image are connected to the quantum processor, e.g., the Sycamore chip, bringing the temperature of the lowest stage to a few tens of milli-degrees above absolute zero temperature.

Computing Electronic Properties of Quantum Materials
In “Accurately computing electronic properties of a quantum ring”, to be published in Nature, we show how to reconstruct key electronic properties of quantum materials. The focus of this work is on one-dimensional conductors, which we simulate by forming a loop out of 18 qubits on the Sycamore processor in order to mimic a very narrow wire. We illustrate the underlying physics through a series of simple text-book experiments, starting with a computation of the “band-structure” of this wire, which describes the relationship between the energy and momentum of electrons in the metal. Understanding such structure is a key step in computing electronic properties such as current and conductance. Despite being an 18-qubit algorithm consisting of over 1,400 logical operations, a significant computational task for near-term devices, we are able to achieve a total error as low as 1%.

The key insight enabling this level of accuracy stems from robust properties of the Fourier transform. The quantum signal that we measure oscillates in time with a small number of frequencies. Taking a Fourier transform of this signal reveals peaks at the oscillation frequencies (in this case, the energy of electrons in the wire). While experimental imperfections affect the height of the observed peaks (corresponding to the strength of the oscillation), the center frequencies are robust to these errors. On the other hand, the center frequencies are especially sensitive to the physical properties of the wire that we hope to study (e.g., revealing small disorders in the local electric field felt by the electrons). The essence of our work is that studying quantum signals in the Fourier domain enables robust protection against experimental errors while providing a sensitive probe of the underlying quantum system.

(Left) Schematic of the 54-qubit quantum processor, Sycamore. Qubits are shown as gray crosses and tunable couplers as blue squares. Eighteen of the qubits are isolated to form a ring. (Middle) Fourier transform of the measured quantum signal. Peaks in the Fourier spectrum correspond to the energy of electrons in the ring. Each peak can be associated with a traveling wave that has fixed momentum. (Right) The center frequency of each peak (corresponding to the energy of electrons in the wire) is plotted versus the peak index (corresponding to the momentum). The measured relationship between energy and momentum is referred to as the ‘band structure’ of the quantum wire and provides valuable information about electronic properties of the material, such as current and conductance.

Quantum Simulation of the Fermi-Hubbard Model
In “Observation of separated dynamics of charge and spin in the Fermi-Hubbard model”, we focus on the dynamics of interacting electrons. Interactions between particles give rise to novel phenomena such as high temperature superconductivity and spin-charge separation. The simplest model that captures this behavior is known as the Fermi-Hubbard model. In materials such as metals, the atomic nuclei form a crystalline lattice and electrons hop from lattice site to lattice site carrying electrical current. In order to accurately model these systems, it is necessary to include the repulsion that electrons feel when getting close to one another. The Fermi-Hubbard model captures this physics with two simple parameters that describe the hopping rate (J) and the repulsion strength (U).

We realize the dynamics of this model by mapping the two physical parameters to logical operations on the qubits of the processor. Using these operations, we simulate a state of the electrons where both the electron charge and spin densities are peaked near the center of the qubit array. As the system evolves, the charge and spin densities spread at different rates due to the strong correlations between electrons. Our results provide an intuitive picture of interacting electrons and serve as a benchmark for simulating quantum materials with superconducting qubits.

(Left top) Illustration of the one-dimensional Fermi-Hubbard model in a periodic potential. Electrons are shown in blue, with their spin indicated by the connected arrow. J, the distance between troughs in the electric potential field, reflects the “hopping” rate, i.e., the rate at which electrons transition from one trough in the potential to another, and U, the amplitude, represents the strength of repulsion between electrons. (Left bottom) The simulation of the model on a qubit ladder, where each qubit (square) represents a fermionic state with spin-up or spin-down (arrows). (Right) Time evolution of the model reveals separated spreading rates of charge and spin. Points and solid lines represent experimental and numerical exact results, respectively. At t = 0, the charge and spin densities are peaked at the middle sites. At later times, the charge density spreads and reaches the boundaries faster than the spin density.

Conclusion
Quantum processors hold the promise to solve computationally hard tasks beyond the capability of classical approaches. However, in order for these engineered platforms to be considered as serious contenders, they must offer computational accuracy beyond the current state-of-the-art classical methods. In our first experiment, we demonstrate an unprecedented level of accuracy in simulating simple materials, and in our second experiment, we show how to embed realistic models of interacting electrons into a quantum processor. It is our hope that these experimental results help progress the goal of moving beyond the classical computing horizon.

Posted by Romina Stella, Product Manager, Google Translate

Advances on neural machine translation (NMT) have enabled more natural and fluid translations, but they still can reflect the societal biases and stereotypes of the data they’re trained on. As such, it is an ongoing goal at Google to develop innovative techniques to reduce gender bias in machine translation, in alignment with our AI Principles.

