Quantum Computers Poised to Unlock Solutions to Complex Physics Problems

Researchers are increasingly exploring the potential of quantum annealing, a computational technique utilising interacting quantum spin systems, not only for optimisation challenges but also for tackling problems within condensed matter physics. Viv Kendon of the University of Strathclyde and Nicholas Chancellor of Newcastle University present a topical review bridging these fields, demonstrating how current quantum annealing hardware can be applied to physics problems. This work is significant because it highlights the reciprocal benefits of collaboration between computer scientists and physicists, fostering both a deeper understanding of quantum annealers and the potential to utilise them for advancements in fundamental physics.

Quantum annealing for condensed matter simulation via transverse field Ising models

Scientists are now leveraging the unique capabilities of quantum annealers to tackle problems extending beyond traditional optimisation, venturing into the realm of condensed matter physics. Current quantum annealing hardware possesses the potential to model and investigate complex physical systems, opening new avenues for scientific discovery.

This topical review provides a comprehensive overview of quantum annealing specifically tailored for condensed matter physicists, highlighting the synergistic benefits of collaboration to refine both the understanding and application of these quantum devices. Researchers detail how quantum annealers, which operate by instantiating an Ising Hamiltonian on quantum spins driven by a transverse field, can be effectively employed to simulate condensed matter physics problems.

A transverse Ising system, a foundational example in phase transition studies, shares significant parallels with the operational principles of quantum annealing. Consequently, established knowledge from condensed matter physics can inform the development of quantum annealing techniques, while quantum annealers offer a promising platform for simulating intricate condensed matter phenomena.

The work focuses on the current state of development of quantum annealers, both theoretical and experimental, identifying areas for improvement to unlock their full scientific potential. It outlines how a problem is encoded into a quantum state and a unitary transformation is applied, transforming the state to encode the desired solution, mirroring the classical circuit model used in digital computers.

Quantum computing, at its core, involves encoding a problem into a quantum state and manipulating it with unitary transformations. The field originated from the realisation that quantum computers could, in principle, solve certain problems more efficiently than their classical counterparts, a concept first proposed over forty years ago.

Today’s development focuses on overcoming the practical challenges of realising this potential, with a diverse range of hardware platforms including superconducting circuits, silicon-based electron spins, trapped ions, and photons currently under investigation. A crucial aspect of progress is quantum error correction, which utilises multiple physical qubits to represent a single logical qubit, enabling the detection and correction of errors caused by environmental interactions.

This research details how qubits, instantiated in two-state quantum systems, are controlled and measured to perform computations. Various quantum universal gate sets allow the construction of any unitary transformation, with the output obtained through measurement of the qubits. While quantum state preparation is often considered engineering, it is closely linked to the computational process. The study does not present a comprehensive review of all condensed matter applications, but rather focuses on current developments and potential improvements needed to establish quantum annealing as a valuable tool for scientific advancement.

Quantum annealing as a condensed matter physics problem

A transverse Ising system, frequently introduced in condensed matter physics textbooks as an example of phase transitions, underpins the operation of a quantum annealer. This device computes by instantiating an Ising Hamiltonian on a network of quantum spins, driven by a transverse field to explore potential solutions.

The work focuses on bridging the gap between quantum annealing and condensed matter physics, highlighting the potential for mutual benefit in both understanding and improving annealer functionality and applying them to physics problems. This topical review provides an overview of quantum annealing specifically tailored for physicists, acknowledging that many current applications serve as algorithm development and hardware testing rather than delivering immediate physics breakthroughs.

The study begins by contextualising quantum annealing within the broader field of quantum computing, explaining how problems are encoded into quantum states and transformed using unitary operations. Classical bits are replaced with qubits, two-state quantum systems, and computations are performed by applying sequences of one and two-qubit unitary quantum gates, analogous to classical circuits.

Obtaining the computational output involves measuring the qubits, yielding a binary string that is then decoded to reveal the solution, or alternatively, utilising the final quantum state itself. Further exploration details adiabatic quantum computing, computation by quantum walk, and quantum annealing as closely related computational models.

Quantum Monte Carlo methods are then discussed as a means of informing the understanding of how quantum annealing functions, alongside an analysis of the physics governing the diabatic regime of operation. The research also addresses the practical challenges of encoding computational problems into quantum Hamiltonians, considering the balance between physical constraints and resource minimisation, particularly concerning hardware graph connectivity. This encoding process is crucial for translating abstract problems into a form solvable by the quantum annealer.

Quantum annealing and the pursuit of scalable error-corrected computation

Researchers detail the physics underpinning quantum annealing and its potential for solving complex computational problems. Quantum computing generally encodes a problem into a quantum state and applies a unitary transformation to obtain a solution. The field originated from the realisation that quantum computers could, in principle, solve certain problems more efficiently than their classical counterparts, beginning with work by Feynman in 1982 and Deutsch in 1985.

Current hardware development focuses on translating this potential into reality, with diverse platforms including superconducting circuits, silicon electron spins, trapped ions, and photons currently under investigation. A key challenge in building practical quantum computers is error correction, essential for suppressing unwanted environmental interactions with quantum systems.

This involves representing a single logical qubit with multiple physical qubits, enabling the detection and correction of errors before they corrupt the computation. Roadmaps for quantum computing typically envision a progression from noisy quantum processors to large-scale, fault-tolerant, error-corrected digital computers, mirroring the development of classical silicon CMOS technology.

However, alternative models, such as quantum simulation, are also being actively pursued. Direct quantum simulation involves engineering the Hamiltonian of a controllable quantum system to match the system of interest, allowing for the direct measurement of properties without discretisation. Encoding computational problems into quantum Hamiltonians requires careful consideration of physical constraints and resource minimisation.

Current quantum computers primarily utilise binary integers, as floating-point representations are not yet practical due to hardware limitations. The work highlights the need for continued development in both theory and experiments to unlock the full potential of quantum annealing for scientific applications.

Regime analysis defines quantum annealing operational characteristics

Quantum annealing offers a method for tackling computational problems, particularly optimisation tasks, but is increasingly applicable to solving problems in physics. This topical review clarifies the principles of quantum annealing specifically for physicists, highlighting potential synergies between the fields to refine the functionality of quantum annealers and to utilise them for advancements in physics research.

Key to understanding quantum annealing is the concept of adiabaticity, defined by the minimum energy gap during the annealing process, alongside the coupling coefficient to an external thermal bath. By comparing these values, distinct regimes of operation can be mathematically defined, ranging from adiabatic, where quantum effects dominate, to quasistatic, where thermal equilibration prevails.

The analysis of these regimes, adiabatic, intermediate, and diabatic, reveals how different annealing protocols behave, with quantum walks operating in the diabatic regime and adiabatic quantum computing inherently in the adiabatic regime. Investigations into intermediate regimes, such as those by Venuti and colleagues, extend the understanding of adiabaticity to open systems.

Recent work indicates that smooth annealing schedules are optimal for physically realisable, discretised quantum annealing, surpassing earlier proposals of alternating driver and problem Hamiltonians, and multi-stage quantum walks offer a more accurate approximation of quantum annealing than simple Hamiltonian alternation. The authors acknowledge limitations in applying formal optimal control theory due to the unphysical nature of infinitely rapid parameter changes, and future research may focus on identifying optimal protocols within physically implementable constraints.