Digital Quantum Simulation Research Articles

Quantum entanglement to extract a true ground state from an approximate ground state

Abstract We propose a procedure to extract a true ground state from an approximate ground state by using quantum entanglement. We use plural ancilla qubits with hierarchical structure, intending to gradually put up approximate precision. We demonstrate the procedure for quantum systems with a few qubits that derive from the (1+1)-dimensional Schwinger model by classically emulated digital quantum simulation. Although we use for simplicity an approximate ground state prepared by the adiabatic quantum computation, our procedure is applicable any approximate ground state that is a superposition of a true ground state and excited states. Our procedure is applicable for an N-qubits Hamiltonian with a non-degenerate ground state.

Progress in Trapped-Ion Quantum Simulation

Trapped ions offer long coherence times and high fidelity, programmable quantum operations, making them a promising platform for quantum simulation of condensed matter systems, quantum dynamics, and problems related to high-energy physics. We review selected developments in trapped-ion qubits and architectures and discuss quantum simulation applications that utilize these emerging capabilities. This review emphasizes developments in digital (gate-based) quantum simulations that exploit trapped-ion hardware capabilities, such as flexible qubit connectivity, selective mid-circuit measurement, and classical feedback, to simulate models with long-range interactions, explore nonunitary dynamics, compress simulations of states with limited entanglement, and reduce the circuit depths required to prepare or simulate long-range entangled states.

Time-Dependent Hamiltonian Simulation Using Discrete-Clock Constructions

Compared with time-independent Hamiltonians, the dynamics of generic quantum Hamiltonians H(t) are complicated by the presence of time ordering in the evolution operator. In the context of digital quantum simulation, this difficulty prevents a direct adaptation of many time-independent simulation algorithms for time-dependent simulation. However, there exists a framework within the theory of dynamical systems that eliminates time ordering by adding a “clock” degree of freedom. In this work, we provide a computational framework, based on this reduction, for encoding time-dependent dynamics as time-independent systems. As a result, we make two advances in digital Hamiltonian simulation. First, we create a time-dependent simulation algorithm based on performing qubitization on the augmented clock system and, in doing so, provide the first qubitization-based approach to time-dependent Hamiltonians that goes beyond Trotterization of the ordered exponential. Second, we define a natural generalization of multiproduct formulas for time-ordered exponentials and then propose and analyze an algorithm based on these formulas. Unlike other algorithms of similar accuracy, the multiproduct approach achieves commutator scaling, meaning that this method outperforms existing methods for physically local time-dependent Hamiltonians with sufficient smoothness. Our work reduces the disparity between time-dependent and time-independent simulation and indicates a step toward optimal quantum simulation of time-dependent Hamiltonians. Published by the American Physical Society 2024

Digital Quantum Simulation of a (1+1)D SU(2) Lattice Gauge Theory with Ion Qudits

We present a quantum simulation strategy for a (1+1)-dimensional SU(2) non-Abelian lattice gauge theory with dynamical matter, a hardcore-gluon Hamiltonian Yang-Mills, tailored to a six-level trapped-ion-qudit quantum processor, as recently experimentally realized [Nat. Phys. 18, 1053 (2022)]. We employ a qudit encoding fulfilling gauge invariance, an SU(2) Gauss’s law. We discuss the experimental feasibility of generalized Mølmer-Sørensen gates used to efficiently simulate the dynamics. We illustrate how a shallow circuit with these resources is sufficient to implement scalable digital quantum simulation of the model. We also numerically show that this model, albeit simple, can dynamically manifest physically relevant properties specific to non-Abelian field theories, such as baryon excitations. Published by the American Physical Society 2024

Reflection and transmission amplitudes in a digital quantum simulation

In this paper we show how to measure in the setting of digital quantum simulations the reflection and transmission amplitudes of the one-dimensional scattering of a particle with a short-ranged potential. The main feature of the protocol is the coupling between the particle and an ancillary spin-1/2 degree of freedom. This allows us to reconstruct tomographically the scattering amplitudes, which are in general complex numbers, from the readout of one qubit. Applications of our results are discussed.

