Optimizing Electronic Structure Simulations on a Trapped-ion Quantum Computer using Problem Decomposition
Yukio Kawashima, Erika Lloyd, Marc P. Coons, Yunseong Nam, Shunji Matsuura, Alejandro J. Garza, Sonika Johri, Lee Huntington, Valentin Senicourt, Andrii O. Maks… 展开作者
Yukio Kawashima, Erika Lloyd, Marc P. Coons, Yunseong Nam, Shunji Matsuura, Alejandro J. Garza, Sonika Johri, Lee Huntington, Valentin Senicourt, Andrii O. Maksymov, Jason H. V. Nguyen, Jungsang Kim, Nima Alidoust, Arman Zaribafiyan, Takeshi Yamazaki
Quantum computers have the potential to advance material design and drug discovery by performing costly electronic structure calculations. A critical aspect of this application requires optimizing the limited resources of the quantum hardware. Here, we experimentally demonstrate an end-to-end pipeline that focuses on minimizing quantum resources while maintaining accuracy. Using density matrix embedding theory as a problem decomposition technique, and an ion-trap quantum computer, we simulate a ring of 10 hydrogen atoms without freezing any electrons. The originally 20-qubit system is decomposed into 10 two-qubit problems, making it amenable to currently available hardware. Combining this decomposition with a qubit coupled cluster circuit ansatz, circuit optimization, and density matrix purification, we accurately reproduce the potential energy curve in agreement with the full configuration interaction energy in the minimal basis set. Our experimental results are an early demonstration of the potential for problem decomposition to accurately simulate large molecules on quantum hardware.
Trapped, laser-cooled atoms and ions are quantum systems which can be experimentally controlled with an as yet unmatched degree of precision. Due to the control of the motion and the internal degrees of freedom, these quantum systems can be adequately described by a well known Hamiltonian. In this colloquium, we present powerful numerical tools for the optimization of the external control of the motional and internal states of trapped neutral atoms, explicitly applied to the case of trapped laser-cooled ions in a segmented ion-trap. We then delve into solving inverse problems, when optimizing …
Optimal control techniques are applied for the decomposition of unitary quantum operations into a sequence of single-qubit gates and entangling operations. To this end, we modify a gradient-ascent algorithm developed for systems of coupled nuclear spins in molecules to make it suitable for trapped ion quantum computing. We decompose unitary operations into entangling gates that are based on a nonlinear collective spin operator and complemented by global spinflip and local light shift gates. Among others, we provide explicit decompositions of controlled-NOT and Toffoli gates, and a simple quant…
Optimal control theory is a versatile tool that presents a route to significantly improving figures of merit for quantum information tasks. We combine it here with the geometric theory for local equivalence classes of two-qubit operations to derive an optimization algorithm that determines the best entangling two-qubit gate for a given physical setting. We demonstrate the power of this approach for trapped polar molecules and neutral atoms.
We propose a method to simulate spin models in trapped ions using a digital-analog approach, consisting in a suitable gate decomposition in terms of analog blocks and digital steps. In this way, we show that the quantum dynamics of an enhanced variety of spin models could be implemented with substantially less number of gates than a fully digital approach. Typically, analog blocks are built of multipartite dynamics providing the complexity of the simulated model, while the digital steps are local operations bringing versatility to it. Finally, we describe a possible experimental implementation…
Although quantum computing hardware has evolved significantly in recent years, spurred by increasing industrial and government interest, the size limitation of current generation quantum computers remains an obstacle when applying these devices to relevant, real-world problems. In order to effectively exploit the potential benefits of quantum computing, heterogeneous approaches that combine both classical and quantum computing techniques are needed. In this work, we explore multiple heterogeneous approaches to solving multiple industry-relevant benchmark problems in order to understand how bes…
We propose an all optical quantum computation scheme, with trapped electron spin qubits, using their Coulomb exchange interaction with optically excited microcavity exciton-polaritons. This paper describes a single qubit rotation, which together with two-qubit controlled-z gate presented in PRB 85, 241403(R) (2012), form a set of universal logic gates. The errors due to finite cavity lifetime and incorrect orientation of the rotation axis are minimized by optimizing pump pulse parameters. With projective homodyne phase measurement and initialization, our scheme is a promising candidate for the…
We show how to construct a multi-qubit control gate on a quantum register of an arbitrary size N. This gate performs a single-qubit operation on a specific qubit conditioned by the state of other N-1 qubits. We provide an algorithm how to build up an array of networks consisting of single-qubit rotations and multi-qubit control-NOT gates for the synthesis of an arbitrary entangled quantum state of N qubits. We illustrate the algorithm on a system of cold trapped ions. This example illuminates the efficiency of the direct implementation of the multi-qubit CNOT gate compared to its decomposition…
It is well known that the neutrino flavor in extreme astrophysical environments changes under the effect of three contributions: the vacuum oscillation, the interaction with the surrounding matter, and the collective oscillations due to interactions between different neutrinos. The latter adds a non-linear contribution to the equations of motion, making the description of their dynamics complex. In this work we study various strategies to simulate the coherent collective oscillations of a system of N neutrinos in the two-flavor approximation using quantum computation. This was achieved by usin…
Promise of Graph Sparsification and Decomposition for Noise Reduction in QAOA: Analysis for Trapped-Ion Compilations
Carnegie Mellon University（卡内基梅隆大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；Georgia Tech Research Institute（佐治亚理工学院研究院）；Massachusetts Institute of Technology（麻省理工学院）
