Linear and Logarithmic Time Compositions of Quantum Many-Body Operators

Motzoi, Felix; Kaicher, Michael P.; Wilhelm, Frank K.

doi:10.1103/physrevlett.119.160503

Cited by 31 publications

(26 citation statements)

References 58 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some routes to reduce the number of experiments by collecting Hamiltonian terms into commuting groups and dropping Hamiltonian terms with small coefficients have already been proposed [23,46,51,57]. Wecker et al [48], estimated that for simulating the energy of ferrodoxin using this approach would require 10 19 total measurements. Though this estimate was made with pessimistic assumptions, the sheer number of measurements motivates one to pursue techniques to accelerate the operator averaging step of VQE and other hybrid algorithms.…”

Section: Introductionmentioning

confidence: 99%

Application of fermionic marginal constraints to hybrid quantum algorithms

2018

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Application of fermionic marginal constraints to hybrid quantum algorithms

2018

View full text Add to dashboard Cite

show abstract

“…Since the number of electrons n e for a given molecular system or a chemical reaction is constant, the total number of qubit excitations is also constant. Exchangetype interactions, which preserve the number of excitations on the qubit processor are, therefore, better suited than other two-qubit gates to compute molecular eigenstates [8,28]. In fact, using only excitation-preserving gates constrains the accessible state space to a subspace of the full 2 N -dimensional Hilbert space: only the N nedimensional manifold with n e electrons is explored in VQE.…”

mentioning

confidence: 99%

Gate-Efficient Simulation of Molecular Eigenstates on a Quantum Computer

et al. 2019

View full text Add to dashboard Cite

A key requirement to perform simulations of large quantum systems on near-term quantum hardware is the design of quantum algorithms with short circuit depth that finish within the available coherence time. A way to stay within the limits of coherence is to reduce the number of gates by implementing a gate set that matches the requirements of the specific algorithm of interest directly in hardware. Here, we show that exchange-type gates are a promising choice for simulating molecular eigenstates on near-term quantum devices since these gates preserve the number of excitations in the system. Complementing the theoretical work by Barkoutsos et al. [PRA 98, 022322 (2018)], we report on the experimental implementation of a variational algorithm on a superconducting qubit platform to compute the eigenstate energies of molecular hydrogen. We utilize a parametrically driven tunable coupler to realize exchange-type gates that are configurable in amplitude and phase on two fixed-frequency superconducting qubits. With gate fidelities around 95% we are able to compute the eigenstates within an accuracy of 50 mHartree on average, a limit set by the coherence time of the tunable coupler.The simulation of the electronic structure of molecular and condensed matter systems is a challenging computational task as the cost of resources increases exponentially with the number of electrons when accurate solutions are required. With the tremendous improvements in our ability to control complex quantum systems this bottleneck may be overcome by the use of quantum computing hardware [1]. In theory, various algorithms for quantum simulation have been designed to that end, including quantum phase estimation [2] or adiabatic algorithms [3]. With these algorithms the challenges for practical applications lie in the efficient mapping of the electronic Hamiltonian onto the quantum computer and in the required number of quantum gates that remains prohibitive on current and near-term quantum hardware [4] without quantum error correction schemes [5]. On the other hand, variational quantum eigensolver (VQE) methods [6, 7] can produce accurate results with a small number of gates [8] using for instance algorithms with low circuit depth [9] and do not require a direct mapping of the electronic Hamiltonian onto the hardware. Moreover, such algorithms are inherently robust against certain errors [8, 10, 11] and are therefore considered as ideal candidates for first practical implementations on non error-corrected, near-term quantum hardware.Recently, the molecular ground state energy of hydrogen and helium have been computed via VQE in proof of concept experiments using NMR quantum simulators [12][13][14], photonic architectures [6] or nitrogenvacancy centers in diamond [15]. Although very accurate energy estimates are obtained, quantum simulation of larger systems remains an intractable problem on these platforms because of the difficulties arising in scaling them up to more than a few qubits. For this reason trapped ions [16][17][18][19] and supe...

show abstract

“…Recent progress on technologies with quantum speedup focuses largely on optimizing dynamical quantum cost functionals via a set of external classical parameters. Such research includes quantum variational eigensolvers [1], annealers [2], simulators [3,4], circuit optimization [5,6], optimal control theory [7][8][9], and Boltzmann machines [10]. The minimized functional could be for example the energy of a simulated system, or the distance to a quantum computational gate.…”

mentioning

confidence: 99%

Global optimization of quantum dynamics with AlphaZero deep exploration

et al. 2020

View full text Add to dashboard Cite

While a large number of algorithms for optimizing quantum dynamics for different objectives have been developed, a common limitation is the reliance on good initial guesses, being either random or based on heuristics and intuitions. Here we implement a tabula rasa deep quantum exploration version of the Deepmind AlphaZero algorithm for systematically averting this limitation. AlphaZero employs a deep neural network in conjunction with deep lookahead in a guided tree search, which allows for predictive hidden variable approximation of the quantum parameter landscape. To emphasize transferability, we apply and benchmark the algorithm on three classes of control problems using only a single common set of algorithmic hyperparameters. AlphaZero achieves substantial improvements in both the quality and quantity of good solution clusters compared to earlier methods. It is able to spontaneously learn unexpected hidden structure and global symmetry in the solutions, going beyond even human heuristics. arXiv:1907.05672v1 [quant-ph]

show abstract

Linear and Logarithmic Time Compositions of Quantum Many-Body Operators

Cited by 31 publications

References 58 publications

Application of fermionic marginal constraints to hybrid quantum algorithms

Application of fermionic marginal constraints to hybrid quantum algorithms

Gate-Efficient Simulation of Molecular Eigenstates on a Quantum Computer

Global optimization of quantum dynamics with AlphaZero deep exploration

Contact Info

Product

Resources

About