Bulletin of the American Physical Society
2023 APS March Meeting
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session Y72: Time Evolution Quantum Algorithms |
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Sponsoring Units: DQI Chair: Eli Chertkov, Quantinuum Room: Room 406 |
Friday, March 10, 2023 8:00AM - 8:12AM |
Y72.00001: An Alternative Approach to Quantum Imaginary Time Evolution Pejman Jouzdani, Calvin W Johnson, Eduardo R Mucciolo, Ionel Stetcu There is increasing interest in quantum algorithms that are based on the imaginary-time evolution (ITE), a successful classical numerical approach to obtain ground states. However, most of the proposals so far require heavy post-processing computational steps on a classical computer, such as solving linear equations. Here we provide an alternative approach to implement ITE. A key feature in our approach is the use of an orthogonal basis set: the propagated state is efficiently expressed in terms of orthogonal basis states at every step of the evolution. We argue that the number of basis states needed at those steps to achieve an accurate solution can be kept of the order of n, the number of qubits, by controlling the precision (number of significant digits) and the imaginary-time increment. The number of quantum gates per imaginary-time step is estimated to be polynomial in n. Additionally, while in many QAs the locality of the Hamiltonian is a key assumption, in our algorithm this restriction is not required. This characteristic of our algorithm renders it useful for studying highly nonlocal systems, such as the occupation-representation nuclear shell model. We illustrate our algorithm through numerical implementation on an IBM quantum simulator. |
Friday, March 10, 2023 8:12AM - 8:24AM |
Y72.00002: Improving success probability of imaginary-time evolution on a quantum computer Hirofumi Nishi, Taichi Kosugi, Yusuke Nishiya, Yu-ichiro Matsushita Quantum algorithms based on the imaginary-time evolution (ITE) method are actively researched due to their characteristics of the exponential decay of high-energy states. One proposal realizes the action of the ITE operator by introducing an ancilla qubit with some probability, called its probabilistic ITE (PITE) method. The advantage of the PITE method over other types of the ITE method on a quantum computer is the unnecessity of many evaluations of quantum circuits to obtain the next imaginary-time steps. However, the probabilistic nature of the PITE method brings us the drawback that a success probability, the probability of obtaining the state acted on by the ITE operator, exponentially decreases along with an increase of imaginary time. Here, we cope with the undesirable nature by using quantum amplitude amplification. The developed quantum circuits for PITE combined with quantum amplitude amplification (QAA) succeeded in the reduction of the circuit depth and improvement of the success probability. We present the simulation results employed by the proposed technique with a discussion of the computational overhead of the amplification circuits. |
Friday, March 10, 2023 8:24AM - 8:36AM |
Y72.00003: Efficient quantum time dynamics using the Yang-Baxter equation Sahil Gulania, Zichang He, Bo Peng, Niranjan Govind, Yuri Alexeev This study demonstrates how the Yang-Baxter equation (YBE) can be efficiently utilized to compress and produce a constant depth quantum circuit for efficient time dynamics of 1D lattice spin chains with nearest-neighbor interactions on real quantum devices. We show that the depth of quantum circuits for each time step is independent of time and step size and depends only on the number of spins. The depth of the compressed circuit is a linear function of the system size for the classes of Heisenberg model Hamiltonians studied in this work. We rigorously show that the number of CNOT gates in the compressed circuit only scales quadratically with system size [1]. This allows for simulations of time dynamics of very large 1D spin chains. To demonstrate the efficacy of the developed technique, we have performed time dynamics simulations of three and five spins on an IBM quantum computer and compared the results from both compressed and uncompressed quantum circuits. We have also developed an open-source algebraic compiler (QuYBE) based on this approach to compress quantum circuits [2]. QuYBE is a first step towards making this technique available to the broader community of scientists from multiple domains. |
Friday, March 10, 2023 8:36AM - 8:48AM |