We study variants of Shor's code that are adept at handling single-axis correlated idling errors, which are commonly observed in many quantum systems. By using the repetition code structure of the Shor's code basis states, we calculate the logical channel applied to the encoded information when subjected to coherent and correlated single qubit idling errors, followed by stabilizer measurement. Changing the signs of the stabilizer generators allows us to change how the coherent errors interfere, leading to a quantum error correcting code which performs as well as a classical repetition code of …
Trapped ions offer long internal state (spin) coherence times and strong inter-particle interactions mediated by the Coulomb force. This makes them interesting candidates for quantum simulation of coupled lattices. To this end it is desirable to be able to trap ions in arbitrary conformations with precisely controlled local potentials. We provide a general method for optimizing periodic planar radio-frequency electrodes for generating ion trapping potentials with specified trap locations and curvatures above the electrode plane. A linear-programming algorithm guarantees globally optimal electr…
Large-scale portfolio optimization on a trapped-ion quantum computer
Kipu Quantum GmbH（基普量子有限公司）；Department of Physical Chemistry, University of the Basque Country EHU（巴斯克大学物理化学系）；TUM School of Management, Technische Universität München（慕尼黑工业大学管理学院）；Instituto de Ciencia de Materiales de Madrid (CSIC)（马德里材料科学研究所（西班牙国家研究委员会））；Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid（马德里自治大学凝聚态物质理论物理系）；IDAL, Electronic Engineering Department, ETSE-UV, University of Valencia（瓦伦西亚大学电子工程学院IDAL）；IonQ Inc.（IonQ公司）；IonQ Italia（IonQ意大利分公司）
We develop a global variable substitution method that reduces $n$-variable monomials in combinatorial optimization problems to equivalent instances with monomials in fewer variables. We apply this technique to $3$-SAT and analyze the optimal quantum circuit depth needed to solve the reduced problem using the quantum approximate optimization algorithm. For benchmark $3$-SAT problems, we find that the upper bound of the circuit depth is smaller when the problem is formulated as a product and uses the substitution method to decompose gates than when the problem is written in the linear formulatio…
We propose the implementation of the Holstein model by means of digital methods in a linear chain of trapped ions. We show how the simulation fidelity scales with the generation of phononic excitations. We propose a decomposition and a stepwise trapped-ion implementation of the Holstein Hamiltonian. Via numerical simulations, we study how the protocol is affected by realistic gates. Finally, we show how measurements of the size of the simulated polaron can be performed.
Efficient realization of quantum algorithms is among main challenges on the way towards practical quantum computing. Various libraries and frameworks for quantum software engineering have been developed. Here we present a software package containing implementations of various quantum gates and well-known quantum algorithms using PennyLane library. Additoinally, we used a simplified technique for decomposition of algorithms into a set of gates which are native for trapped-ion quantum processor and realized this technique using PennyLane library. The decomposition is used to analyze resources re…
Protein folding on a 64 qubit trapped-ion hardware via counterdiabatic quantum optimization
Kipu Quantum GmbH（Kipu Quantum有限公司）；University of the Basque Country EHU（巴斯克大学）；Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC)（马德里材料科学研究所）；Universidad Autónoma de Madrid（马德里自治大学）；University of Valencia（瓦伦西亚大学）；IonQ Inc.（IonQ公司）
We investigate theoretically the spectrum of resonance fluorescence of a harmonically trapped atom, whose internal transitions are $Λ$--shaped and driven at two-photon resonance by a pair of lasers, which cool the center--of--mass motion. For this configuration, photons are scattered only due to the mechanical effects of the quantum interaction between light and atom. We study the spectrum of emission in the final stage of laser--cooling, when the atomic center-of-mass dynamics is quantum mechanical and the size of the wave packet is much smaller than the laser wavelength (Lamb--Dicke limit). …
We implement direct readout of the symmetric characteristic function of quantum states of the motional oscillation of a trapped calcium ion. Using suitably chosen internal electronic state-dependent displacements based on bi-chromatic laser fields we map the expectation value of the real or imaginary part of the displacement operator to the internal states, which are subsequently read out using fluorescence detection. Combining the two readout results provides full information about the symmetric characteristic function. We characterize the performance of the technique by applying it to a rang…
The time evolution of a closed quantum system is connected to its Hamiltonian through Schroedinger's equation. The ability to estimate the Hamiltonian is critical to our understanding of quantum systems, and allows optimization of control. Though spectroscopic methods allow time-independent Hamiltonians to be recovered, for time-dependent Hamiltonians this task is more challenging. Here, using a single trapped ion, we experimentally demonstrate a method for estimating a time-dependent Hamiltonian of a single qubit. The method involves measuring the time evolution of the qubit in a fixed basis …
The quest for experimental platforms that allow for the exploration, and even control, of the interplay of low dimensionality and frustration is a fundamental challenge in several fields of quantum many-body physics, such as quantum magnetism. Here, we propose the use of cold crystals of trapped ions to study a variety of frustrated quantum spin ladders. By optimizing the trap geometry, we show how to tailor the low dimensionality of the models by changing the number of legs of the ladders. Combined with a method for selectively hiding of ions provided by laser addressing, it becomes possible …
We propose a new protocol to implement ultra-fast two-qubit phase gates with trapped ions using spin-dependent kicks induced by resonant transitions. By only optimizing the allocation of the arrival times in a pulse train sequence the gate is implemented in times faster than the trapping oscillation period $T<2π/ω$. Such gates allow us to increase the number of gate operations that can be completed within the coherence time of the ion-qubits favoring the development of scalable quantum computers.
