Simulations of collisions of fundamental particles on a quantum computer are expected to have an exponential advantage over classical methods and promise to enhance searches for new physics. Furthermore, scattering in scalar field theory has been shown to be BQP-complete, making it a representative problem for which quantum computation is efficient. As a step toward large-scale quantum simulations of collision processes, scattering of wavepackets in one-dimensional scalar field theory is simulated using 120 qubits of IBM's Heron superconducting quantum computer ibm_fez. Variational circuits compressing vacuum preparation, wavepacket initialization, and time evolution are determined using classical resources. By leveraging physical properties of states in the theory, such as symmetries and locality, the variational quantum algorithm constructs scalable circuits that can be used to simulate arbitrarily-large system sizes. A new strategy is introduced to mitigate errors in quantum simulations, which enables the extraction of meaningful results from circuits with up to 4924 two-qubit gates and two-qubit gate depths of 103. The effect of interactions is clearly seen, and is found to be in agreement with classical Matrix Product State simulations. The developments that will be necessary to simulate high-energy inelastic collisions on a quantum computer are discussed.
Simulations of collisions of fundamental particles on a quantum computer are expected to have an exponential advantage over classical methods and promise to enhance searches for new physics. Furthermore, scattering in scalar field theory has been shown to be BQP-complete, making it a representative problem for which quantum computation is efficient. As a step toward large-scale quantum simulations of collision processes, scattering of wavepackets in one-dimensional scalar field theory is simulated using 120 qubits of IBM's Heron superconducting quantum computer ibm_fez. Variational circuits compressing vacuum preparation, wavepacket initialization, and time evolution are determined using classical resources. By leveraging physical properties of states in the theory, such as symmetries and locality, the variational quantum algorithm constructs scalable circuits that can be used to simulate arbitrarily-large system sizes. A new strategy is introduced to mitigate errors in quantum simulations, which enables the extraction of meaningful results from circuits with up to 4924 two-qubit gates and two-qubit gate depths of 103. The effect of interactions is clearly seen, and is found to be in agreement with classical Matrix Product State simulations. The developments that will be necessary to simulate high-energy inelastic collisions on a quantum computer are discussed.
The last few years have seen rapid development of applications of quantum computation to quantum field theory. The first algorithms for quantum simulation of scattering have been proposed in the context of scalar and fermionic theories, requiring thousands of logical qubits. These algorithms are not suitable to simulate scattering of incoming bound states, as the initial-state preparation relies typically on adiabatically transforming wavepackets of the free theory into wavepackets of the interacting theory. In this paper we present a strategy to excite wavepackets of the interacting theory directly from the vacuum of the interacting theory, allowing the preparation of states of composite particles. This is the first step towards digital quantum simulation of scattering of bound states. The approach is based on the Haag-Ruelle scattering theory, which provides a way to construct creation and annihilation operators of a theory in a full, nonperturbative framework. We provide a quantum algorithm requiring a number of ancillary qubits that is logarithmic in the size of the wavepackets, and with a success probability vanishing at most like a polynomial in the lattice parameters and the energy of the wavepacket. The gate complexity for a single iteration of the circuit is equivalent to that of a time evolution for a fixed time. Furthermore, we propose a complete protocol for scattering simulation using this algorithm. We study its efficiency and find improvements with respect to previous algorithms in the literature. Published by the American Physical Society 2024
Hadron wave packets are prepared and time evolved in the Schwinger model using 112 qubits of IBM's 133-qubit Heron quantum computer ibm_torino. The initialization of the hadron wave packet is performed in two steps. First, the vacuum is prepared across the whole lattice using the recently developed SC-ADAPT-VQE algorithm and workflow. SC-ADAPT-VQE is then extended to the preparation of localized states, and used to establish a hadron wave packet on top of the vacuum. This is done by adaptively constructing low-depth circuits that maximize the overlap with an adiabatically prepared hadron wave packet. Due to the localized nature of the wavepacket, these circuits can be determined on a sequence of small lattices using classical computers, and then robustly scaled to prepare wave packets on large lattices for simulations using quantum computers. Time evolution is implemented with a second-order Trotterization. To reduce both the required qubit connectivity and circuit depth, an approximate quasilocal interaction is introduced. This approximation is made possible by the emergence of confinement at long distances, and converges exponentially with increasing distance of the interactions. Using multiple error-mitigation strategies, up to 14 Trotter steps of time evolution are performed, employing 13,858 two-qubit gates (with a CNOT depth of 370). The propagation of hadrons is clearly identified, with results that compare favorably with Matrix Product State simulations. Prospects for a near-term quantum advantage in simulations of hadron scattering are discussed.
