Variational fast forwarding for quantum simulation beyond the coherence time

Quantum computers are currently regarded as an emerging computing technology that can solve problems more quickly than classical computers. However, since constructing a general quantum computer is technically difficult, quantum computer simulation has been used instead of real quantum computers. Simulating quantum computers on classical computers is challenging because the time and resources required for the vectormatrix multiplication (VMM) increase exponentially with the number of qubits. This paper proposes a new accelerator architecture called ReQUSA that leverages resistive random access memory (ReRAM) to accelerate the quantum computer simulation. The ReQUSA employs a ReRAM crossbar array structure, which is specialized for implementing the VMM, and a realized state method for reduced VMM operation. To the best of our knowledge, ReRAM-based accelerators for quantum computer simulators has not been previously reported. Here, we describe the hardware design of the architecture and compare the performances (hardware resource, simulation time, and accuracy) of our accelerator with those of current quantum computer simulators (QuEST, QPlayer, and Qiskit). On average, our proposed architecture reduced the simulation times by factors of ×104 and ×103 (×102) on average from those of QuEST and QPlayer (also Qiskit), respectively. In addition, our architecture achieved 99% accuracy in 16-bit fixed-point data representation.

U(1) lattice gauge theories (LGTs) offer a way to simulate quantum electrodynamics, one of the three forces unified by the Standard Model of particles physics. Here we provide complete, quantum-gate-by-quantum-gate algorithms to simulate U(1) LGTs on a fault-tolerant quantum computer. We further perform rigorous error analysis in order to derive concrete estimates of the quantum computational resources required for an accurate simulation of U(1) LGTs using a second-order product formula. We show that U(1) LGTs in any spatial dimension can be simulated using non-Clifford T gates, where T is the simulation time, N is the number of lattice sites, Λ is the truncation parameter for the bosonic gauge fields, and ε is the simulation error. This work paves the way towards fault-tolerant quantum simulations of physical models closely related to the Standard Model of particle physics.

We briefly review what a quantum computer is, what it promises to do for us and why it is so hard to build one. Among the first applications anticipated to bear fruit is the quantum simulation of quantum systems. While most quantum computation is an extension of classical digital computation, quantum simulation differs fundamentally in how the data are encoded in the quantum computer. To perform a quantum simulation, the Hilbert space of the system to be simulated is mapped directly onto the Hilbert space of the (logical) qubits in the quantum computer. This type of direct correspondence is how data are encoded in a classical analogue computer. There is no binary encoding, and increasing precision becomes exponentially costly: an extra bit of precision doubles the size of the computer. This has important consequences for both the precision and error-correction requirements of quantum simulation, and significant open questions remain about its practicality. It also means that the quantum version of analogue computers, continuous-variable quantum computers, becomes an equally efficient architecture for quantum simulation. Lessons from past use of classical analogue computers can help us to build better quantum simulators in future.

Quantum computing has been gradually developed from a theory to practice in recent years. The desire for more powerful computational capability keeps promoting the scaling up of quantum computers. For quantum machines with large scales, limited coherence time and bloated instruction bandwidth may obstruct the continuous scaling up. In this paper, we propose a new quantum computing architecture named QuPAA, which leverages multiple layers of arbitrary waveform generator (AWG) units to exploit the parallelism among quantum operations. QuPAA provides a series of mechanisms, including parallelism exploitation, microcode streaming, and a quantum flexible instruction set (QuFIS). These mechanisms assist QuPAA to generate instructions adaptively and reduce the requirement for coherence time and instruction bandwidth. The evaluation results show that, compared to the baseline quantum computer with a single AWG unit, QuPAA reduces 25.9% to 97.4% coherence time requirement, and saves 26.9% to 79.1 % instruction bandwidth. The improvement effectively breaks the limitations and provides strong support for the extension of the scale for quantum computers.

