SimuQ: A Framework for Programming Quantum Hamiltonian Simulation with Analog Compilation

Quantum Hamiltonian simulation, which simulates the evolution of quantum systems and probes quantum phenomena, is one of the most promising applications of quantum computing. Recent experimental results suggest that Hamiltonian-oriented analog quantum simulation would be advantageous over circuit-oriented digital quantum simulation in the Noisy Intermediate-Scale Quantum (NISQ) machine era. However, programming analog quantum simulators is much more challenging due to the lack of a unified interface between hardware and software. In this paper, we design and implement SimuQ, the first framework for quantum Hamiltonian simulation that supports Hamiltonian programming and pulse-level compilation to heterogeneous analog quantum simulators. Specifically, in SimuQ, front-end users specify the target quantum system with Hamiltonian Modeling Language, and the Hamiltonian-level programmability of analog quantum simulators is specified through a new abstraction called the abstract analog instruction set (AAIS) and programmed in AAIS Specification Language by hardware providers. Through a solver-based compilation, SimuQ generates executable pulse schedules for real devices to simulate the evolution of desired quantum systems, which is demonstrated on superconducting (IBM), neutral-atom (QuEra), and trapped-ion (IonQ) quantum devices. Moreover, we demonstrate the advantages of exposing the Hamiltonian-level programmability of devices with native operations or interaction-based gates and establish a small benchmark of quantum simulation to evaluate SimuQ's compiler with the above analog quantum simulators.

[1]  Xiaodi Wu,et al.  Quantum Hamiltonian Descent , 2023, ArXiv.

[2]  K. Khadiev.  Lecture Notes on Quantum Algorithms , 2022, ArXiv.

[3]  F. Mintert,et al.  Analogue Quantum Simulation with Fixed-Frequency Transmon Qubits , 2022, Quantum.

[4]  M. Lukin,et al.  Quantum optimization of maximum independent set using Rydberg atom arrays , 2022, Science.

[5]  Yuan Xie,et al.  Paulihedral: a generalized block-wise compiler optimization framework for Quantum simulation kernels , 2021, ASPLOS.

[6]  W. D. de Jong,et al.  ArQTiC: A Full-stack Software Package for Simulating Materials on Quantum Computers , 2021, ACM Transactions on Quantum Computing.

[7]  D. Egger,et al.  Pulse-efficient circuit transpilation for quantum applications on cross-resonance-based hardware , 2021, Physical Review Research.

[8]  Andrew W. Cross,et al.  OpenQASM 3: A Broader and Deeper Quantum Assembly Language , 2021, ACM Transactions on Quantum Computing.

[9]  Peter J. Karalekas,et al.  Pulser: An open-source package for the design of pulse sequences in programmable neutral-atom arrays , 2021, Quantum.

[10]  M. Lukin,et al.  Probing topological spin liquids on a programmable quantum simulator , 2021, Science.

[11]  Nicolas P. D. Sawaya,et al.  Graph Optimization Perspective for Low-Depth Trotter-Suzuki Decomposition , 2021, 2103.08602.

[12]  B. Nachman,et al.  Quantum Algorithm for High Energy Physics Simulations. , 2021, Physical review letters.

[13]  Minh C. Tran,et al.  Theory of Trotter Error with Commutator Scaling , 2021 .

[14]  Rajiv K. Kalia,et al.  MISTIQS: An open-source software for performing quantum dynamics simulations on quantum computers , 2021, SoftwareX.

[15]  M. Lukin,et al.  Quantum phases of matter on a 256-atom programmable quantum simulator , 2020, Nature.

[16]  D. Pekker,et al.  Simulating the dynamics of braiding of Majorana zero modes using an IBM quantum computer , 2020, Physical Review Research.

[17]  J. Cong,et al.  Optimal Layout Synthesis for Quantum Computing , 2020, 2020 IEEE/ACM International Conference On Computer Aided Design (ICCAD).

[18]  Margaret Martonosi,et al.  Resource-Efficient Quantum Computing by Breaking Abstractions , 2020, Proceedings of the IEEE.

[19]  Easwar Magesan,et al.  First-principles analysis of cross-resonance gate operation , 2020, 2005.00133.

[20]  Daniel J. Egger,et al.  Qiskit pulse: programming quantum computers through the cloud with pulses , 2020, Quantum Science and Technology.

[21]  Kristan Temme,et al.  Circuit optimization of Hamiltonian simulation by simultaneous diagonalization of Pauli clusters , 2020, Quantum.

[22]  Jad C. Halimeh,et al.  Observation of gauge invariance in a 71-site Bose–Hubbard quantum simulator , 2020, Nature.

[23]  Johannes Bausch,et al.  Hamiltonian simulation algorithms for near-term quantum hardware , 2020, Nature Communications.

[24]  Martin Rinard,et al.  Noise-Aware Dynamical System Compilation for Analog Devices with Legno , 2020, ASPLOS.

[25]  M. Martonosi,et al.  Software Mitigation of Crosstalk on Noisy Intermediate-Scale Quantum Computers , 2020, ASPLOS.

[26]  Shih-Han Hung,et al.  A verified optimizer for Quantum circuits , 2019, Proc. ACM Program. Lang..

[27]  Moinuddin K. Qureshi,et al.  Mitigating Measurement Errors in Quantum Computers by Exploiting State-Dependent Bias , 2019, MICRO.