Near-term applications of superconducting digital quantum simulation

Near-term applications of superconducting digital quantum simulation

Overview of Digital Quantum Simulator: Applications and Comparison with Latest Methods

Overview of Digital Quantum Simulator: Applications and Comparison with Latest Methods

Primitive quantum gates for an SU(3) discrete subgroup: Σ(36×3)

We construct the primitive gate set for the digital quantum simulation of the 108-element Σ(36×3) group. This is the first time a non-Abelian crystal-like subgroup of SU(3) has been constructed for quantum simulation. The gauge link registers and necessary primitives—the inversion gate, the group multiplication gate, the trace gate, and the Σ(36×3) Fourier transform—are presented for both an eight-qubit encoding and a heterogeneous three-qutrit plus two-qubit register. For the latter, a specialized compiler was developed for decomposing arbitrary unitaries onto this architecture. Published by the American Physical Society 2024

Simulating spin biology using a digital quantum computer: Prospects on a near-term quantum hardware emulator

Understanding the intricate quantum spin dynamics of radical pair reactions is crucial for unraveling the underlying nature of chemical processes across diverse scientific domains. In this work, we leverage Trotterization to map coherent radical pair spin dynamics onto a digital gate-based quantum simulation. Our results demonstrated an agreement between the idealized noiseless quantum circuit simulations and established master equation approaches for homogeneous radical pair recombination, identifying ∼15 Trotter steps to be sufficient for faithfully reproducing the coupled spin dynamics of a prototypical system. By utilizing this computational technique to study the dynamics of spin systems of biological relevance, our findings underscore the potential of digital quantum simulation (DQS) of complex radical pair reactions and builds the groundwork toward more utilitarian investigations into their intricate reaction dynamics. We further investigate the effect of realistic error models on our DQS approach and provide an upper limit for the number of Trotter steps that can currently be applied in the absence of error mitigation techniques before losing simulation accuracy to deleterious noise effects.

Photonic cellular automaton simulation of relativistic quantum fields: Observation of Zitterbewegung

Quantum cellular automaton (QCA) is a model for universal quantum computation and a natural candidate for digital quantum simulation of relativistic quantum fields. Here we introduce the first photonic platform for implementing QCA simulation of a free relativistic Dirac quantum field in 1+1 dimension, through a Dirac quantum cellular automaton (DQCA). Encoding the field position degree of freedom in the orbital angular momentum (OAM) of single photons, our state-of-the-art setup experimentally realizes eight steps of a DQCA, with the possibility of having complete control over the input OAM state preparation and the output measurement making use of two spatial light modulators. Therefore, studying the distribution in the OAM space at each step, we were able to reproduce the time evolution of the free Dirac field observing the , an oscillatory movement extremely difficult to see in a real-case experimental scenario that is a signature of the interference of particle and antiparticle states. The accordance between the expected and measured oscillations certifies the simulator performances, paving the way towards the application of photonic platforms to the simulation of more complex relativistic effects. Published by the American Physical Society 2024

Modeling the unphysical pseudomode model with physical ensembles: Simulation, mitigation, and restructuring of non-Markovian quantum noise

The influence of a Gaussian environment on a quantum system can be described by effectively replacing the continuum with a discrete set of ancillary quantum and classical degrees of freedom. This defines a pseudomode model which can be used to classically simulate the reduced system dynamics. Here we consider an alternative point of view and analyze the potential benefits of an analog or digital quantum simulation of the pseudomode model itself. Superficially, such a direct experimental implementation is, in general, impossible due to the unphysical properties of the effective degrees of freedom involved. However, we show that the effects of the unphysical pseudomode model can still be reproduced using measurement results over an ensemble of physical systems involving ancillary harmonic modes and an optional stochastic driving field. This is done by introducing an extrapolation technique whose efficiency is limited by stability against imprecision in the measurement data. We examine how such a simulation would allow us to (i) perform a quantum simulation of the effects of complex nonperturbative and non-Markovian environments in regimes that are challenging for classical simulation; (ii) conversely, mitigate potential unwanted non-Markovian noise present in quantum devices; and (iii) restructure some of the properties of a given physical bath, such as its temperature. Published by the American Physical Society 2024

