We introduce a general method based on the operators of the Dyson-Masleev transformation to map the Hamiltonian of an arbitrary model system into the Hamiltonian of a circuit Quantum Electrodynamics (cQED) processor. Furthermore, we introduce a modular approach to programming a cQED processor with components corresponding to the mapping Hamiltonian. The method is illustrated as applied to quantum dynamics simulations of the Fenna-Matthews-Olson (FMO) complex and the spin-boson model of charge transfer. Beyond applications to molecular Hamiltonians, the mapping provides a general approach to implement any unitary operator in terms of a sequence of unitary transformations corresponding to powers of creation and annihilation operators of a single bosonic mode in a cQED processor.
We introduce a general method based on the operators of the Dyson-Masleev transformation to map the Hamiltonian of an arbitrary model system into the Hamiltonian of a circuit Quantum Electrodynamics (cQED) processor. Furthermore, we introduce a modular approach to programming a cQED processor with components corresponding to the mapping Hamiltonian. The method is illustrated as applied to quantum dynamics simulations of the Fenna-Matthews-Olson (FMO) complex and the spin-boson model of charge transfer. Beyond applications to molecular Hamiltonians, the mapping provides a general approach to implement any unitary operator in terms of a sequence of unitary transformations corresponding to powers of creation and annihilation operators of a single bosonic mode in a cQED processor.
Extracting the Hamiltonian of interacting quantum-information processing systems is a keystone problem in the realization of complex phenomena and large-scale quantum computers. The remarkable growth of the field increasingly requires precise, widely-applicable, and modular methods that can model the quantum electrodynamics of the physical circuits, and even of their more-subtle renormalization effects. Here, we present a computationally-efficient method satisfying these criteria. The method partitions a quantum device into compact lumped or quasi-distributed cells. Each is first simulated individually. The composite system is then reduced and mapped to a set of simple subsystem building blocks and their pairwise interactions. The method operates within the quasi-lumped approximation and, with no further approximation, systematically accounts for constraints, couplings, parameter renormalizations, and non-perturbative loading effects. We experimentally validate the method on large-scale, state-of-the-art superconducting quantum processors. We find that the full method improves the experimental agreement by a factor of two over taking standard coupling approximations when tested on the most sensitive and dressed Hamiltonian parameters of the measured devices.
Quantum simulation is a promising near term application for quantum information processors with the potential to solve computationally intractable problems using just a few dozen interacting qubits. A range of experimental platforms have recently demonstrated the basic functionality of quantum simulation applied to quantum magnetism, quantum phase transitions and relativistic quantum mechanics. However, in all cases, the physics of the underlying hardware restricts the achievable inter-particle interactions and forms a serious constraint on the versatility of the simulators. To broaden the scope of these analog devices, we develop a suite of pulse sequences that permit a user to efficiently realize average Hamiltonians that are beyond the native interactions of the system. Specifically, this approach permits the generation of all symmetrically coupled translation-invariant two-body Hamiltonians with homogeneous on-site terms, a class which includes all spin- XYZ chains, but generalized to include long-range couplings. Our work builds on previous work proving that universal simulation is possible using both entangling gates and single-qubit unitaries. We show that determining the appropriate 'program' of unitary pulse sequences which implements an arbitrary Hamiltonian transformation can be formulated as a linear program over functions defined by those pulse sequences, running in polynomial time and scaling efficiently in hardware resources. Our analysis extends from circuit model quantum information to adiabatic quantum evolutions, representing an important and broad-based success in applying functional analysis to the field of quantum information.
Abstract. Quantum simulation is a promising near term application for quantum information processors with the potential to solve computationally intractable problems using just a few dozen interacting qubits [1, 2, 3]. A range of experimental platforms have recently demonstrated the basic functionality of quantum simulation applied to quantum magnetism, quantum phase transitions, and relativistic quantum mechanics [4, 5, 6, 7, 8, 9, 10, 11]. However, in all cases, the physics of the underlying hardware restricts the achievable inter-particle interactions and forms a serious constraint on the versatility of the simulators. To broaden the scope of these analog devices, we develop a suite of pulse sequences that permit a user to efficiently realize average Hamiltonians that are beyond the native interactions of the system [12, 13]. Specifically, this approach permits the generation of all symmetrically coupled translation-invariant two-body Hamiltonians with homogeneous on-site terms, a class which includes all spin-1/2 XYZ chains, but generalized to include long-range couplings. Our work builds on previous work proving that universal simulation is possible using both entangling gates and single-qubit unitaries [14, 15, 16]. We show that determining the appropriate “program ” of unitary pulse sequences which implements an arbitrary Hamiltonian transformation can be formulated as a linear program over functions defined by those pulse sequences, running in polynomial time and scaling efficiently in hardware resources. Our analysis extends from circuit model quantum information to adiabatic quantum evolutions, representing an important and broad-based success in applying functional analysis to the field of quantum information. ar X iv
We introduce quantum circuits for simulations of multimode state vectors on 3D circuit quantum electrodynamics (cQED) processors using matrix product state representations. The circuits are demonstrated as applied to simulations of molecular docking based on holographic Gaussian boson sampling (GBS), as illustrated for the binding of a thiol-containing aryl sulfonamide ligand to the tumor necrosis factor-α converting enzyme receptor. We show that cQED devices with a modest number of modes could be employed to simulate multimode systems by repurposing working modes through measurement and reinitialization. We anticipate that a wide range of GBS applications could be implemented on compact 3D cQED processors analogously using the holographic approach. Simulations on qubit-based quantum computers could be implemented analogously using circuits that represent continuous variables in terms of truncated expansions of Fock states.
Quantum computing offers promising new avenues for tackling the long-standing challenge of simulating the quantum dynamics of complex chemical systems, particularly open quantum systems coupled to external baths. However, simulating such nonunitary dynamics on quantum computers is challenging since quantum circuits are specifically designed to carry out unitary transformations. Furthermore, chemical systems are often strongly coupled to the surrounding environment, rendering the dynamics non-Markovian and beyond the scope of Markovian quantum master equations like Lindblad or Redfield. In this work, we introduce a quantum algorithm designed to simulate non-Markovian dynamics of open quantum systems. Our approach enables the implementation of arbitrary quantum master equations on noisy intermediate-scale quantum (NISQ) computers. We illustrate the method as applied in conjunction with the numerically exact hierarchical equations of motion (HEOM) method. The effectiveness of the resulting quantum HEOM algorithm is demonstrated as applied to simulations of the non-Lindbladian electronic energy and charge transfer dynamics in models of the carotenoid-porphyrin-C 60 molecular triad dissolved in tetrahydrofuran and the Fenna–Matthews–Olson complex.
We introduce the qumode subspace variational quantum eigensolver (QSS-VQE), a hybrid quantum-classical algorithm for computing molecular excited states using the Fock basis of bosonic qumodes in circuit quantum electrodynamics (cQED) devices. This approach harnesses the native universal gate sets of qubit-qumode architectures to construct highly expressive variational ansatze, offering potential advantages over conventional qubit-based methods. In QSS-VQE, the electronic structure Hamiltonian is first mapped to a qubit representation and subsequently embedded into the Fock space of bosonic qumodes, enabling efficient state preparation and reduced quantum resource requirements. We demonstrate the performance of QSS-VQE through simulations of molecular excited states, including dihydrogen and a conical intersection in cytosine. Additionally, we explore a bosonic model Hamiltonian to assess the expressivity of qumode gates, identifying regimes where qumode-based implementations outperform purely qubit-based approaches. These results highlight the promise of leveraging bosonic degrees of freedom for enhanced quantum simulation of complex molecular systems.