[28]  Johannes L. Schönberger,et al.  SciPy 1.0: fundamental algorithms for scientific computing in Python , 2019, Nature Methods.

[29]  John Chiaverini,et al.  Trapped-ion quantum computing: Progress and challenges , 2019, Applied Physics Reviews.

[30]  Nicolas P. D. Sawaya,et al.  Quantum Chemistry in the Age of Quantum Computing. , 2018, Chemical reviews.

[31]  Tao Qin,et al.  Quantum simulation of strongly correlated condensed matter systems , 2018 .

[32]  Andrew W. Cross,et al.  The IBM Q experience and QISKit open-source quantum computing software , 2018 .

[33]  John Preskill,et al.  Quantum Computing in the NISQ era and beyond , 2018, Quantum.

[34]  Dmitri Maslov,et al.  Toward the first quantum simulation with quantum speedup , 2017, Proceedings of the National Academy of Sciences.

[35]  Yudong Cao,et al.  OpenFermion: the electronic structure package for quantum computers , 2017, Quantum Science and Technology.

[36]  M. Lukin,et al.  Probing many-body dynamics on a 51-atom quantum simulator , 2017, Nature.

[37]  P. Schauss.  Quantum simulation of transverse Ising models with Rydberg atoms , 2017, 1706.09014.

[38]  Jennifer Paykin,et al.  QWIRE: a core language for quantum circuits , 2017, POPL.

[39]  J. Gambetta,et al.  Efficient Z gates for quantum computing , 2016, 1612.00858.

[40]  G. Wendin.  Quantum information processing with superconducting circuits: a review , 2016, Reports on progress in physics. Physical Society.

[41]  I. Chuang,et al.  Optimal Hamiltonian Simulation by Quantum Signal Processing. , 2016, Physical review letters.

[42]  Rahul Sarpeshkar,et al.  Configuration synthesis for programmable analog devices with Arco , 2016, PLDI.

[43]  S. Ravets,et al.  Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models , 2016, Nature.

[44]  M. Saffman.  Quantum computing with atomic qubits and Rydberg interactions: progress and challenges , 2016, 1605.05207.

[45]  S. Debnath,et al.  Demonstration of a small programmable quantum computer with atomic qubits , 2016, Nature.

[46]  Benni Reznik,et al.  Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices , 2015, Reports on progress in physics. Physical Society.

[47]  E. Farhi,et al.  A Quantum Approximate Optimization Algorithm , 2014, 1411.4028.

[48]  Edmund M. Clarke,et al.  dReal: An SMT Solver for Nonlinear Theories over the Reals , 2013, CADE.

[49]  Benoît Valiron,et al.  Quipper: a scalable quantum programming language , 2013, PLDI.

[50]  Yazhen Wang,et al.  Quantum Computation and Quantum Information , 2012, 1210.0736.

[51]  D. Loss,et al.  Prospects for Spin-Based Quantum Computing in Quantum Dots , 2012, 1204.5917.

[52]  Andrew M. Childs,et al.  Hamiltonian simulation using linear combinations of unitary operations , 2012, Quantum Inf. Comput..

[53]  Franco Nori,et al.  QuTiP: An open-source Python framework for the dynamics of open quantum systems , 2011, Comput. Phys. Commun..

[54]  U. Schollwoeck.  The density-matrix renormalization group in the age of matrix product states , 2010, 1008.3477.

[55]  J. Rarity,et al.  Photonic quantum technologies , 2009, 1003.3928.

[56]  P. Zoller,et al.  Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms , 2009, 0905.2610.

[57]  D. Gottesman.  An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation , 2009, 0904.2557.

[58]  J M Gambetta,et al.  Simple pulses for elimination of leakage in weakly nonlinear qubits. , 2009, Physical review letters.

[59]  Andrew M. Childs.  On the Relationship Between Continuous- and Discrete-Time Quantum Walk , 2008, 0810.0312.

[60]  D. Lauvergnat,et al.  A simple and efficient evolution operator for time-dependent Hamiltonians: the Taylor expansion. , 2007, The Journal of chemical physics.

[61]  K. Mølmer,et al.  Entanglement and quantum computation with ions in thermal motion , 2000, quant-ph/0002024.

[62]  R. Feynman.  Simulating physics with computers , 1999 .

[63]  A. Kitaev.  Quantum computations: algorithms and error correction , 1997 .

[64]  J. Oitmaa,et al.  Series expansions for the massive Schwinger model in Hamiltonian lattice theory , 1997, hep-lat/9701015.

[65]  Seth Lloyd,et al.  Universal Quantum Simulators , 1996, Science.

[66]  Kristen Nygaard,et al.  The development of the SIMULA languages , 1978, SIGP.

[67]  L. Boehnke,et al.  Density Matrix Renormalization Group , 2008 .

[68]  Aric Hagberg,et al.  Exploring Network Structure, Dynamics, and Function using NetworkX , 2008, Proceedings of the Python in Science Conference.

[69]  R. Needs,et al.  Quantum Monte Carlo simulations of solids , 2001 .

[70]  B. Chakrabarti,et al.  Quantum Ising Phases and Transitions in Transverse Ising Models , 1996 .

[71]  A. Auerbach.  Interacting electrons and quantum magnetism , 1994 .