Complexity of Digital Quantum Simulation in the Low-Energy Subspace: Applications and a Lower Bound

Digital quantum simulation has broad applications in approximating unitary evolution of Hamiltonians. In practice, many simulation tasks for quantum systems focus on quantum states in the low-energy subspace instead of the entire Hilbert space. In this paper, we systematically investigate the complexity of digital quantum simulation based on product formulas in the low-energy subspace. We show that the simulation error depends on the effective low-energy norm of the Hamiltonian for a variety of digital quantum simulation algorithms and quantum systems, allowing improvements over the previous complexities for full unitary simulations even for imperfect state preparations due to thermalization. In particular, for simulating spin models in the low-energy subspace, we prove that randomized product formulas such as qDRIFT and random permutation require smaller Trotter numbers. Such improvement also persists in symmetry-protected digital quantum simulations. We prove a similar improvement in simulating the dynamics of power-law quantum interactions. We also provide a query lower bound for general digital quantum simulations in the low-energy subspace.

Quantum circuit simulation of linear optics using fermion to qubit encoding

This work proposes a digital quantum simulation protocol for the linear scattering process of bosons, which provides a simple extension to partially distinguishable boson cases. Our protocol is achieved by combining the boson-fermion correspondence relation and fermion to qubit encoding protocols. As a proof of concept, we designed quantum circuits for generating the Hong-Ou-Mandel dip by varying particle distinguishability. The circuits were verified with the classical and quantum simulations using the IBM Quantum and IonQ cloud services.

Ising meson spectroscopy on a noisy digital quantum simulator

Quantum simulation has the potential to be an indispensable technique for the investigation of non-perturbative phenomena in strongly-interacting quantum field theories (QFTs). In the modern quantum era, with Noisy Intermediate Scale Quantum (NISQ) simulators widely available and larger-scale quantum machines on the horizon, it is natural to ask: what non-perturbative QFT problems can be solved with the existing quantum hardware? We show that existing noisy quantum machines can be used to analyze the energy spectrum of several strongly-interacting 1+1D QFTs, which exhibit non-perturbative effects like ‘quark confinement’ and ‘false vacuum decay’. We perform quench experiments on IBM’s quantum simulators to compute the energy spectrum of 1+1D quantum Ising model with a longitudinal field. Our results demonstrate that digital quantum simulation in the NISQ era has the potential to be a viable alternative to numerical techniques such as density matrix renormalization group or the truncated conformal space methods for analyzing QFTs.

Adaptive Trotterization for Time-Dependent Hamiltonian Quantum Dynamics Using Piecewise Conservation Laws.

Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical trade-off between improved accuracy for finer time steps, and increased error rate on account of the larger circuit depth. We present an adaptive Trotterization algorithm to cope with time dependent Hamiltonians, where we propose a concept of piecewise "conserved" quantities to estimate errors in the time evolution between two (nearby) points in time; these allow us to bound the errors accumulated over the full simulation period. They reduce to standard conservation laws in the case of time independent Hamiltonians, for which we first developed an adaptive Trotterization scheme [H. Zhao et al., Making Trotterization adaptive and energy-self-correcting for NISQ devices and beyond, PRX Quantum 4, 030319 (2023).2691-339910.1103/PRXQuantum.4.030319]. We validate the algorithm for a time dependent quantum spin chain, demonstrating that it can outperform the conventional Trotter algorithm with a fixed step size at a controlled error.

