Simulating Large Quantum Circuits on a Small Quantum Computer

Abstract

Limited quantum memory is one of the most important constraints for near-term quantum devices. Understanding whether a small quantum computer can simulate a larger quantum system, or execute an algorithm requiring more qubits than available, is both of theoretical and practical importance. In this Letter, we introduce cluster parameters $K$ and $d$ of a quantum circuit. The tensor network of such a circuit can be decomposed into clusters of size at most $d$ with at most $K$ qubits of inter-cluster quantum communication. We propose a cluster simulation scheme that can simulate any $(K,d)$-clustered quantum circuit on a $d$-qubit machine in time roughly $2^{O(K)}$, with further speedups possible when taking more fine-grained circuit structure into account. We show how our scheme can be used to simulate clustered quantum systems -- such as large molecules -- that can be partitioned into multiple significantly smaller clusters with weak interactions among them. By using a suitable clustered ansatz, we also experimentally demonstrate that a quantum variational eigensolver can still achieve the desired performance for estimating the energy of the BeH${}_2$ molecule while running on a physical quantum device with half the number of required qubits.

Codes are available at https://github.com/TianyiPeng/Partiton_VQE

References in corpus (40)

• Quantum Computing in the NISQ era and beyond
• Quantum Machine Learning
• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Area laws for the entanglement entropy - a review
• Efficient classical simulation of slightly entangled quantum computations
• The theory of variational hybrid quantum-classical algorithms
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Quantum support vector machine for big data classification
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• A Quantum Approximate Optimization Algorithm
• Efficient simulation of one-dimensional quantum many-body systems
• Scalable Quantum Simulation of Molecular Energies
• Optimal Hamiltonian Simulation by Quantum Signal Processing
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Towards Practical Quantum Variational Algorithms
• Lieb-Schultz-Mattis in Higher Dimensions
• Efficient quantum algorithms for simulating sparse Hamiltonians
• Quantum optimization using variational algorithms on near-term quantum devices
• Classical simulation of quantum many-body systems with a tree tensor network
• Quantum autoencoders for efficient compression of quantum data
• Realization of a scalable Shor algorithm
• Simulating quantum computation by contracting tensor networks
• Digitized adiabatic quantum computing with a superconducting circuit
• Distributed Quantum Computation Based-on Small Quantum Registers
• Trading classical and quantum computational resources
• Novel schemes for measurement-based quantum computation
• Scalable Architecture for a Room Temperature Solid-State Quantum Information Processor
• Measurement-based quantum computation beyond the one-way model
• Tapering off qubits to simulate fermionic Hamiltonians
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• 64-Qubit Quantum Circuit Simulation
• Efficient factorization with a single pure qubit and $logN$ mixed qubits
• Lowering qubit requirements for quantum simulations of fermionic systems
• Simulation of low-depth quantum circuits as complex undirected graphical models
• Classical Simulation of Intermediate-Size Quantum Circuits
• Optimizing qubit resources for quantum chemistry simulations in second quantization on a quantum computer
• Simulating Quantum Fields with Cavity QED
• On the simulation of quantum circuits
• From estimation of quantum probabilities to simulation of quantum circuits

Cited by in corpus (121)