Y72.00004: Algebraic Compression of Quantum Circuits for Hamiltonian Evolution: Part Two Roel Van Beeumen, Efekan Kökcü, Lindsay Bassman, Natalia Wilson, Daan Camps, Bert de Jong, Alexander F Kemper Generating efficient circuits for time evolution is an important step in furthering the use of quantum computers as a tool for simulating many-body physics, which involves evolving states and computing their overlaps. For certain Hamiltonians, including often-studied ones such as the transverse field Ising model, using compression methods that rely on local algebraic relations between quantum gates [1,2] the time evolution may be significantly shortened into a circuit with a depth independent of simulation time. While powerful, the compression method is still missing several key features: it can only compress 1D chains, and cannot compress the controlled evolution that is necessary for computing wave function overlaps. Here, we present an advanced algebraic compression algorithm that overcomes these hurdles. First, we develop the necessary mathematics to enable compression of free fermionic evolution on any lattice topology, enabling embedding mismatching topologies on available quantum computers. Secondly, by extending the algebraic structure to controlled gates, we enable compression of controlled evolution with the addition of O($n$) controlled gates. In both cases, the compression for $n$ qubits results in a circuit with O($n$) depth and O($n^2$) gates. We demonstrate these developments in the contexts of two-dimensional free fermionic evolution and in the evaluation of the Zak phase in the Creutz model. These developments now enable the full range of necessary capabilities for simulating free fermionic and corresponding spin models, e.g., the 1D TFIM, TFXY, and Kitaev type models. [1] E. Kökcü et al., Phys. Rev. A 105, 032420 (2021). [2] D. Camps et al., SIAM Journal on Matrix Analysis and Applications, 43:3, pp. 1084-1108 (2022). |
Friday, March 10, 2023 8:48AM - 9:00AM |
Y72.00005: Optimal Hamiltonian simulation for time-periodic systems Kaoru Mizuta Implementing time-evolution operators under many-body Hamiltonians, called Hamiltonian simulation, is one of the most important tasks for potential applications of quantum computers toward condensed matter physics and quantum chemistry. Recently, the qubitization has achieved a comparably good way to organize time-evolution under time-independent Hamiltonians, with an arbitrarily small error . The number of gates required for the qubitization has a theoretically optimal scaling both in time and inverse error . In contrast, for time-dependent Hamiltonians, the existing algorithms largely rely on the truncated Dyson-series expansion. Due to the difficulty of handling time-dependency, we need much resources compared to the qubitization. It is a nontrivial and important question whether there exists an optimal algorithm for time-dependent cases whose resource is as large as that for time-independent cases. |
Friday, March 10, 2023 9:00AM - 9:12AM |
Y72.00006: Quantum time dynamics of qudit Hamiltonians employing the Yang-Baxter equation for circuit compression Bo Peng, Andrey B Khesin, A. Baris Ozguler, Oluwadara Ogunkoya, Matthew Otten, Yuri Alexeev, Niranjan Govind Quantum time dynamics is considered a promising problem for quantum advantage. It has been shown that employing Yang-Baxter symmetry can improve quantum simulations by circuit compression [1]. Generalizing the results to qudits is of great interest since even shallower circuits can be produced by exploiting higher levels. We derive the compressed circuit representations for different special cases of qudit Hamiltonians. We showcase the effectiveness of this approach by performing simulations and compare our results with the ones obtained using qubit-only circuits. |
Friday, March 10, 2023 9:12AM - 9:24AM |
Y72.00007: Imaginary-time evolution with a single ancilla: first-quantized eigensolver for electronic structure calculation in quantum chemistry Yusuke Nishiya, Taichi Kosugi, Hirofumi Nishi, Yu-ichiro Matsushita Imaginary-time evolution (ITE) on a quantum computer is a promising formalism for obtaining the ground state of a quantum system. The probabilistic ITE (PITE) exploits measurements to implement nonunitary operations, it can avoid the restriction of dynamics to a low-dimensional subspace imposed by variational |
Friday, March 10, 2023 9:24AM - 9:36AM |
Y72.00008: Solving MAXCUT with Quantum Imaginary Time Evolution Rizwanul Alam, George Siopsis, Rebekah Herrman, James Ostrowski, Phillip C Lotshaw, Travis S Humble We introduce a method to solve the MaxCut problem efficiently based on quantum imaginary time evolution (QITE). We employ a linear Ansatz for unitary updates and an initial state involving no entanglement, as well as an imaginary-time-dependent Hamiltonian interpolating between a given graph and a subgraph with two edges excised. We apply the method to thousands of randomly selected graphs with up to fifty vertices. We show that our algorithm exhibits a 93% and above performance converging to the maximum solution of the MaxCut problem for all considered graphs, to be compared with the worst-case 87.8% performance of the Goemans-Williamson algorithm. |
Friday, March 10, 2023 9:36AM - 9:48AM |