We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve these improvements through two optimizations. First, we consider a finite volume approach for estimating the elements of the S-matrix. This approach is appropriate in general for 1+1D and for certain low-energy elastic collisions in higher dimensions. Second, we implement our approach using a series of different fault-tolerant simulation algorithms for Hamiltonians formulated both in the field occupation basis and field amplitude basis. Our algorithms are based on either second-order Trotterization or qubitization. The cost of Trotterization in occupation basis scales as O ( λ N 7 | Ω | 3 / ( M 5 / 2 ϵ 3 / 2 ) ) where λ is the coupling strength, N is the occupation cutoff, | Ω | is the volume of the spatial lattice, M is the mass of the particles and ϵ is the uncertainty in the energy calculation used for the S -matrix determination. Qubitization in the field basis scales as O ( | Ω | 2 ( k 2 Λ + k M 2 ) / ϵ ) , where k is the cutoff in the field and Λ is a scaled coupling constant. We find in both cases that the bounds suggest physically meaningful simulations can be performed using on the order of 4 × 10 6 physical qubits and 10 12 T -gates which corresponds to roughly one day on a superconducting quantum computer with surface code and a cycle time of 100 ns. This places the simulation of scalar field theory within striking distance of the gate counts for the best available chemistry simulation results.
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. Access to a computational space that incorporates quantum effects, such as superposition and entanglement, enables the derivation of promising quantum algorithms for important tasks, including preparing the ground state of a quantum system or predicting its evolution over time. Successfully tackling these tasks promises insights into significant theoretical and technological questions, such as superconductivity and the design of new materials. The aim of quantum algorithms is to use a series of quantum operations in a quantum circuit to solve a problem beyond the reach of classical computers. However, the noise and limited scale of current quantum computers restricts these circuits to moderate sizes and depths. As a result, many prominent algorithms are currently infeasible to run for problem sizes of practical interest. In response, recent research focused on variational quantum algorithms, which allow the selection of circuits that act within a quantum device's capabilities. Yet, these algorithms can require the execution of a large number of circuits, leading to prohibitively long computation times. This doctoral thesis develops two main techniques to reduce these quantum computational resource requirements, with the goal of scaling up application sizes on current quantum processors. The first approach is based on stochastic approximations of computationally costly quantities, such as quantum circuit gradients or the quantum geometric tensor (QGT). The second method takes a different perspective on the QGT, leading to a potentially more efficient description of time evolution on current quantum computers. Both techniques rely on maintaining available information and only computing necessary corrections, instead of re-computing possibly redundant data. The main focus of application for our algorithms is the simulation of quantum systems, broadly defined as including the preparation of ground and thermal states, and the real- and imaginary-time propagation of a system. The developed subroutines, however, can further be utilized in the fields of optimization or machine learning. Our algorithms are benchmarked on a range of representative models, such as Ising or Heisenberg spin models, both in numerical simulations and experiments on the hardware. In combination with error mitigation techniques, the latter is scaled up to 27 qubits; into a regime that variational quantum algorithms are challenging to scale to on noisy quantum computers without our algorithms.
Quantum computing offers a new, orthogonal direction for investigating fundamental physics, extending beyond classical numerical methods and conventional observables. Realizing this potential requires directly confronting the noise limiting currently available quantum computers. Progress rests on advancing algorithms, interpreting their results, and managing their errors together. This thesis presents several advancements in the use of quantum simulation and quantum information to probe fundamental physics.
The first is in the use of quantum computers to simulate collisions in quantum field theories. Central to these simulations are new wavepacket preparation, time evolution, and error mitigation techniques, which allow for simulations with some of the largest effective circuit volumes to date. These methods enable the first quantum simulation providing numerical evidence for inelastic particle production, a key process in fundamental physics.
The second advancement centers on the role quantum-information-theoretic quantities play in physical processes. Beyond mere correlations with the physics of the process, entanglement and magic are shown to probe the interactions present in scattering and hadronization dynamics.
A precision study requires a complete quantification of algorithmic and hardware uncertainties, an outstanding goal as quantum simulations mature. The third advancement in this thesis addresses error management. A framework minimizing the effect of algorithmic errors in analog quantum simulations is presented. In a step toward fault tolerance, error detection in encoded quantum simulations is shown to improve estimation of local observables relative to unencoded runs.
Together, the developments in this thesis mark practical progress toward fault-tolerant quantum simulations of fundamental physics capable of scientific discovery.
Scattering processes are essential for understanding the structure of matter, yet their real-time dynamics remain challenging to simulate classically. Quantum computers offer a promising path toward efficient simulation of such physical systems. Here, we present a general and scalable framework for simulating meson scattering in lattice gauge theories on digital quantum hardware. Our approach addresses two key challenges: First, we introduce a symmetry-preserving quantum subspace expansion method for constructing high-fidelity meson creation operators across a wide range of coupling and momenta. Second, we design a quantum circuit for meson wave packet preparation using Givens rotations, improving accuracy while reducing circuit depth compared to existing approaches. We demonstrate the method in a ( 1 + 1 )-dimensional Z 2 gauge theory and explore meson scattering dynamics with tensor network simulations. We study both elastic and inelastic scattering and provide a comprehensive characterization of the scattering process in terms of energy transfer, entanglement entropy, and heavier particle production during the dynamics. Our work provides a scalable, nonvariational approach for simulating meson scattering on near-term quantum devices and offers a concrete strategy for probing nonperturbative dynamics in confining gauge theories.