The prevalent approach to executing quantum algorithms on quantum computers is to break-down the algorithms to a concatenation of universal gates, typically single and two-qubit gates. However such a decomposition results in long gate sequences which are exponential in the qubit register size. Furthermore, gate fidelities tend to decrease when acting in larger qubit registers. Thus high-fidelity implementations in large qubit registers is still a prominent challenge. Here we propose and investigate multi-qubit entangling gates for trapped-ions. Our gates couple many qubits at once, allowing to…
A scheme to generate shared tripartite entangled states, with two-trapped atoms in a cavity held by Alice (qubits A1 and A2) entangled to a single trapped atom in a remote lab owned by Bob (B), is proposed. The entanglement is generated through interaction of trapped atoms with two mode squeezed light shared by the two cavities. The proposed scheme is an extension of the proposal of ref. [W. Son, M. S. Kim, J. Lee, and D. Ahn, J. Mod. Opt. 49, 1739 (2002)], where the possibility of entangling two remote qubits using a bipartite continuous variable state was examined. While the global negativit…
We identify gauge freedoms in quantum error correction (QEC) codes and introduce strategies for optimal control algorithms to find the gauges which allow the easiest experimental realization. Hereby, the optimal gauge depends on the underlying physical system and the available means to manipulate it. The final goal is to obtain optimal decompositions of QEC codes into elementary operations which can be realized with high experimental fidelities. In the first part of this paper, this subject is studied in a general fashion, while in the second part, a system of trapped ions is treated as a conc…
Optimizing Resource Costs: A Practical Guide to Achieving Target Security in Verifiable Blind Quantum Computing
QuTech, Delft University of Technology（代尔夫特理工大学 QuTech）；Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学 卡弗里纳米科学研究所）；Quantum Computer Science, EEMCS, Delft University of Technology（代尔夫特理工大学 EEMCS 量子计算机科学）
We describe, realize, and experimentally investigate a method to perform physical rotations of ion chains, trapped in a segmented surface Paul trap, as a building block for large scale quantum computational sequences. Control of trapping potentials is achieved by parametrizing electrode voltages in terms of spherical harmonic potentials. Voltage sequences that enable crystal rotations are numerically obtained by optimizing time-dependent ion positions and motional frequencies, taking into account the effect of electrical filters in our set-up. We minimize rotation-induced heating by expanding …
We analyze the quantum entanglement between two interacting atoms trapped in a spherical harmonic potential. At ultra-cold temperature, ground state entanglement is generated by the dominated s-wave interaction. Based on a regularized pseudo-potential Hamiltonian, we examine the quantum entanglement by performing the Schmidt decomposition of low-energy eigenfunctions. We indicate how the atoms are paired and quantify the entanglement as a function of a modified s-wave scattering length inside the trap.
Amplitude Amplification -- a key component of Grover's Search algorithm -- uses an iterative approach to systematically increase the probability of one or multiple target states. We present novel strategies to enhance the amplification procedure by partitioning the states into classes, whose probabilities are increased at different levels before or during amplification. The partitioning process is based on the binomial distribution. If the classes to which the search target states belong are known in advance, the number of iterations in the Amplitude Amplification algorithm can be drastically …
Controlling the interaction graph between spins or qubits in a quantum simulator allows user-controlled tailoring of native interactions to achieve a target Hamiltonian. The flexibility of engineering long-ranged phonon-mediated spin-spin interactions in a trapped ion quantum simulator offers such a possibility. Trapped ions, a leading candidate for simulating computationally hard quantum many-body dynamics, are most readily trapped in a linear 1D chain, limiting their utility for readily simulating higher dimensional spin models. In this work, we introduce a hybrid method of analog-digital si…
Optimizing Doppler laser cooling protocols for quantum sensing with 3D ion crystals in a Penning trap
University of Colorado, Boulder（科罗拉多大学博尔德分校）；Sandia National Laboratories（桑迪亚国家实验室）；Indian Institute of Technology Madras（马德拉斯印度理工学院）；National Institute of Standards and Technology（美国国家标准与技术研究院）；University of California, San Diego（加州大学圣地亚哥分校）
