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Simulating chemistry using quantum computers
Ivan Kassal, James D. Whitfield, Alejandro Perdomo-Ortiz, Man-Hong Yung, Alán Aspuru-Guzik
TL;DR
Quantum chemistry is difficult because exact simulation scales steeply with system size. This review surveys quantum algorithms and computational models for chemical simulation, finding theoretical advantages and early experimental realizations, while identifying important complexity and research boundaries.
Problem
Quantum-system simulation becomes computationally unreachable on current computers as Hilbert spaces grow exponentially with system size.
Method
The review surveys quantum algorithms and adiabatic or circuit-model approaches for electronic structure, chemical dynamics, protein folding, observables, and thermal states.
Results
Quantum computers can simulate chemical systems more efficiently in some cases, certain chemical ground states can be found efficiently, and chemical simulations have been experimentally realized.
Takeaways & Limitations
Quantum simulation provides a potential tool for chemical properties and dynamics, with applications including correlation functions, reaction rates, and lattice protein folding.
Takeaways & Limitations
First-quantization simulations may require dozens of qubits and millions of gates, while ground- and thermal-state scaling for chemical systems remains an open question.
Abstract
from arXiv · showhide
The difficulty of simulating quantum systems, well-known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on conventional computers, by mapping the quantum system to another, more controllable one. In this review, we discuss to what extent the ideas in quantum computation, now a well-established field, have been applied to chemical problems. We describe algorithms that achieve significant advantages for the electronic-structure problem, the simulation of chemical dynamics, protein folding, and other tasks. Although theory is still ahead of experiment, we outline recent advances that have led to the first chemical calculations on small quantum information processors.
1 INTRODUCTION
Quantum chemistry faces exponentially growing computational requirements as electronic-structure methods scale to larger or more accurate systems. The review examines quantum simulation as a way to apply quantum computation to difficult chemical problems.
- Electronic-structure calculations become unreachable on current computers because quantum-system Hilbert spaces grow exponentially with system size.
- The review covers quantum algorithms for exact non-adiabatic chemical dynamics, full-configuration-interaction electronic structure, and chemical optimization.
- The review also discusses experimental implementations, including the first quantum simulations of chemical systems.
2 QUANTUM COMPUTATION
Quantum computation represents information with qubits and manipulates it through circuit or adiabatic models, while measurement and complexity constrain attainable advantages. Quantum simulation uses these models and tools such as the QFT to analyze chemical systems and computational scaling.
- 2.1 Differences between quantum and classical computation: Qubits occupy superpositions in an exponentially large Hilbert space, and entanglement is necessary for quantum-computational advantage.
- 2.1 Differences between quantum and classical computation: Quantum parallelism produces information about many function outputs at once, but measurement does not make all individual outputs directly accessible.
- 2.2.1 The circuit model: A quantum circuit applies a multi-qubit unitary transformation, typically decomposed into elementary one- or two-qubit gates.
- 2.2.1 The circuit model: Universal quantum computers can approximate any unitary transformation using suitable universal gate sets.
- 2.2.1 The circuit model: For n qubits, the quantum Fourier transform requires O(n^2) elementary gates and is used for quantum dynamics simulation and observable measurement.
- 2.2.2 Adiabatic quantum computation: In adiabatic computation, slowly changing a Hamiltonian from Hi to Hf carries its ground state into a solution-encoding ground state.
- 2.3 Computational complexity: Quantum speed-up is evaluated by asymptotic operation or time scaling, with P, NP, BQP, and QMA providing complexity-theoretic categories.
3 QUANTUM SIMULATION
Quantum simulation maps chemical systems onto controllable quantum systems to address classically difficult problems, with algorithms spanning electronic structure, dynamics, state preparation, and observable measurement. The review also identifies resource costs and scalability limits, while reporting early chemical calculations on small processors.
- Quantum simulation: Universal quantum simulation maps a target quantum system onto a controllable quantum computer, offering a framework for chemical problems difficult on conventional computers.The review distinguishes universal simulation from dedicated quantum simulation, which engineers one quantum system to simulate another.
- Electronic-structure simulation: Second quantization uses one qubit per basis state and classically precomputed integrals, while first quantization supports processes difficult to represent in a small fixed basis.Second-quantized electronic-structure simulation has cost O(M5), whereas pairwise Coulomb interactions enable first-quantized scaling of O(B2).
- Chemical dynamics: Exact simulation can outperform the Born-Oppenheimer approach for reactions involving more than about four atoms because the quantum computer evaluates the potential on the fly.In the exact approach, the potential is the pairwise Coulomb interaction; the Born-Oppenheimer approach requires evaluating V(r1, . . . , rB) during simulation.
- Measuring observables: Phase estimation and related methods extract molecular energies, eigenstates, correlation functions, reaction rates, branching ratios, and scattering matrices from simulated quantum dynamics.Correlation functions can be estimated efficiently when the associated pseudo-dynamics are efficiently simulable, without the dynamic sign problem affecting classical Monte Carlo sampling.