Quantum machine learning recently gained prominence due to the computational ability of quantum computers in solving machine learning problems that are intractable on a classical computer. However, achieving a quantum advantage on present-day quantum computers remains an open challenge. In this work, we primarily focus on solving machine learning problems using a hybrid model based on both quantum and classical computers together for the classification task. We propose the quantum multi-class classifier (QMCC) as a variational circuit with a hybrid classical-quantum approach using quantum mechanical properties such as superposition and entanglement. A unitary operation on a single qubit for the state preparation is designed and also demonstrated using a real quantum computer on the IBMQX platform. The entire variational circuit for the classification task is implemented on a quantum simulator. We performed our quantum simulations on three benchmark datasets: Iris dataset, Banknote Authentication (BNA) dataset, and Wireless Indoor Localization (WIL) dataset for machine learning algorithms. Our simulation results show that the proposed QMCC model classified Iris dataset with an accuracy of 92.10%, BNA dataset with an accuracy of 89.50%, and WIL dataset with an accuracy of 91.73%. The proposed model can also be extended to multiple class classifiers.

Ultracold polar molecules (UPMs) are emerging as a novel and powerful platform for fundamental applications in quantum science. Here, we report characterization of the coherence between nuclear spin levels of ultracold ground-state sodium-rubidium molecules loaded into a 3D optical lattice with a nearly photon scattering limited trapping lifetime of 9(1)seconds. After identifying and compensating the main sources of decoherence, we achieve a maximum nuclear spin coherence time of T_{2}^{*}=3.3(6) s with two-photon Ramsey spectroscopy. Furthermore, based on the understanding of the main factor limiting the coherence of the two-photon Rabi transition, we obtain a Rabi line shape with linewidth below 0.8Hz. The simultaneous realization of long lifetime and coherence time, and ultrahigh spectroscopic resolution in our system unveils the great potentials of Ultracold polar molecules in quantum simulation, computation, and metrology.

Neutral atoms are a ubiquitous platform for various quantum sciences with applications in quantum computing, simulation, and metrology across many different atomic species. In these systems, control over the electronic states is given by suitable laser pulses typically applied at the single-particle level. Here, we present fast coherent control over the meta-stable clock states in bosonic strontium-88 using two- and three-photon couplings. Compared to the direct single-photon drive on these transitions, the realistically achievable Rabi frequencies are substantially higher at significantly relaxed magnetic field strength. By applying a magnetic quantization axis under a judiciously chosen angle with respect to the linear trap polarization, we realize an optical qutrit comprising the ground state 1S0 as well as both clock states 3P0 and 3P2, and characterize in detail the coherence of the system. Remarkably, the observed coherence time on the fine-structure qubit (given by the 3P0 and 3P2,mj=0 states) of 715(30) ms demonstrates, for the first time, that state-of-the-art coherence times are compatible with tweezer-based polarizability-engineered trapping potentials, which is applicable across a broad range of wavelengths and atomic species. We identify laser phase noise as the main limitation of the current operation fidelity and discuss methods for characterizing, modelling, and compensating optical phase noise. The multi-photon couplings not only allow for substantially faster Rabi frequencies under realistic experimental conditions, but additionally offer controlled dissipation via the 3P1 state, which we use to demonstrate a measurement-free qubit reset. Combined with three-photon couplings to the 3P2 clock state, we realize resolved sideband cooling in an optical lattice potential and benchmark the fine-structure qubit at various infrared wavelengths. In addition, we introduce a hybrid lattice-tweezer setup and demonstrate the preparation of programmable atom configurations in a single plane of the two-dimensional optical lattice potential. Using single-site addressing with optical tweezers, we present a protocol for the iterative assembly of large-scale atom arrays. Furthermore, we use the lattice-tweezer combination to continuously operate a configurable atom array, which provides means to overcome scaling limitations by repeatedly adding atoms to the system and enables entirely novel approaches to operating neutral-atom arrays. To enable reliable image processing with a fast reconstruction of the lattice occupation, we introduce a novel algorithm based on a convolutional neural network, which provides a rapid and noise-resilient reconstruction compatible with arbitrary lattice geometries. Moreover, we benchmark a new phase-only spatial light modulator based on a micromirror array, which paves the way towards holographic beam shaping at fast update rates compatible with a broad range of wavelengths, including the ultraviolet spectral range.