• Quantum algorithms for quantum chemistry and quantum materials science
• A Theory of Trotter Error
• The Future of Quantum Computing with Superconducting Qubits
• Quantum Simulation for High Energy Physics
• Nearly optimal lattice simulation by product formulas
• Doubling the size of quantum simulators by entanglement forging
• CutQC: Using Small Quantum Computers for Large Quantum Circuit Evaluations
• Digital quantum simulation of open quantum systems using quantum imaginary time evolution
• Parallel Quantum Simulation of Large Systems on Small Quantum Computers
• Circuit knitting with classical communication
• Review of Distributed Quantum Computing. From single QPU to High Performance Quantum Computing
• Approximate amplitude encoding in shallow parameterized quantum circuits and its application to financial market indicator
• Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation
• Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions
• Quantum simulation with hybrid tensor networks
• Fast quantum circuit cutting with randomized measurements
• Multicore Quantum Computing
• Nearly tight Trotterization of interacting electrons
• Quantum Circuit Cutting with Maximum Likelihood Tomography
• Suppressing quantum circuit errors due to system variability
• Variational quantum eigensolver for the Heisenberg antiferromagnet on the kagome lattice
• Combining quantum processors with real-time classical communication
• Overhead for simulating a non-local channel with local channels by quasiprobability sampling
• Quantum advantage and noise reduction in distributed quantum computing
• Qubit-efficient entanglement spectroscopy using qubit resets
• High Dimensional Quantum Machine Learning With Small Quantum Computers
• Stabilizer Tensor Networks: universal quantum simulator on a basis of stabilizer states
• State Preparation on Quantum Computers via Quantum Steering
• An Expressive Ansatz for Low-Depth Quantum Approximate Optimisation
• Investigating the effect of circuit cutting in QAOA for the MaxCut problem on NISQ devices
• Perturbative quantum simulation
• N-electron valence perturbation theory with reference wavefunctions from quantum computing: application to the relative stability of hydroxide anion and hydroxyl radical
• Quantum Divide and Compute: Exploring The Effect of Different Noise Sources
• Quantum Divide and Compute: Hardware Demonstrations and Noisy Simulations
• Experimental Simulation of Larger Quantum Circuits with Fewer Superconducting Qubits
• Cutting multi-control quantum gates with ZX calculus
• Architectural Vision for Quantum Computing in the Edge-Cloud Continuum
• Virtual quantum resource distillation
• Simulating quantum circuits using tree tensor networks
• Preparing quantum many-body scar states on quantum computers
• Doubly optimal parallel wire cutting without ancilla qubits
• Enabling Large-Scale and High-Precision Fluid Simulations on Near-Term Quantum Computers
• Quantum computing quantum Monte Carlo with hybrid tensor network for electronic structure calculations
• Classical Splitting of Parametrized Quantum Circuits
• Variational Quantum Optimization of Nonlocality in Noisy Quantum Networks
• Qurzon: A Prototype for a Divide and Conquer Based Quantum Compiler
• Networked Quantum Services
• Quantum computation of molecular structure using data from challenging-to-classically-simulate nuclear magnetic resonance experiments
• Optimal joint cutting of two-qubit rotation gates
• Quantum circuit compilation and hybrid computation using Pauli-based computation
• The minimal canonical form of a tensor network
• Overhead-constrained circuit knitting for variational quantum dynamics
• Differentiable Programming of Isometric Tensor Networks
• Optimal quantum circuit cuts with application to clustered Hamiltonian simulation
• Single Qubit Error Mitigation by Simulating Non-Markovian Dynamics
• Variational quantum eigensolver with linear depth problem-inspired ansatz for solving portfolio optimization in finance
• $i$-QER: An Intelligent Approach towards Quantum Error Reduction
• A Multiscale Simulation Approach for Germanium-Hole-Based Quantum Processor
• A hybrid algorithm framework for small quantum computers with application to finding Hamiltonian cycles
• Experimental demonstration of a high-fidelity virtual two-qubit gate
• Error suppression by a virtual two-qubit gate
• A Hardware-Aware Gate Cutting Framework for Practical Quantum Circuit Knitting
• Experimental virtual distillation of entanglement and coherence
• Cutting circuits with multiple two-qubit unitaries
• Hybrid divide-and-conquer approach for tree search algorithms
• Modeling Short-Range Microwave Networks to Scale Superconducting Quantum Computation
• Distributed Quantum Computing for Chemical Applications
• Distributed quantum machine learning via classical communication
• Cutting a Wire with Non-Maximally Entangled States
• Divide-and-conquer verification method for noisy intermediate-scale quantum computation
• FragQC: An Efficient Quantum Error Reduction Technique using Quantum Circuit Fragmentation
• Reduce&chop: Shallow circuits for deeper problems
• Optimal wire cutting with classical communication
• Exponential Qubit Reduction in Optimization for Financial Transaction Settlement
• A Multilevel Framework for Partitioning Quantum Circuits
• Energy risk analysis with Dynamic Amplitude Estimation and Piecewise Approximate Quantum Compiling
• Noise reduction using past causal cones in variational quantum algorithms
• Network Operations Scheduling for Distributed Quantum Computing
• Machine-Learning Insights into the Entanglement-trainability Correlation of Parameterized Quantum Circuits
• QuTracer: Mitigating Quantum Gate and Measurement Errors by Tracing Subsets of Qubits
• The resource theory of tensor networks
• Folding-Free ZNE: A Comprehensive Quantum Zero-Noise Extrapolation Approach for Mitigating Depolarizing and Decoherence Noise
• Shadow Simulation of Quantum Processes
• Joint Wire Cutting with Non-Maximally Entangled States
• Single entanglement connection architecture between multi-layer bipartite Hardware Efficient Ansatz
• Parallel-in-time quantum simulation via Page and Wootters quantum time
• Quantum Circuit Distillation and Compression
• Tabu-driven Quantum Neighborhood Samplers
• Multithreaded parallelism for heterogeneous clusters of QPUs
• Multi-agent blind quantum computation without universal cluster states
• Quantum channel decomposition with pre- and post-selection
• Expanding variational quantum eigensolvers to larger systems by dividing the calculations between classical and quantum hardware
• Quantum Circuit Cutting for Classical Shadows
• Density matrix representation of hybrid tensor networks for noisy quantum devices
• A Cross-Platform Execution Engine for the Quantum Intermediate Representation
• Parallel Quantum Signal Processing Via Polynomial Factorization
• Entanglement-informed Construction of Variational Quantum Circuits
• Perspectives on Utilization of Measurements in Quantum Algorithms
• Three ways to share a QPU: Scheduling strategies for hybrid Quantum-HPC applications
• A Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics
• Distributing Quantum Computations, Shot-wise
• Dual Map Framework for Noise Characterization of Quantum Computers
• Gibbs state sampling via cluster expansions
• Making the cut: two methods for breaking down a quantum algorithm
• Correcting and extending Trotterized quantum many-body dynamics
• Parallelized Givens Ansatz for Molecular ground-states: Bridging Accuracy and Efficiency on NISQ Platforms
• Circuit cutting with classical side information
• Compiling universal quantum circuits
• Dynamic LOCC Circuits for Automated Entanglement Manipulation
• Matrix Product State on a Quantum Computer
• Joint Cutting for Hybrid Schrödinger-Feynman Simulation of Quantum Circuits
• Unitary-transformed projective squeezing: applications for circuit-knitting and state-preparation of non-Gaussian states
• Distributed variational quantum computing with deterministic entanglement tuning
• Circuit connectivity boosts by quantum-classical-quantum interfaces
• Implementation of Tensor Network Simulation TN-Sim under NWQ-Sim
• Hybrid Classical-Quantum Simulation of MaxCut using QAOA-in-QAOA
• Improving the trainability of VQE on NISQ computers for solving portfolio optimization using convex interpolation
• Qubit-efficient quantum combinatorial optimization solver
• Theoretical Chemistry Course for Students in Chemistry
• CutReg: A loss regularizer for enhancing the scalability of QML via adaptive circuit cutting
• Power and limitations of distributed quantum state purification