Simulating quantum many-body dynamics on a current digital quantum computer

Smith, Adam; Kim, M. S.; Pollmann, Frank; Knolle, Johannes

doi:10.1038/s41534-019-0217-0

Cited by 282 publications

(186 citation statements)

References 101 publications

(136 reference statements)

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“…Notwithstanding significant progress thanks to the development of sophisticated numerical methods [2][3][4][5][6][7] and groundbreaking experiments with cold-atom or trappedion platforms [8,9], simulations on universal quantum computers promise to yield major advancements in a multitude of research areas [10,11]. While a fault-tolerant quantum computer is still far into the future, noisy intermediate-scale quantum (NISQ) devices are available and their current capabilities have been demonstrated for various problems such as electronic structure calculations [12,13], simulations of spectral functions [14,15], measurement of entanglement [16,17], topological phase transitions [18], and out-of-equilibrium dynamics [19][20][21][22].…”

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confidence: 99%

Simulating Hydrodynamics on Noisy Intermediate-Scale Quantum Devices with Random Circuits

Richter

Pal

2021

Phys. Rev. Lett.

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In a recent milestone experiment, Google's processor Sycamore heralded the era of "quantum supremacy" by sampling from the output of (pseudo-)random circuits. We show that such random circuits provide tailor-made building blocks for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. Specifically, we propose an algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution to study hydrodynamics and to extract transport coefficients in the linear response regime. We numerically demonstrate the algorithm by simulating the buildup of spatiotemporal correlation functions in one-and two-dimensional quantum spin systems, where we particularly scrutinize the inevitable impact of errors present in any realistic implementation. Importantly, we find that the hydrodynamic scaling of the correlations is highly robust with respect to the size of the Trotter step, which opens the door to reach nontrivial time scales with a small number of gates. While errors within the random circuit are shown to be irrelevant, we furthermore unveil that meaningful results can be obtained for noisy time evolutions with error rates achievable on near-term hardware. Our work emphasizes the practical relevance of random circuits on NISQ devices beyond the abstract sampling task.

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confidence: 99%

Simulating Hydrodynamics on Noisy Intermediate-Scale Quantum Devices with Random Circuits

Richter

Pal

2021

Phys. Rev. Lett.

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“…This could be a direct consequence of the many transitions that must be addressed on a chip consisting of several qubits with only slightly different transition frequency (the so‐called frequency crowding). In fact, recent quantum simulations of similar models performed on a 20‐qubit quantum hardware show that a proper accounting of such errors is essential to obtain a reasonable agreement with expected results …”

Section: Experimental Achievements and Prospective Technologiesmentioning

confidence: 76%

“…[]. More recently, dynamical correlation functions have been experimentally simulated on the quantum processors made freely available by IBM, through the IBM Quantum Experience (see quantumexperience.ng.bluemix.net/qx/experience) . These processors are based on fixed frequency superconducting qubits allowing the experimenter to implement arbitary single‐qubit rotations and CNOT two‐qubit gates, along the lines of scheme (ii) described above (see qiskit.org).…”

Section: Experimental Achievements and Prospective Technologiesmentioning

confidence: 99%

“…Nevertheless, similar conclusions apply here as already given for the trapped ion quantum hardware: despite considerable progress and the first attempts at performing full digital quantum simulations, several challenges need to be addressed before quantitative and not only qualitative accuracy be reached, especially on larger system sizes and running deeper quantum circuits. Specifically, a deeper understanding of error and noise sources, as well as suitable strategies to mitigate them on hardware with larger number of qubits is crucial at this NISQ stage, which will be the focus of intense research and development in the coming years.…”

Section: Experimental Achievements and Prospective Technologiesmentioning

confidence: 99%

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Quantum Computers as Universal Quantum Simulators: State‐of‐the‐Art and Perspectives

et al. 2019

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The past few years have witnessed the concrete and fast spreading of quantum technologies for practical computation and simulation. In particular, quantum computing platforms based on either trapped ions or superconducting qubits have become available for simulations and benchmarking, with up to few tens of qubits that can be reliably initialized, controlled, and measured. The present Review aims at giving a comprehensive outlook on the state‐of‐the‐art capabilities offered from these near‐term noisy devices as universal quantum simulators, that is, programmable quantum computers potentially able to calculate the time evolution of many physical models. First, a pedagogic overview on the basic theoretical background pertaining digital quantum simulations is given, with a focus on hardware‐dependent mapping of spin‐type Hamiltonians into the corresponding quantum circuit as a key initial step toward simulating more complex models. Then, the main experimental achievements obtained in the last decade are reviewed, focusing on the digital quantum simulation of such spin models by employing two leading quantum architectures. Their performances are compared, and future challenges are outlined, also in view of prospective hybrid technologies, towards the ultimate goal of reaching the long‐sought quantum advantage for the simulation of complex many‐body models in the physical sciences.

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“…This remarkable feature is what enables simulation out to arbitrarily large numbers of time-steps and thus permits long-time dynamic simulations. Most other methods for circuit generation will produce circuits that grow linearly with increasing numbers of time-steps [10,11]. This prohibits dynamic simulations beyond a certain number of time-steps due to the quantum computer encountering circuits that are too large, and thus accumulate too much error due to gate errors and qubit decoherence.…”

Section: Construction Of Constant-depth Circuitsmentioning

confidence: 99%

Domain-specific compilers for dynamic simulations of quantum materials on quantum computers

Bassman¹,

Gulania²,

Powers³

et al. 2020

Quantum Sci. Technol.

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Dynamic simulation of materials is a promising application for noisy intermediate-scale quantum (NISQ) computers. The difficulty in carrying out such simulations is that a quantum circuit must be executed for each time-step, and in general, these circuits grow in size with the number of time-steps simulated. NISQ computers can only produce high-fidelity results for circuits up to a given size due to gate error rates and qubit decoherence times, limiting the number of time-steps that can be successfully simulated. Here, we present a method for producing circuits that are constant in depth with increasing number of simulated time-steps for dynamic simulations of quantum materials for a specialized set of Hamiltonians derived from the one-dimensional Heisenberg model. We show how to build the constant-depth circuit structure for each system size, where the number of CNOT gates in the N -qubit constant-depth circuit structure grows only quadratically with N . The constantdepth circuits, which comprise an array of two-qubit matchgates on nearest-neighbor qubits, are constructed based on a set of multi-matchgate identities that we introduce as conjectures. Tutorials with the full code for generating our constant-depth circuits for the XY and transverse field Ising models are included. Using our constant-depth circuits, we are successfully able to demonstrate longtime dynamic simulations of quantum systems with up to five spins on available quantum hardware. Such constant-depth circuits could enable simulations of long-time dynamics for scientifically and technologically relevant quantum materials, enabling the observation of interesting and important atomic-level physics.

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Simulating quantum many-body dynamics on a current digital quantum computer

Cited by 282 publications

References 101 publications

Simulating Hydrodynamics on Noisy Intermediate-Scale Quantum Devices with Random Circuits

Simulating Hydrodynamics on Noisy Intermediate-Scale Quantum Devices with Random Circuits

Quantum Computers as Universal Quantum Simulators: State‐of‐the‐Art and Perspectives

Domain-specific compilers for dynamic simulations of quantum materials on quantum computers

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