Fixed-frequency transmon quantum computers (QCs) have advanced in coherence times, addressability, and gate fidelities. Unfortunately, these devices are restricted by the number of on-chip qubits, capping processing power and slowing progress toward fault-tolerance. Although emerging transmon devices feature over 100 qubits, building QCs large enough for meaningful demonstrations of quantum advantage requires overcoming many design challenges. For example, today’s transmon qubits suffer from significant variation due to limited precision in fabrication. As a result, barring significant improvements in current fabrication techniques, scaling QCs by building ever larger individual chips with more qubits is hampered by device variation. Severe device variation that degrades QC performance is referred to as a defect. Here, we focus on a specific defect known as a frequency collision. When transmon frequencies collide, their difference falls within a range that limits two-qubit gate fidelity. Frequency collisions occur with greater probability on larger QCs, causing collision-free yields to decline as the number of on-chip qubits increases. As a solution, we propose exploiting the higher yields associated with smaller QCs by integrating quantum chiplets within quantum multi-chip modules (MCMs). Yield, gate performance, and application-based analysis show the feasibility of QC scaling through modularity. Our results demonstrate that chiplet architectures, relative to monolithic designs, benefit from average yield improvements ranging from 9.6 – 92.6 × for ≲5 qubit machines. In addition, our simulations explore the design space of chiplet systems and discover configurations that demonstrate average two-qubit gate infidelity reductions that are at best 0.815 × their monolithic counterpart. Finally, we observe that carefully-selected modular systems achieve fidelity improvements on a range of benchmark circuits.

Developing quantum systems which are robust against noise are of prime importance to the realisation of quantum technologies. Without fault tolerance, we will never be able to preserve delicate quantum states for macroscopic time scales, a necessary requirement in the construction of scalable quantum computer. Topologically ordered models offer very beautiful mechanisms for preserving quantum states. In such models, quantum information is encoded globally over a degenerate topological Hilbert space which offers a natural robustness against local environmental noise. Remarkably, topological order is present in certain realistic condensed-matter systems. This provides a platform for accessing topological order in a laboratory. Moreover, considering condensed-matter systems enables us to combine topological features with other physical effects to enhance their behaviour. In this Thesis we study the physics of topologically ordered lattice models with defects. We seek practical applications of lattice defects for the realisation of a fault-tolerant quantum computer. The first result we present shows that anyonic data of point-like lattice defects, called twists, can be found by measuring the entanglement of the ground state of the host system. The data we learn relates to the capacity of a twist defect to perform quantum computational tasks. The second result in this Thesis concerns the dynamics of the qudit toric code model with line-like defects coupled to a thermal bath. We show we can entropically inspire fragile glassy dynamics in the system. Such dynamics qualitatively improve the coherence times of quantum information encoded in the ground state of the lattice. A novel way of achieving fault-tolerant quantum computation is by producing and manipulating twist defects of topologically ordered systems. In many ways, this paradigm of topological quantum computation is analogous to quantum computation using anyons. The first area of study in this Thesis extends the analogy between anyons and twists. Specifically, we show that the anyonic data of twists in Kitaev’s toric code model can be extracted

