Quantum simulation in its current state faces experimental overhead in terms of physical space and cooling. We propose boson sampling as an alternative compact synthetic platform performing at room temperature. Identifying the capability of estimating matrix permanents, we explore the applicability of boson sampling for tackling the dynamics of quantum systems without having access to information about the full state vector. By mapping the time-evolution unitary of a Hamiltonian onto an interferometer via continuous-variable gate decompositions, we present proof-of-principle results of localization characteristics of a single particle. We study the dynamics of one-dimensional tight-binding systems in the clean and quasiperiodic-disordered limits to observe Bloch oscillations and dynamical localization, and the delocalization-to-localization phase transition in the Aubry-Andr\'e-Harper model, respectively. Our computational results obtained using boson sampling are in complete agreement with the dynamical and static results of noninteracting tight-binding systems obtained using conventional numerical calculations. Additionally, our study highlights the role of the number of sampling measurements or ``shots'' for simulation accuracy.
Quantum simulation in its current state faces experimental overhead in terms of physical space and cooling. We propose boson sampling as an alternative compact synthetic platform performing at room temperature. Identifying the capability of estimating matrix permanents, we explore the applicability of boson sampling for tackling the dynamics of quantum systems without having access to information about the full state vector. By mapping the time-evolution unitary of a Hamiltonian onto an interferometer via continuous-variable gate decompositions, we present proof-of-principle results of localization characteristics of a single particle. We study the dynamics of one-dimensional tight-binding systems in the clean and quasiperiodic-disordered limits to observe Bloch oscillations and dynamical localization, and the delocalization-to-localization phase transition in the Aubry-Andr'e-Harper model, respectively. Our computational results obtained using boson sampling are in complete agreement with the dynamical and static results of noninteracting tight-binding systems obtained using conventional numerical calculations. Additionally, our study highlights the role of the number of sampling measurements or ``shots'' for simulation accuracy.
We explore the free boson unitary dynamics subject to repeated random forced measurement. The input state is chosen as a Fock state in real space with the particle number conserved in the entire dynamics. We show that each boson is performing a non-unitary quantum walk in real space and its dynamics can be mapped to directed polymers in a random medium with complex amplitude. We numerically show that in the one dimensional system, when the measurement strength is finite, the system is in the frozen phase with all the bosons localized in the real space. Furthermore, these single particle wave functions take the same probability distribution in real space after long time evolution. Due to this property, the boson sampling for the output state becomes easy to solve. We further investigate circuit with non-local unitary dynamics and numerically demonstrate that there could exist a phase transition from a localized phase to a delocalized phase by varying the measurement strength.
Simulations play a crucial role in the investigation of complex quantum systems. In this thesis, locality structures of quantum systems are exploited to obtain complexity theoretic results with various physical implications. More specifically, rigorous mathematical tools are used and developed further, to investigate open quantum systems and thermal states. Moreover, important advances in photonic quantum simulations are discussed. For open quantum spin lattice systems new simulation schemes are provided. It is shown that Markovian dynamics can be simulated efficiently in the unitary circuit model, which can be seen as a dissipative Church-Turing type theorem. Moreover, Markovian dynamics is quasi-local and can be locally simulated on classical computers with a cost scaling polynomially in the system size. These results generalize standard tools from the investigation of Hamiltonian systems to open quantum systems. In particular, they provide a rigorous basis for their numerical simulation. However, also a major roadblock for making such simulations reliable is identified: Testing positivity of certain common approximations to mixed quantum states, called matrix product operators, is shown to be NP-hard in the system size and undecidable in the thermodynamic limit. Also more state space structures, originating from the spatial locality structure are discussed: Most states in state space cannot be generated efficiently with local Liouvillian dynamics and pure states generated in real- space renormalization schemes turn out to have local corrections in spatial dimensions larger than one. For thermal states on spin and fermionic lattice systems, a perturbation formula is provided and exponential clustering of correlations at high enough temperature is proven. This has various consequences: It leads to the extension of the concept of intensive temperature to interacting quantum systems, allows for efficient classical local simulations at high enough temperature, provides an upper bound on phase transition temperatures, and implies stability of thermal states against Hamiltonian perturbations. For photonic quantum simulations, sample complexity lower bounds for the verification of Boson-Sampling simulations are explained, which are applicable to a restricted setting. These bounds rely on a lower bound on the min-entropy of the output distribution of Boson-Sampling. This indicates that Boson-Sampling cannot be verified efficiently classically. Complementary to that, a reliable verification scheme for photonic state preparations is discussed, which uses single mode measurements as a simple quantum resource. The verification scheme is efficient for a large class of photonic simulations, including Boson-Sampling experiments with constantly many photons and state preparations necessary for measurement based quantum computing.
