Optimizing qubit resources for quantum chemistry simulations in second quantization on a quantum computer

Moll, Nikolaj; Fuhrer, Andreas; Staar, Peter; Tavernelli, Ivano

doi:10.1088/1751-8113/49/29/295301

Cited by 70 publications

(70 citation statements)

References 35 publications

(53 reference statements)

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“…A particular attention is dedicated to generating compact qubit forms for symmetry projectors, which was a problem discovered in earlier studies. 20,21 This appears to be possible only for some symmetries while for others only approximate expressions are feasible. Generally, time complexity of a single step of VQE is tied to the number of terms to be measured and their variances.…”

Section: Introductionmentioning

confidence: 99%

Exact and approximate symmetry projectors for the electronic structure problem on a quantum computer

Yen

Lang

Izmaylov

2019

The Journal of Chemical Physics

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Solving the electronic structure problem on a universal-gate quantum computer within the variational quantum eigensolver (VQE) methodology requires constraining the search procedure to a subspace defined by relevant physical symmetries. Ignoring symmetries results in convergence to the lowest eigenstate of the Fock space for the second quantized electronic Hamiltonian. Moreover, this eigenstate can be symmetry broken due to limitations of the wavefunction ansatz. To address this VQE problem, we introduce and assess methods of exact and approximate projectors to irreducible eigen-subspaces of available physical symmetries. Feasibility of symmetry projectors in the VQE framework is discussed, and their efficiency is compared with symmetry constraint optimization procedures. Generally, projectors introduce higher numbers of terms for VQE measurement compare to the constraint approach. On the other hand, the projection formalism improves accuracy of the variational wavefunction ansatz without introducing additional unitary transformations, which is beneficial for reducing depths of quantum circuits.

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Section: Introductionmentioning

confidence: 99%

Exact and approximate symmetry projectors for the electronic structure problem on a quantum computer

Yen

Lang

Izmaylov

2019

The Journal of Chemical Physics

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“…In previous works, trading quantum resources has been addressed for general algorithms [29], and quantum simulations [30][31][32]. In the two works of Moll et al and Bravyi et al, qubit requirements are reduced with a scheme that is different from ours.…”

Section: Resultsmentioning

confidence: 99%

“…In [11], the actions on two qubits are replaced with their expectation values after inspection of the Hamiltonian. In [30], on the other hand, the Hamiltonian is reduced to two qubits in a systematic fashion. Finally, the case is revisited in [31], where the problem is reduced below the combinatorical limit to one qubit.…”

Section: The Physical Hamiltonianmentioning

confidence: 99%

“…Overview of mappings presented in this paper, listed by the complexity of their code functions, their qubit savings, qubit requirements (n), properties of the resulting gates and first appearance. Mappings can be compared with respect to the size of plain words (N) and their targeted Hamming weight K. We also refer to different methods that are not listed, as they do not rely on codes in any way [30,31]. where h ab are complex coefficients, chosen in a way as to render H Hermitian.…”

Section: Introductionmentioning

confidence: 99%

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Fermion-to-qubit mappings with varying resource requirements for quantum simulation

Steudtner

Wehner

2018

New J. Phys.

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The mapping of fermionic states onto qubit states, as well as the mapping of fermionic Hamiltonian into quantum gates enables us to simulate electronic systems with a quantum computer. Benefiting the understanding of many-body systems in chemistry and physics, quantum simulation is one of the great promises of the coming age of quantum computers. Interestingly, the minimal requirement of qubits for simulating Fermions seems to be agnostic of the actual number of particles as well as other symmetries. This leads to qubit requirements that are well above the minimal requirements as suggested by combinatorial considerations. In this work, we develop methods that allow us to tradeoff qubit requirements against the complexity of the resulting quantum circuit. We first show that any classical code used to map the state of a fermionic Fock space to qubits gives rise to a mapping of fermionic models to quantum gates. As an illustrative example, we present a mapping based on a nonlinear classical error correcting code, which leads to significant qubit savings albeit at the expense of additional quantum gates. We proceed to use this framework to present a number of simpler mappings that lead to qubit savings with a more modest increase in gate difficulty. We discuss the role of symmetries such as particle conservation, and savings that could be obtained if an experimental platform could easily realize multi-controlled gates.

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“…[], where a superconducting circuit made of frequency‐tunable qubits and implementing two‐qubit controlled‐phase gates according to scheme (i) was used to probe the dynamics of a chain of nine interacting spins, starting in a factorized state and evolving along an adiabatic trajectory by switching on an anisotropic exchange interaction term. Recent results in hybrid quantum‐classical approaches, such as the VQE method already recalled at the end of the previous Section, have been efficiently employed to show quantum chemistry simulations on superconducting NISQ processors, in which the ground state energy of multi‐atomic molecules was calculated with precision approaching the chemical accuracy limits . Using an evolution of the VQE algorithm, nuclear physics quantum simulations have also been reported in superconducting quantum hardware, with the cloud computing of the deuteron binding energy .…”

Section: Experimental Achievements and Prospective Technologiesmentioning

confidence: 99%

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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Optimizing qubit resources for quantum chemistry simulations in second quantization on a quantum computer

Cited by 70 publications

References 35 publications

Exact and approximate symmetry projectors for the electronic structure problem on a quantum computer

Exact and approximate symmetry projectors for the electronic structure problem on a quantum computer

Fermion-to-qubit mappings with varying resource requirements for quantum simulation

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

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