N@C60 and other group V endohedral fullerenes have recently been proposed as quantum bits for a quantum computer due to their long spin relaxation times. So far quantum computing (QC) experiments have been limited to standard relaxation measurements and simple spin rotations. The purpose of the presented work was perform basic quantum computation experiments including entangled states on this system using electron spin resonance (ESR and ENDOR). In order to allow access the full 3/2 spin character, the symmetry of the fullerenes was lowered by encapsulating them in a crystalline matrix. Co-crystallization of endohedral fullerenes with bromophenoxy triazine (BrPOT) afforded two host-guest structures. In the first, hexagonal, structure fullerenes are situated together with solvent molecules in parallel channels formed by BrPOT molecules. The ESR lines are inhomogeneously broadened compared to those of non-encapsulated fullerenes with no observable fine structure in the case of crystals obtained from toluene solution. In the rhombohedral crystal of N@C60 and P@C60 in BrPOT the fullerenes are fully oriented in individual pockets formed by the BrPOT molecules, hence there are no channels and no solvent inclusion is observed. The ESR spectra show significant fine structure (FS) with D = 8.01 MHz and D = 127 MHz for N@C60 and P@C60, respectively. The presence of FS means that the degeneracy of the electron spin S = 3/2 system is lifted so that all Zeeman sublevels can be addressed individually. In order to elucidate the decoherence mechanisms in P@C60, several polycrystalline samples with low spin concentrations were prepared. The phase memory time Tm and the spin-spin relaxation time T2 were measured using the Hahn echo and Carr-Purcell-Meiboom-Gill (CPMG) pulse sequences, respectively. Tm and T2 increase up to 113.25 ms and 417 ms respectively with decreasing spin concentration. It was found that instant diffusion does not significantly influence the spin-spin relaxation and that the phase memory time is determined mainly by spectral diffusion due to coupling between the P@C60 molecules. The spin relaxation of P@C60 in rhombohedral BrPOT was studied at various temperatures in W-band. Two longitudinal relaxation times T1a and T1b with similar temperature dependence were found in bulk P@C60. The encapsulation of P@C60 in BrPOT has shortened the relaxation but not too much to prevent the realization of QC experiments. The coherence time Tm is not equal for the different ESR transitions and increases decreasing the temperature. For the transition with ms = +1/2 to ms = -1/2 Tm has a minimum at T = 210 K. A subsystem of four states from the total eight levels of P@C60 in BrPOT was selected for QC experiments in which pseudo-pure states were prepared and their diagonal matrix elements were measured. The experimental density matrices deviate slightly (about 3 %) from the theoretically calculated ones due to pulse imperfections. Pseudo-entanglement was created in this subsystem with a Hadamard transform. Phase rotations on both electron and nuclear spins were used for the tomography of the entangled state. The lifetime of the entangled state depends on the type of states used for its creation. For two states with |ms| = 1/2, the coherence time was so short that the entanglement between them was partially destroyed during the preparation. If one of the energy levels had |ms| = 3/2, pseudo-entanglement could be prepared with a decay time of Tent = 55 ns, much shorter than the electron spin coherence time at that temperature, Tm = 17 ms. A possible reason for the fast decay is the coupling of the endohedral electrons to protons in the BrPOT matrix.

Quantum simulation is one of the main contents of quantum information science, aiming to simulate and investigate poorly controllable or unobtainable quantum systems by using controllable quantum systems. Quantum simulation can be implemented in quantum computers, quantum simulators, and small quantum devices. Non-Hermitian systems have aroused research interest increasingly in recent two decades. On one hand, non-Hermitian quantum theories can be seen as the complex extensions of the conventional quantum mechanics, and are closely related to open systems and dissipative systems. On the other hand, both quantum systems and classical systems can be constructed as non-Hermitian systems with novel properties, which can be used to improve the precision of precise measurements. However, a non-Hermitian system is more difficult to simulate than a Hermitian system in that the time evolution of it is no longer unitary. In this review, we introduce recent research progress of quantum simulations of non-Hermitian systems. We mainly introduce theoretical researches to simulate typical non-Hermitian quantum systems by using the linear combinations of unitaries, briefly showing the advantages and limitations of each proposal, and we briefly mention other theoretical simulation methods, such as quantum random walk, space embedded and dilation. Moreover, we briefly introduce the experimental quantum simulations of non-Hermitian systems and novel phenomena in nuclear magnetic resonance, quantum optics and photonics, classical systems, etc. The recent progress of the combinations of quantum simulation and non-Hermitian physics has promoted the development of the non-Hermitian theories, experiments and applications, and expand the scope of application of quantum simulations and quantum computers.