Abstract Quantum computers hold the potential to unlock new discoveries in complex quantum systems by enabling the simulation of physical systems that have heretofore been impossible to implement on classical computers due to intractability. A system of particular interest is that of dirty bosons, whose physics highlights the intriguing interplay of disorder and interactions in quantum systems, playing a central role in describing, for instance, ultracold gases in a random potential, doped quantum magnets, and amorphous superconductors. Here, we demonstrate how quantum computers can be used to elucidate the physics of dirty bosons in one and two dimensions. Specifically, we explore the disorder-induced delocalized-to-localized transition using adiabatic state preparation. In one dimension, the quantum circuits can be compressed to small enough depths for execution on currently available quantum computers. In two dimensions, the compression scheme is no longer applicable, thereby requiring the use of large-scale classical state vector simulations to emulate quantum computer performance. In addition, simulating interacting bosons via emulation of a noisy quantum computer allowed us to study the effect of quantum hardware noise on the physical properties of the simulated system. Our results suggest that scaling laws control how noise modifies observables versus its strength, the circuit depth, and the number of qubits. Moreover, we observe that noise impacts the delocalized and localized phases differently. A better understanding of how noise alters the observed properties of the simulated system is essential for leveraging near-term quantum devices for simulation of dirty bosons, and indeed for condensed matter systems in general.
Quasiperiodicity is easily realized with ultracold atoms in optical lattices and has been used to simulate the delocalization-localization transition. Random local potentials can also be implemented by spatial light modulators. Programmable hopping disorder, however, remains difficult to realize in conventional optical lattices. Momentum-space lattice (MSL) offers a platform to address this. We implement the MSL using an 87Rb Bose-Einstein condensate via multiple Bragg diffraction and benchmark the platform by simulating wavepacket dynamics with hopping disorder on top of the generalized Aubry-André (GAA) model. We test programmable hopping disorder added to localized/delocalized backgrounds tunable by the Aubry-André potential strength, as well as systems with mobility edges. Uncorrelated hopping disorder smooths the AA transition into a crossover between weakly (large localization lengths) and strongly localized regimes; the resulting enhancement in localization suppresses wavepacket spreading. We also implement spatially correlated hopping disorder and compare its dynamics with uncorrelated disorder of the same final width, demonstrating a correlation-induced enhancement in spreading. Measured dynamics agrees with trends from ideal tight-binding simulations. Trends in non-universal features depending on microscopic structure and short-time dynamics as functions of quasiperiodic potential strength, hopping-disorder strength, and GAA deformation also match numerical results, with better agreement at larger hopping-disorder strengths. Numerical simulations of the MSL dynamics provide insights into sources of corrections. Our results demonstrate that MSL provides a versatile platform for realizing general disordered quantum systems with programmable hopping amplitudes beyond quasiperiodic models.
Boson sampling is a computational problem that has recently been proposed as a candidate to obtain an unequivocal quantum computational advantage. The problem consists in sampling from the output distribution of indistinguishable bosons in a linear interferometer. There is strong evidence that such an experiment is hard to classically simulate, but it is naturally solved by dedicated photonic quantum hardware, comprising single photons, linear evolution, and photodetection. This prospect has stimulated much effort resulting in the experimental implementation of progressively larger devices. We review recent advances in photonic boson sampling, describing both the technological improvements achieved and the future challenges. We also discuss recent proposals and implementations of variants of the original problem, theoretical issues occurring when imperfections are considered, and advances in the development of suitable techniques for validation of boson sampling experiments. We conclude by discussing the future application of photonic boson sampling devices beyond the original theoretical scope.
Quantum chaos plays a key role in understanding complex quantum dynamics, while integrated photonics offers unique advantages for quantum applications, including high-speed operation, scalability, and programmable unitary transformations. However, integrated photonic approaches to probing quantum chaos remain largely unexplored, owing to the absence of a clear connection between programmable photonic dynamics and established chaos diagnostics. In this work, we establish Fock-state boson sampling as a practical probe of quantum chaos by exploiting the sensitivity of multiphoton interference to the random-matrix properties of underlying single-particle unitary dynamics. More importantly, we design and fabricate a programmable quantum photonic chip to experimentally implement this framework, achieving the first integrated-photonic demonstration of quantum-chaos probes based on boson sampling. Experimental results show that the three complementary probes proposed in this work, namely the distance to Porter--Thomas statistics, Shannon entropy, and Out-of-Time-Ordered-Correlator-equivalent observables, exhibit close agreement with theoretical predictions and consistently distinguish chaotic and integrable dynamics. Our work provides a scalable route for investigating complex quantum dynamics on programmable photonic platforms while leveraging the intrinsic advantages of boson sampling through multiphoton interference and complex output statistics.