Computation of Molecular Spectra on a Quantum Processor with an Error-Resilient Algorithm

Colless, James; Ramasesh, Vinay; Dahlen, Dar; Blok, Machiel; Schwartz, Maurice L.; McClean, Jarrod R.; Carter, J.; Jong, Wibe A. de; Siddiqi, Irfan

doi:10.1103/physrevx.8.011021

Cited by 519 publications

(562 citation statements)

References 31 publications

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“…In order improve the projection criteria we add additional n-representability constraints to the minimization procedure outlined in equation (55). Given a collection of 2-RDM elements at some unknown precision, or possibly missing crucial elements, our reconstruction scheme seeks to minimize the Frobenius norm of the difference between the reconstructed 2-RDM and the set of known measurements subject to approximate nrepresentability constraints.…”

Section: Rdm Reconstruction With Approximate Representability Constramentioning

confidence: 99%

Application of fermionic marginal constraints to hybrid quantum algorithms

2018

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Many quantum algorithms, including recently proposed hybrid classical/quantum algorithms, make use of restricted tomography of the quantum state that measures the reduced density matrices, or marginals, of the full state. The most straightforward approach to this algorithmic step estimates each component of the marginal independently without making use of the algebraic and geometric structure of the marginals. Within the field of quantum chemistry, this structure is termed the fermionic n-representability conditions, and is supported by a vast amount of literature on both theoretical and practical results related to their approximations. In this work, we introduce these conditions in the language of quantum computation, and utilize them to develop several techniques to accelerate and improve practical applications for quantum chemistry on quantum computers. As a general result, we demonstrate how these marginals concentrate to diagonal quantities when measured on random quantum states. We also show that one can use fermionic n-representability conditions to reduce the total number of measurements required by more than an order of magnitude for medium sized systems in chemistry. As a practical demonstration, we simulate an efficient restoration of the physicality of energy curves for the dilation of a four qubit diatomic hydrogen system in the presence of three distinct one qubit error channels, providing evidence these techniques are useful for pre-fault tolerant quantum chemistry experiments. semidefinite-ness, constrained spin-, and particle-numbers are expected to increase the observed energy of the 2-RDM with respect to the uncorrected noisy 2-RDM.

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Section: Rdm Reconstruction With Approximate Representability Constramentioning

confidence: 99%

Application of fermionic marginal constraints to hybrid quantum algorithms

2018

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“…However, this comes at the cost of an increased number of measurements, and the introduction of a wavefunction ansatz that can limit the accuracy of the simulation (although our recent approach, ADAPT-VQE, can remove the ansatz error). 8 The initial demonstration of VQE 7 was followed by several theoretical studies [9][10][11][12][13][14][15] and demonstrations on other hardware such as superconducting qubits 10,14,16 and trapped ions. 17,18 A key ingredient in VQE is the ansatz, which is implemented as a quantum circuit which constructs trial wavefunctions that are measured and then updated in a classical optimization loop.…”

Section: Introductionmentioning

confidence: 99%

Is the Trotterized UCCSD Ansatz Chemically Well-Defined?

Grimsley

Claudino

Economou

et al. 2019

J. Chem. Theory Comput.

139

148

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The variational quantum eigensolver (VQE) has emerged as one of the most promising near-term quantum algorithms that can be used to simulate many-body systems such as molecular electronic structures. Serving as an attractive ansatz in the VQE algorithm, unitary coupled cluster (UCC) theory has seen a renewed interest in recent literature. However, unlike the original classical UCC theory, implementation on a quantum computer requires a finite-order Suzuki-Trotter decomposition to separate the exponentials of the large sum of Pauli operators. While previous literature has recognized the non-uniqueness of different orderings of the operators in the Trotterized form of UCC methods, the question of whether or not different orderings matter at the chemical scale has not been addressed. In this letter, we explore the effect of operator ordering on the Trotterized UCCSD ansatz, as well as the much more compact k-UpCCGSD ansatz recently proposed by Lee et al. We observe a significant, system-dependent variation in the energies of Trotterizations with different operator orderings. The energy variations occur on a chemical scale, sometimes on the order of hundreds of kcal/mol. This letter establishes the need to define not only the operators present in the ansatz, but also the order in which they appear. This is necessary for adhering to the quantum chemical notion of a "model chemistry", in addition to the general importance of scientific reproducibility. As a final note, we suggest a useful strategy to select out of the combinatorial number of possibilities, a single well-defined and effective ordering of the operators.

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“…In addition to these techniques, other methods have been proposed that are more problem-specific. The quantum subspace expansion method [96], [97] involves the measurement of additional excitation operators for variational ground states, and in addition to providing excited state energies, also mitigates on energy estimates. Other recent approaches to error mitigation for fermionic problems rely on the conservation of "known quantities", such as particle number [98]- [100].…”

Section: Error Mitigation and Correctionmentioning

confidence: 99%

Challenges and Opportunities of Near-Term Quantum Computing Systems

et al. 2020

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The concept of quantum computing has inspired a whole new generation of scientists, including physicists, engineers, and computer scientists, to fundamentally change the landscape of information technology. With experimental demonstrations stretching back more than two decades, the quantum computing community has achieved a major milestone over the past few years: the ability to build systems that are stretching the limits of what can be classically simulated, and which enable cloudbased research for a wide range of scientists, thus increasing the pool of talent exploring early quantum systems. While such noisy near-term quantum computing systems fall far short of the requirements for fault-tolerant systems, they provide unique testbeds for exploring the opportunities for quantum applications.Here we highlight the facets associated with these systems, including quantum software, cloud access, benchmarking quantum systems, error correction and mitigation in such systems, and understanding the complexity of quantum circuits and how early quantum applications can run on near term quantum computers.

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Computation of Molecular Spectra on a Quantum Processor with an Error-Resilient Algorithm

Cited by 519 publications

References 31 publications

Application of fermionic marginal constraints to hybrid quantum algorithms

Application of fermionic marginal constraints to hybrid quantum algorithms

Is the Trotterized UCCSD Ansatz Chemically Well-Defined?

Challenges and Opportunities of Near-Term Quantum Computing Systems

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