Simulating particle creation in an expanding universe using quantum computers

A new study published in Scientific Reports simulates particle creation in an expanding universe using IBM quantum computers, demonstrating the digital quantum simulation of quantum field theory for curved spacetime (QFTCS).

While attempts to create a complete quantum theory of gravity have been unsuccessful, there is another approach to exploring and explaining cosmological events.

QFTCS maintains spacetime as a classical background described by general relativity, while treating the matter and force fields within it quantum mechanically. This allows physicists to study quantum effects in “curved spacetime” without needing a complete theory of quantum gravity.

This semi-classical theory has already predicted phenomena like Hawking radiation from black holes and particle creation in expanding spacetimes. However, these predictions have been hard to verify experimentally.

Scientists have therefore used analog quantum simulations, such as Bose-Einstein condensates, to verify these phenomena, leaving digital quantum simulations unexplored.

Phys.org spoke to the first author of the study, Marco Díaz Maceda, a graduate student at Universidad Autónoma de Madrid.

“I believe quantum computing has a promising future for advancing research in physics. I have always loved studying the universe and its phenomena, so I was naturally drawn to quantum fields in curved spacetime. This research represents a fascinating intersection of these two fields, making it a natural and inspiring choice for me,” said Maceda.

Error mitigation vs. error correction

In the present “noisy intermediate-scale quantum” (NISQ) era, quantum computers have three main characteristics. This includes noise, meaning the qubits and quantum gates are susceptible to environmental noise, and these devices roughly have tens or a few hundred qubits.

While these devices are powerful and can be used for applications like optimization problems and machine learning tasks, they have a major bottleneck, which is hardware.

Quantum error correcting codes (QECCs) have been shown to work theoretically, but are hard to implement. They require many physical qubits to create a single logical qubit.

This overhead requirement makes QECCs impractical to implement on current quantum computers that only have tens or hundreds of physical qubits.

In the present study, the researchers overcome this by suggesting error mitigation as opposed to error correction. The idea behind this is to understand how the system’s errors scale with noise.

Once understood, researchers can work backward to estimate the error-free result.

Maceda explained the importance of this technique with respect to the study, “We used only four qubits, one for each possible state of the field. However, since our circuit involved a large number of quantum gates, errors accumulated throughout the execution. To obtain reliable results, we applied error mitigation techniques, which helped improve the fidelity of our computations.”

Particle creation

In QFT, a flat spacetime is assumed, known as “Minkowski space.” However, when spacetime is curved or dynamic (like in an expanding universe), the physics changes.

As spacetime stretches or expands (during inflation), the vacuum state (or zero-point energy state) becomes excited in this new spacetime, leading to the creation of new particles. This particle creation process is believed to have happened in the early universe.

To simulate this process, the researchers chose the Friedman-Lemaitre-Robertson-Walker (FLRW) universe metric to describe spacetime. This metric describes how spacetime expands homogeneously and isotropically.

For the quantum field, they consider a massive scalar field that evolves according to the modified Klein-Gordon equation to account for the curved, expanding spacetime.

Finally, to describe the particle creation process, the researchers used Bogoliubov transformations. These transformations provide a way for the researchers to calculate how many particles would be created in changing spacetimes, i.e., initial and final states.

Implementing the quantum circuit

The researchers designed a quantum circuit to simulate this process using IBM’s 127-qubit Eagle processor.

The initial state of the universe was designed to start in the vacuum state or “zero-point energy” state, with a restriction of one excitation per mode.

Following this, the researchers implemented the quantum circuit for the particle creation process.

Maceda explained the process of designing the quantum circuit, saying, “The first step in designing the quantum circuit was to determine the time evolution operator of the system. This was achieved by relating the initial and final states through Bogoliubov transformations.”

This step allowed them to calculate the number of particles created during the process.

Maceda continued, “Once we established this relationship, we assigned the excited states of the scalar field to specific qubits in the quantum computer.”

The researchers encoded the quantum field states to actual physical qubits, each corresponding to the four excitation levels of the system. This included the ground state, one excitation each in the positive and negative modes, and one in both modes.

“Finally, applying techniques developed by my mentor Dr. Sabín, we mapped the time evolution operator to unitary operations acting on these qubits, ensuring that their evolution accurately reflected the dynamics of the scalar field in an expanding universe,” said Maceda.

To achieve the mapping of the time evolution operator to unitary operators that can act on qubits, the researchers used hundreds of quantum gates.

For error mitigation, the researchers applied “zero-noise extrapolation” (ZNE). This method works by deliberately adding noise to the system in a controlled manner, measuring how the noise affects the results, and then extrapolating backward to the zero-noise state.

A feasible tool for future research

The simulations successfully demonstrated particle creation in expanding spacetime, with results matching theoretical predictions. Although the results from the quantum computer showed higher noise, it demonstrated feasibility.

Additionally, the ZNE techniques significantly improved the results, demonstrating the viability of using quantum simulations for studying complex systems.

Explaining the impact of their work on cosmology, Maceda said, “Our work provides a new way to simulate particle creation in the early universe, offering deeper insights into fundamental processes that shape the cosmos.”

The researchers also believe digital quantum simulations are already becoming and will continue becoming viable tools for investigating cosmological phenomena.

“Digital quantum simulations have already been used by my mentor Dr. Sabín to research topics such as gravitational entanglement, Rindler transformations that account for black hole evaporation, and the causal structure of the universe,” commented Maceda.

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