Exploring Finite Temperature Properties of Materials with Quantum Computers

Powers, Connor; Bassman, Lindsay; Jong, Wibe A. de

doi:10.48550/arxiv.2109.01619

Cited by 4 publications

(4 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…III B was used to calculate dynamical spin-spin correlation functions in a driven Floquet spin chain in order to verify the occurrence of discrete time-crystalline eigenstate order. Moreover, in [179], quantum typicality was used to evaluate thermodynamic expectation values at finite temperature (cf. Box 2), which involved the approximation of the imaginary time-evolution of random states on a NISQ device [180].…”

Section: Discussionmentioning

confidence: 99%

Quantum simulation using noisy unitary circuits and measurements

Lunt¹,

Richter²,

Pal³

2021

Preprint

View full text Add to dashboard Cite

Many-body quantum systems are notoriously hard to study theoretically due to the exponential growth of their Hilbert space. It is also challenging to probe the quantum correlations in many-body states in experiments due to their sensitivity to external noise. Using synthetic quantum matter to simulate quantum systems has opened new ways of probing quantum many-body systems with unprecedented control, and of engineering phases of matter which are otherwise hard to find in nature. Noisy quantum circuits have become an important cornerstone of our understanding of quantum many-body dynamics. In particular, random circuits act as minimally structured toy models for chaotic nonintegrable quantum systems, faithfully reproducing some of their universal properties. Crucially, in contrast to the full microscopic model, random circuits can be analytically tractable under a reasonable set of assumptions, thereby providing invaluable insights into questions which might be out of reach even for state-of-the-art numerical techniques. Here, we give an overview of two classes of dynamics studied using random-circuit models, with a particular focus on the dynamics of quantum entanglement. We will especially pay attention to potential near-term applications of random-circuit models on noisy-intermediate scale quantum (NISQ) devices. In this context, we cover hybrid circuits consisting of unitary gates interspersed with nonunitary projective measurements, hosting an entanglement phase transition from a volume-law to an area-law phase of the steadystate entanglement. Moreover, we consider random-circuit sampling experiments and discuss the usefulness of random quantum states for simulating quantum many-body dynamics on NISQ devices by leveraging the concept of quantum typicality. We highlight how emergent hydrodynamics can be studied by utilizing random quantum states generated by chaotic circuits.

show abstract

Section: Discussionmentioning

confidence: 99%

Quantum simulation using noisy unitary circuits and measurements

Lunt¹,

Richter²,

Pal³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The Heisenberg model is of fundamental importance in the study of quantum materials [39][40][41][42] and is therefore a standard benchmark for thermal state preparation methods [29,30,43].…”

Section: B Transverse Field Ising Chainmentioning

confidence: 99%

Noise-Assisted Variational Quantum Thermalization

Foldager¹,

Pesah²,

Hansen³

2021

Preprint

View full text Add to dashboard Cite

Preparing thermal states on a quantum computer can have a variety of applications, from simulating many-body quantum systems to training machine learning models. Variational circuits have been proposed for this task on near-term quantum computers, but several challenges remain, such as finding a scalable cost-function, avoiding the need of purification, and mitigating noise effects. We propose a new algorithm for thermal state preparation that tackles those three challenges by exploiting the noise of quantum circuits. We consider a variational architecture containing a depolarizing channel after each unitary layer, with the ability to directly control the level of noise. We derive a closed-form approximation for the free-energy of such circuit and use it as a cost function for our variational algorithm. By evaluating our method on a variety of Hamiltonians and system sizes, we find several systems for which the thermal state can be approximated with a high fidelity. However, we also show that the ability for our algorithm to learn the thermal state strongly depends on the temperature: while a high fidelity can be obtained for high and low temperatures, we identify a specific range for which the problem becomes more challenging. We hope that this first study on noise-assisted thermal state preparation will inspire future research on exploiting noise in variational algorithms.

show abstract

“…One promising route to quantum computing thermal systems is the thermal pure-quantum-(TPQ-) state formulation of statistical mechanics [21]. While originally developed without quantum technology in mind, this ansatz offers a promising route to simulating quantum systems at finite temperature and chemical potential, enabling estimations of thermal expectation values of a large class of observables from only a single properly prepared pure state in the thermodynamic limit [22,23]. Canonical TPQ states are obtained from a Haar-random state evolved in imaginary time [21],…”

Section: Introductionmentioning

confidence: 99%

Toward Exploring Phase Diagrams of Gauge Theories on Quantum Computers with Thermal Pure Quantum States

Powers¹,

Davoudi²,

Mueller³

2023

Proceedings of the 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)

View full text Add to dashboard Cite

Aiming at evading the notorious sign problem in classical Monte-Carlo approaches to lattice quantum chromodynamics, we present an approach for quantum computing finite-temperature lattice gauge theories at non-zero density. Based on the thermal pure-quantum-state formalism of statistical mechanics when extended to gauge-theory systems, our approach [1] allows for signproblem-free quantum computations of thermal expectation values and non-equal time correlation functions. By taking a simple lattice gauge theory for which classical benchmarks are possible, namely Z 2 lattice gauge theory in 1+1 dimensions at finite chemical potential, we discuss resource requirements and robustness to algorithmic and hardware imperfections for near-term quantumhardware realizations.

show abstract

Exploring Finite Temperature Properties of Materials with Quantum Computers

Cited by 4 publications

References 29 publications

Quantum simulation using noisy unitary circuits and measurements

Quantum simulation using noisy unitary circuits and measurements

Noise-Assisted Variational Quantum Thermalization

Toward Exploring Phase Diagrams of Gauge Theories on Quantum Computers with Thermal Pure Quantum States

Contact Info

Product

Resources

About