Co-Design quantum simulation of nanoscale NMR

The development of near-term quantum computers, referred to as Noisy Intermediate-Scale Quantum (NISQ) computers, has progressed rapidly in the past few years resulting in several quantum computers which vary in their underlying technology and physical constraints. The performance of these computers also varies from one quantum algorithm to another. To enable efficient selection of the quantum computer that provides the highest output fidelity for a given application, an accurate noise modeling of each quantum hardware is required. However, noise modeling for a given application is a complex problem because of the unknown interaction between the quantum circuit parameters and the noise parameters of NISQ devices. We propose the use of Machine Learning (ML) to model the performance of different quantum computers at the application level. The ML models predict the output fidelity of the quantum application executed on different quantum computers given their publicly available physical constraints. We use a diverse training dataset to cover the key features for application-level benchmarking of the quantum hardware. Our results obtained from different superconducting quantum devices show that our proposed ML models enable cost-effective quantum computer selection for different quantum applications with different fidelity metrics.

Simulation of the dynamics of quantum materials is emerging as a promising scientific application for noisy intermediate-scale quantum (NISQ) computers. Due to their high gate-error rates and short decoherence times, however, NISQ computers can only produce high-fidelity results for those quantum circuits smaller than some given circuit size. Dynamic simulations, therefore, pose a challenge as current algorithms produce circuits that grow in size with each subsequent time-step of the simulation. This underscores the crucial role of quantum circuit compilers to produce executable quantum circuits of minimal size, thereby maximizing the range of physical phenomena that can be studied within the NISQ fidelity budget. Here, we present two domain-specific (DS) quantum circuit compilers for the Rigetti and IBM quantum computers, specifically designed to compile circuits simulating dynamics under a special class of time-dependent Hamiltonians. The compilers outperform state-of-the-art general-purpose compilers in terms of circuit size reduction by around 25%–30% as well as wall-clock compilation time by around 40% (dependent on system size and simulation time-step). Drawing on heuristic techniques commonly used in artificial intelligence, both compilers scale well with simulation time-step and system size. Code for both compilers is open-source and packaged into a full-stack quantum simulation software with tutorials included for ease of use for future researchers wishing to perform dynamic simulations of quantum materials on quantum computers. As our DS compilers provide significant improvements in both compilation time and simulation fidelity, they provide a building block for accelerating progress toward physical quantum supremacy.

Compiling high-level quantum programs to machines that are size constrained (i.e. limited number of quantum bits) and time constrained (i.e. limited number of quantum operations) is challenging. In this paper, we present SQUARE (Strategic QUantum Ancilla REuse), a compilation infrastructure that tackles allocation and reclamation of scratch qubits (called ancilla) in modular quantum programs. At its core, SQUARE strategically performs uncomputation to create opportunities for qubit reuse. Current Noisy Intermediate-Scale Quantum (NISQ) computers and forward-looking Fault-Tolerant (FT) quantum computers have fundamentally different constraints such as data locality, instruction parallelism, and communication overhead. Our heuristic-based ancilla-reuse algorithm balances these considerations and fits computations into resource-constrained NISQ or FT quantum machines, throttling parallelism when necessary. To precisely capture the workload of a program, we propose an improved metric, the "active quantum volume," and use this metric to evaluate the effectiveness of our algorithm. Furthermore, our results show that SQUARE improves the average success rate of NISQ applications by 1.47X. Surprisingly, the additional gates for uncomputation create ancilla with better locality, and result in substantially fewer swap gates and less gate noise overall. SQUARE also achieves an average reduction of 1.5X (and up to 9.6X) in active quantum volume for FT machines.