Quantum mechanics is the most ground-breaking and fascinating theoretical concept developed in physics during the past century. Much of our present understanding of the microscopic world and its extension into the macroscopic world, including modern technical applications, is based upon quantum mechanics. We have experienced a remarkable development of information and communication technology during the past two decades, to a large extent depending upon successful fabrication of smaller and smaller components and circuits. However, we are finally approaching the physical limits of component miniaturization as we enter a microscopic world ruled by quantum mechanics.

In recent years, quantum computers and algorithms have made significant progress indicating the prospective importance of quantum computing (QC). Especially combinatorial optimization has gained a lot of attention as an application field for near-term quantum computers, both by using gate-based QC via the Quantum Approximate Optimization Algorithm and by quantum annealing using the Ising model. However, demonstrating an advantage over classical methods in real-world applications remains an active area of research. In this work, we investigate the robustness verification of ReLU networks, which involves solving many-variable mixed-integer programs (MIPs), as a practical application. Classically, complete verification techniques struggle with large networks as the combinatorial space grows exponentially, implying that realistic networks are difficult to be verified by classical methods. To alleviate this issue, we propose to use QC for neural network verification and introduce a hybrid quantum procedure to compute provable certificates. By applying Benders decomposition, we split the MIP into a quadratic unconstrained binary optimization and a linear program which are solved by quantum and classical computers, respectively. We further improve existing hybrid methods based on the Benders decomposition by reducing the overall number of iterations and placing a limit on the maximum number of qubits required. We show that, in a simulated environment, our certificate is sound, and provides bounds on the minimum number of qubits necessary to approximate the problem. Finally, we evaluate our method within simulations and on quantum hardware.

Quantum computing introduces a revolutionary approach to solving problems that are computationally beyond the reach of classical systems. Among its most promising applications is the simulation of many-body systems, where strong particle interactions lead to complex quantum behaviors. Traditional computational techniques often fail due to exponential resource requirements, but quantum simulators can efficiently model these interactions through entanglement and superposition. Recent advances in superconducting qubits, trapped ions, and photonic quantum devices have enabled small- scale experimental demonstrations of spin models, Hubbard systems, and correlated electron dynamics. These developments offer new insights into condensed matter physics and quantum phase transitions. As quantum technologies continue to evolve, they hold the potential to transform the study of materials, superconductivity, and other many-body phenomena with remarkable precision and scalability.

Quantum computers, although not yet available on the market, will revolutionise the future of information processing. Already now, quantum computers of special purpose, i.e., quantum simulators, are within reach. The physics of ultracold atoms, ions, and molecules offers unprecedented possibilities of control of quantum many systems, and novel possibilities of applications for quantum information and quantum metrology. Particularly fascinating is the possibility of using ultracold atoms in lattices to simulate condensed matter or even high energy physics. This book provides a comprehensive overview of ultracold lattice gases as quantum simulators, an interdisciplinary field involving atomic, molecular, and optical physics; quantum optics; quantum information; and condensed matter and high energy physics. It includes some introductory chapters on basic concepts and methods, and focuses on the physics of spinor, dipolar, disordered, and frustrated lattice gases, before reviewing in detail artificial lattice gauge fields with ultracold gases. The last part of the book moves onto a discussion of possible implementations universal quantum computers with ultracold atoms. After a crash course in quantum information theory, several models of quantum computation with ultracold gases are presented, as well as the current understanding of condensed matter from a quantum information perspective. The book ends with the general discussion of various detection methods that are unique for ultracold atoms.