Y72.00009: Quantum state preparation and nonunitary evolution with diagonal operators Anthony Schlimgen Realizing nonunitary transformations on unitary-gate-based quantum devices is critically important for simulating a variety of physical problems, including open quantum systems and subnormalized quantum states. We present a dilation-based algorithm to simulate nonunitary operations using probabilistic quantum computing with only one ancilla qubit. We utilize the singular-value decomposition (SVD) to decompose any general quantum operator into a product of two unitary operators and a diagonal nonunitary operator, which we show can be implemented by a diagonal unitary operator in a one-qubit dilated space. While dilation techniques increase the number of qubits in the calculation, and thus the gate complexity, our algorithm limits the operations required in the dilated space to a diagonal unitary operator, which has known circuit decompositions. We use this algorithm to prepare random subnormalized two-level states on a quantum device with high fidelity. Furthermore, we present the accurate nonunitary dynamics of two-level open quantum systems in a dephasing channel and an amplitude-damping channel computed on a quantum device. The algorithm presented will be most useful for implementing general nonunitary operations when the SVD can be readily computed, which is the case for most operators in the noisy intermediate-scale quantum computing era. |
Friday, March 10, 2023 9:48AM - 10:00AM |
Y72.00010: Simulating scalar field theories on quantum computers with limited resources Andy C. Y. Li, Alexandru Macridin, Stephen Mrenna, Panagiotis Spentzouris We present a quantum algorithm for implementing Φ^{4} lattice scalar field theory on qubit computers. The field is represented in the discretized field amplitude basis. The number of qubits and elementary gates required by the implementation of the evolution operator is proportional to the lattice size. The algorithm allows efficient Φ^{4} state preparation for a large range of input parameters in both the normal and broken symmetry phases. The states are prepared using a combination of variational and adiabatic evolution methods. First, the ground state of a local Hamiltonian, which includes the Φ^{4} self-interaction, is prepared using short variational circuits. Next, this state is evolved by switching on the coupling between the lattice sites adiabatically. The parameters defining the local Hamiltonian are adjustable and constitute the input of our algorithm. We present a method to optimize these parameters in order to reduce the adiabatic time required for state preparation. For preparing broken symmetry states, the adiabatic evolution problems caused by crossing the phase transition critical line and by the degeneracy of the broken symmetry ground state can be addressed using an auxiliary external field which gradually turns off during the adiabatic process. We show that the time dependence of the external field during the adiabatic evolution is important for addressing the broken symmetry ground state degeneracy. The adiabatic time dependence on the inverse error tolerance can be reduced from quadratic to linear by using a field strength that decreases exponentially in time relative to one that decreases linearly. |
Friday, March 10, 2023 10:00AM - 10:12AM |
Y72.00011: A Quantum Algorithm for the Linearized Vlasov Equation with Collisions Abtin Ameri, Paola Cappellaro, Hari K Krovi, Nuno F Loureiro, Erika Ye Plasma physics is notoriously difficult to simulate. It is natural to seek alternative computational platforms that may speed up such simulations. Quantum computers are an attractive option, as they can solve certain problems exponentially or polynomially faster than classical computers (Grover 1996, Shor 1999). We develop a quantum algorithm for the linearized Vlasov equation with collisions (which offers a first-principles description of plasmas in the linear limit) and apply it to the canonical Landau damping problem. We show that by using a Hermite representation of velocity space and incorporating Hamiltonian simulation and quantum ODE solver algorithms (Low and Chuang 2019, Krovi 2022), we obtain a quadratic speedup in system size compared to the most efficient classical algorithms. However, previous work on this problem (without collisions) has demonstrated an exponential speedup in system size (Engel, Smith, and Parker 2019). We resolve this discrepancy by demonstrating that the Hermite representation yields an exponentially smaller system size. Thus, a classical algorithm implementing the Hermite representation has the same performance as the quantum algorithm of the previous work. |
Friday, March 10, 2023 10:12AM - 10:24AM |
Y72.00012: Limitations of Quantum Algorithms for Nonlinear Partial Differential Equations Dylan Lewis, Balu Nadiga, Stephan Eidenbenz We investigate the limitations of obtaining an exponential quantum advantage for solving nonlinear partial differential equations (PDEs) on a quantum computer. In particular we tighten the worst-case bounds of the algorithm introduced by Liu et al. [Liu et al. PNAS 2020], closing one of their open questions. We also show that no PDE that has positive Lyapunov exponent and solutions that grow sub-exponentially can be solved in time scaling faster than exponentially. |