One research area has been using context from surrounding sentences or passages to improve gender accuracy – this is a challenge because traditional NMT methods translate sentences individually, but gendered information is not always explicitly stated in each individual sentence. For example, in the following passage in Spanish (a language where subjects aren’t always explicitly mentioned), the first sentence refers explicitly to Marie Curie as the subject, but the second one doesn’t explicitly mention the subject. In isolation, this second sentence could refer to a person of any gender. When translating to English, however, a pronoun needs to be picked, and the information needed for an accurate translation is in the first sentence.

Advancing translation techniques beyond single sentences requires new metrics for measuring progress and new datasets with the most common context-related errors. Adding to this challenge is the fact that translation errors related to gender (such as picking the correct pronoun or having gender agreement) are particularly sensitive because they may directly refer to people and how they self identify.

To help facilitate progress against the common challenges on contextual translation (e.g., pronoun drop, gender agreement and accurate possessives), we are releasing the Translated Wikipedia Biographies dataset, which can be used to evaluate the gender bias of translation models. Our intent with this release is to support long-term improvements on ML systems focused on pronouns and gender in translation by providing a benchmark in which translations’ accuracy can be measured pre- and post-model changes.

A Source of Common Translation Errors
Because they are well-written, geographically diverse, contain multiple sentences, and refer to subjects in the third person (so contain plenty of pronouns), Wikipedia biographies offer a high potential for common translation errors associated with gender. These often occur when articles refer to a person explicitly in early sentences of a paragraph, but there is no explicit mention of the person in later sentences. Some examples:

Building the Dataset
The Translated Wikipedia Biographies dataset has been designed to analyze common gender errors in machine translation such as those illustrated above. Each instance of the dataset represents a person (identified in the biographies as feminine or masculine), a rock band or a sports team (considered genderless). Each instance is represented by a long text translation of 8 to 15 connected sentences referring to that central subject (the person, rock band, or sports team). Articles are written in native English and have been professionally translated to Spanish and German. For Spanish, translations were optimized for pronoun-drop, so the same set could be used to analyze pro-drop (Spanish → English) and gender agreement (English → Spanish).

The dataset was built by selecting a group of instances that has equal representation across geographies and genders. To do this, we extracted biographies from Wikipedia according to occupation, profession, job and/or activity. To ensure an unbiased selection of occupations, we chose 9 occupations that represented a range of stereotypical gender associations (either feminine, masculine, or neither) based on Wikipedia statistics. Then, to mitigate any geography-based bias, we divided all these instances based on geographical diversity. For each occupation category, we looked to have one candidate per region (using regions from census.gov as a proxy of geographical diversity). When an instance was associated with a region, we checked that the selected person had a relevant relationship with a country that belongs to a designated region (nationality, place of birth, lived for a big portion of their life, etc.). By using this criteria, the dataset contains entries about individuals from more than 90 countries and all regions of the world.

Although gender is non-binary, we focused on having equal representation of “feminine” and “masculine” entities. It’s worth mentioning that because the entities are represented as such on Wikipedia, the set doesn’t include individuals that identify as non-binary, as unfortunately there are not enough instances currently represented in Wikipedia to accurately reflect the non-binary community. To label each instance as “feminine” or “masculine” we relied on the biographical information from Wikipedia, which contained gender-specific references to the person (she, he, woman, son, father, etc.).

After applying all these filters, we randomly selected an instance for each occupation-region-gender triplet. For each occupation, there are 2 biographies (one masculine and one feminine), for each of the 7 geographic regions.

Finally, we added 12 instances with no gender. We picked rock bands and sports teams because they are usually referred to by non-gendered third person pronouns (such as “it” or singular “they”). The purpose of including these instances is to study over triggering (i.e., when models learn that they are rewarded for producing gender-specific pronouns, soproduce these pronouns in cases where they shouldn’t).

Results and Applications
This dataset enables a new method of evaluation for gender bias reduction in machine translations (introduced in a previous post). Because each instance refers to a subject with a known gender, we can compute the accuracy of the gender-specific translations that refer to this subject. This computation is easier when translating into English (cases of languages with prodrop or neutral pronouns) since computation is mainly based on gender-specific pronouns in English. In these cases, the gender datasets have allowed us to observe a 67% reduction in errors on context-aware models vs. previous models. As mentioned before, the neutral entities have allowed us to discover cases of over triggering like the usage of feminine or masculine pronouns to refer to genderless entities. This new dataset also enables new research directions into the performance of different models across types of occupations or geographic regions.

As an example, the dataset allowed us to discover the following improvements in an excerpt of the translated biography of Marie Curie from Spanish.

Translation result with the previous NMT model.

Translation result with the new contextual model.

Conclusion
This Translated Wikipedia Biographies dataset is the result of our own studies and work on identifying biases associated with gender and machine translation. This set focuses on a specific problem related to gender bias and doesn’t aim to cover the whole problem. It’s worth mentioning that by releasing this dataset, we don’t aim to be prescriptive in determining what’s the optimal approach to address gender bias. This contribution aims to foster progress on this challenge across the global research community.

Acknowledgements
The datasets were built with help from Anja Austermann, Melvin Johnson, Michelle Linch, Mengmeng Niu, Mahima Pushkarna, Apu Shah, Romina Stella, and Kellie Webster.