- Measuring observables: Quantum gradient methods calculate molecular gradients and Hessians with a number of energy evaluations independent of system size, enabling geometry optimization.The same framework applies to properties such as dipole moments and static polarizabilities, which are energy derivatives with respect to external parameters.
- State preparation and limits: Ground- and thermal-state preparation is not fully scalable in general: product-state fidelity can fall as (1 −ϵ)^N, and broad Hamiltonian classes are qma-hard.Quantum procedures can prepare thermal states under assumptions such as efficient phase estimation, and classical Hamiltonians can receive a quadratic quantum speedup in some preparation methods.
4 OPTIMIZATION WITH ADIABATIC QUANTUM SIMULATION
Adiabatic quantum computation encodes chemistry- and biology-related optimization solutions in final Hamiltonian ground states. The review develops lattice protein-folding constructions and discusses their encoding, while noting that general instances remain computationally hard.
- The approach targets chemistry- and biology-related problems including drug design, molecular recognition, geometry optimization, and protein folding.
- Adiabatic quantum computation prepares a final Hamiltonian ground state that encodes the solution to a discrete optimization problem.
- Lattice protein folding: The lattice heteropolymer problem models protein folds as self-avoiding walks whose energies depend on interactions among non-bonded nearest-neighbor amino acids.
- Lattice protein folding: For a two-dimensional N-amino-acid protein, two binary variables encode the direction of each of the N −1 bonds, with the first bond fixed.
- Lattice protein folding: The four-amino-acid chaperone-assisted folding example converts a quartic free-energy function into quadratic form using two extra ancilla binary variables.
- Computational boundary: Solving the hydrophobic-polar model is np-hard, so polynomial-time solution of arbitrary instances is unlikely; exploiting structure or instance information motivates heuristic strategies.
5 EXPERIMENTAL PROGRESS
Experimental quantum simulation has progressed across optical, nuclear-spin, and superconducting platforms, including molecular and optimization demonstrations. The reviewed experiments remain small, while trapped-ion chemical applications had not yet arrived.
- Experimental quantum simulation progressed from early nuclear-magnetic-resonance oscillator studies to chemical applications on available quantum-computational devices.
- Optical systems: An optical quantum computer performed the first quantum simulation of a molecular system using a minimal-basis model of H2 encoded in photon polarization.
- Nuclear magnetic resonance: NMR platforms simulated H2 using two nuclear-spin qubits in 13C-labeled chloroform and achieved 45 bits of precision.
- Superconducting systems: A superconducting-qubit experiment on the four-amino-acid chaperone-assisted peptide found the correct solution with probability 78% at 20 mK.
- Experimental limitations: Characterization of the superconducting device was underway.
- Trapped ions: Cold trapped ions offered highly controllable qubits, but chemical applications on that platform were still forthcoming.
6 CONCLUSIONS
The review concludes that quantum computers offer methods for simulating chemical properties and lattice protein folding, and that quantum information has already influenced quantum chemistry. However, practical systems remained limited by hardware scale and decoherence.
- Quantum computers could simulate chemical systems and properties including correlation functions and reaction rates, while also addressing lattice protein folding.
- Adding qubits increases the need to control decoherence, while practical error correction may face substantial spatial and temporal overheads.
- The review reported first chemistry-relevant experiments and anticipated further advances in the near future.
- Quantum information has influenced new quantum-chemistry methods, including extensions of density matrix renormalization group, and may clarify classical computational complexity.
- As of 2010, quantum information processors were described as being in a vacuum-tube era, limiting routine exact dynamics and full-configuration-interaction calculations.
Summary Points
Quantum computers offer efficient approaches to simulating chemical systems, including certain ground states, quantum dynamics, and protein folding. Experimental implementations have been demonstrated across several quantum-information platforms.
- A universal quantum computer can simulate chemical systems more efficiently than a classical computer, in some cases exponentially so.
- Certain chemical Hamiltonians have efficiently preparable ground states, although preparing an arbitrary Hamiltonian’s ground state is qma-complete.
- Simulation of physical quantum dynamics is generally efficient on a quantum computer.
- Properties of quantum states can be obtained through various measurement methods.
- Adiabatic quantum computation can study classical optimization problems such as lattice protein folding.
- Quantum simulation for chemistry has been experimentally realized using quantum optics, nuclear magnetic resonance, and superconducting devices.
Future Issues
Future work includes expanding experimental quantum simulation beyond condensed-matter systems, addressing decoherence, incorporating error correction, and exploring alternative computation models.
- Developing simulation methods based on alternative models of quantum computation remains an open research direction.
- Dedicated quantum simulators have mostly targeted condensed-matter systems, leaving experimental simulation of chemical systems as a desirable direction.
- Decoherence is currently the major obstacle to scaling existing experimental setups, requiring theoretical and experimental progress.
- Large-scale simulations will require quantum error-correction methods, which this review does not cover.