Friday, March 10, 2023 10:24AM - 10:36AM |
Y72.00013: Interaction Energies on Fault-Tolerant Quantum Computers Nikolaj Moll, Matthias Degroote, Elica Kyoseva, Raffaele Santagati, Michael Streif, Christofer Tautermann, Rachael Alsaadon, Cristian L Cortes, Edward Hohenstein, Matthias Loipersberger, Robert M Parrish, Alicia R Welden, Sam Morley-Short, William Pol, Mark Steudtner The efficient computation of the ab initio interaction energy between a dimer of noncovalently-bound molecular monomers is a crucial quantity in pharmacology, as it provides a path to model the binding strength between proposed drug-ligand and target-protein pairs. Classical electronic structure calculations can determine the interaction energy as a direct observable in energy decomposition analysis methods such as symmetry-adapted perturbation theory (SAPT). Here, we describe the design of a tangible quantum algorithm for computing the intermolecular interaction energy with SAPT for fault-tolerant quantum computers. The algorithm determines the energy by estimating the expectation value of the SAPT operator. We assess the necessary qubit resources, required circuit depth, expected accuracy, and specific steps needed to implement such an algorithm down to the gate level. |
Friday, March 10, 2023 10:36AM - 10:48AM |
Y72.00014: Macromolecular modelling algorithms harnessing quantum computation Vikram K Mulligan, Mohit Pandey, Tristan Zaborniak, Alexey Galda, Hans Melo Proteins, ribonucleic acids, peptides, and synthetic heteropolymers can fold into intricate three-dimensional structures determined by the primary sequence of building-blocks, and can self-assemble into larger multimolecular complexes. The folds and assemblies of macromolecules in turn determine their functions. Although major advances have been made in modelling the sequence-fold-function relationship on classical computers, these are plagued by the vastness of both conformational and sequence spaces accessible to macromolecules. Where classical computers must consider conformations or sequences by iteration over many possibilities, quantum computers have the potential to consider vast numbers of conformations or sequences simultaneously, by implicitly representing these as a superposition of quantum states, and to allow efficient sampling from the low-energy conformations or sequences. This presentation reviews our past work showing that heteropolymer sequences can be robustly designed using adiabatic quantum annealers, and that the design problem can also be mapped to gate-based quantum computers. Here, we also introduce a method for tackling the multimolecular docking problem on adiabatic quantum annealers, without coarsening the molecular representation or simplifying the problem. This problem, which is central both to drug design and validation pipelines and to peptide and protein structure prediction (particularly in the context of solvent molecules), has a solution space that scales exponentially with the number of bodies to be docked, which means that it grows rapidly intractable by classical algorithms. The mapping to quantum computers provides a path to tackling currently intractable multibody docking problems as quantum hardware matures, and could one day greatly accelerate peptide and protein drug development. |
Friday, March 10, 2023 10:48AM - 11:00AM Author not Attending |
Y72.00015: On the sampling complexity of open quantum systems Isobel Aloisio, Gregory A White, Charles D Hill, Kavan Modi The simulation of open quantum systems remains one of the leading candidates for demonstrating quantum advantage, and has widespread applications in the areas of chemistry, condensed matter physics, optics, and many more. Understanding the computational complexity of these systems is a fundamental step towards precisely identifying which problems are beyond the reach of classical computation. Here, we map the temporal complexity of a process to the spatial complexity of a many-body state. With this, we are able to explore the simulation complexity of an open quantum system as a dynamic sampling problem: a system coupled to an environment can be probed at successive points in time -- accessing multi-time correlations. We argue that the complexity of multi-time sampling contains the complexity of master equations and stochastic maps as a special case. We present both analytical and numerical examples whose multi-time sampling is as complex as sampling from a many-body state that is classically hard. This implies that the corresponding family of master equations is also complex. Our results pave the way for studying open quantum systems from a complexity-theoretic perspective, highlighting the role quantum computers will play in our understanding of quantum dynamics. |
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