Non-Abelian braiding of Fibonacci anyons with a superconducting processor

Quantum many-body systems with a non-Abelian topological order can host anyonic quasiparticles. It has been proposed that anyons could be used to encode and manipulate information in a topologically protected manner that is immune to local noise, with quantum gates performed by braiding and fusing anyons. Unfortunately, realizing non-Abelian topologically ordered states is challenging, and it was not until recently that the signatures of non-Abelian statistics were observed through digital quantum simulation approaches. However, not all forms of topological order can be used to realize universal quantum computation. Here we use a superconducting quantum processor to simulate non-Abelian topologically ordered states of the Fibonacci string-net model and demonstrate braidings of Fibonacci anyons featuring universal computational power. We demonstrate the non-trivial topological nature of the quantum states by measuring the topological entanglement entropy. In addition, we create two pairs of Fibonacci anyons and demonstrate their fusion rule and non-Abelian braiding statistics by applying unitary gates on the underlying physical qubits. Our results establish a digital approach to explore non-Abelian topological states and their associated braiding statistics with current noisy intermediate-scale quantum processors.

Digital quantum simulation of gravitational optomechanics with IBM quantum computers

We showcase the digital quantum simulation of the action of a Hamiltonian that governs the interaction between a quantum mechanical oscillator and an optical field, generating quantum entanglement between them via gravitational effects. This is achieved by making use of a boson-qubit mapping protocol and a digital gate decomposition that allow us to run the simulations in the quantum computers available in the IBM Quantum platform. We present the obtained results for the fidelity of the experiment in two different quantum computers, after applying error mitigation and post-selection techniques. The achieved results correspond to fidelities over 90%, which indicates that we were able to perform a faithful digital quantum simulation of the interaction and therefore of the generation of quantum entanglement by gravitational means in optomechanical systems.

Quantum Simulation of Bound State Scattering

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

Embedding Quantum Many-Body Scars into Decoherence-Free Subspaces.

Quantum many-body scars are nonthermal excited eigenstates of nonintegrable Hamiltonians, which could support coherent revival dynamics from special initial states when scars form an equally spaced tower in the energy spectrum. For open quantum systems, engineering many-body scarred dynamics by a controlled coupling to the environment remains largely unexplored. Here, we provide a general framework to exactly embed quantum many-body scars into the decoherence-free subspaces of Lindblad master equations. The dissipative scarred dynamics manifest persistent periodic oscillations for generic initial states, and can be practically utilized to prepare scar states with potential quantum metrology applications. We construct the Liouvillian dissipators with the local projectors that annihilate the whole scar towers, and utilize the Hamiltonian part to rotate the undesired states out of the null space of dissipators. We demonstrate our protocol through several typical models hosting many-body scar towers and propose an experimental scheme to observe the dissipative scarred dynamics based on digital quantum simulations and resetting ancilla qubits.

Effective light cone and digital quantum simulation of interacting bosons

The speed limit of information propagation is one of the most fundamental features in non-equilibrium physics. The region of information propagation by finite-time dynamics is approximately restricted inside the effective light cone that is formulated by the Lieb-Robinson bound. To date, extensive studies have been conducted to identify the shape of effective light cones in most experimentally relevant many-body systems. However, the Lieb-Robinson bound in the interacting boson systems, one of the most ubiquitous quantum systems in nature, has remained a critical open problem for a long time. This study reveals a tight effective light cone to limit the information propagation in interacting bosons, where the shape of the effective light cone depends on the spatial dimension. To achieve it, we prove that the speed for bosons to clump together is finite, which in turn leads to the error guarantee of the boson number truncation at each site. Furthermore, we applied the method to provide a provably efficient algorithm for simulating the interacting boson systems. The results of this study settle the notoriously challenging problem and provide the foundation for elucidating the complexity of many-body boson systems.