The variational quantum eigensolver is a promising way to solve the Schrödinger equation on a noisy intermediate-scale quantum (NISQ) computer, while its success relies on a well-designed wave function ansatz. Inspired by the quantum neural network, we propose a new hardware heuristic ansatz where its expressibility can be improved by increasing either the depth or the width of the circuit. Such a character makes this ansatz adaptable to different hardware environments. More importantly, it provides a general framework to improve the efficiency of the quantum resource utilization. For example, on a superconducting quantum computer where circuit depth is usually the bottleneck and the qubits thus cannot be fully used, circuit depth can be significantly reduced by introducing ancilla qubits. Ancilla qubits also make the circuit less sensitive to noises in practical application. These results open a new avenue to develop practical applications of quantum computation in the NISQ era.

While current quantum computers, referred to as Noisy Intermediate-Scale Quantum (NISQ) computers, are expected to be beneficial for different applications, they are prone to different types of errors. In order to enhance the reliability of quantum systems, noise-aware quantum compilers are used to generate physical quantum circuits to be executed on NISQ computers. The quantum hardware is calibrated very frequently and its error rates are computed accordingly. Based on the hardware error rates, a quantum compiler allocates physical qubits and schedules quantum operations. However, error rates may change post-calibration. To incorporate dynamic error rates into quantum circuit compilation with minimum cost, we propose a Machine Learning (ML)-based scheme to detect the incorrect output of the quantum circuit and predict the Probability of Successful Trials (PST) with high accuracy. Our approach can verify the error rates of the quantum hardware and validate the correctness of the extracted quantum circuit output. We provide a case study of our ML-based reliability models using IBM Q16 Melbourne quantum computer. Our results show that the proposed scheme achieves a very high prediction accuracy.

Quantum state preparation is a key step in all digital quantum simulation algorithms. Here we propose methods to initialize on a gate-based quantum computer a general class of quantum spin wave functions, the so-called valence-bond-solid (VBS) states, that are important for two reasons. First, VBS states are the exact ground states of a class of interacting quantum spin models introduced by Affleck, Kennedy, Lieb, and Tasaki (AKLT). Second, the two-dimensional VBS states are universal resource states for measurement-based quantum computing. We find that schemes to prepare VBS states based on their tensor-network representations yield quantum circuits that are too deep to be within reach of noisy intermediate-scale quantum (NISQ) computers. We then apply the general nondeterministic method herein proposed to the preparation of the spin-1 and spin-3/2 VBS states, the ground states of the AKLT models defined in one dimension and in the honeycomb lattice, respectively. Shallow quantum circuits of depth independent of the lattice size are explicitly derived for both cases, making use of optimization schemes that outperform standard basis gate decomposition methods. The probabilistic nature of the proposed routine translates into an average number of repetitions to successfully prepare the VBS state that scales exponentially with the number of lattice sites N. However, two strategies to quadratically reduce this repetition overhead for any bipartite lattice are devised. Our approach should permit to use NISQ processors to explore the AKLT model and variants thereof, outperforming conventional numerical methods in the near future.

Quantum computing for near-term applications in generative chemistry and drug discovery

The variational quantum eigensolver (VQE) is a promising algorithm to demonstrate quantum advantage on near-term noisy-intermediate-scale quantum (NISQ) computers. One central problem of VQE is the effect of noise, especially physical noise, on realistic quantum computers. We systematically study the effect of noise for the VQE algorithm by performing numerical simulations with various local noise models, including amplitude damping, dephasing, and depolarizing noise. We show that the ground state energy will deviate from the exact value as the noise probability increase, and typically, the noise will accumulate as the circuit depth increase. The results suggest that the noisy quantum system can remain entanglement at the noise level of NISQ devices by comparing the VQE solution with the mean-field solution for the many-body ground state problem. We build a noise model to capture the noise in a real quantum computer, and the corresponding numerical simulation is consistent with experimental results on IBM Quantum computers through cloud. Our work sheds new light on the practical research of noisy VQE, and the deep understanding of the noise effect of VQE will also help develop error mitigation techniques on near-term quantum computers.

Two-qubit entangling gates for superconducting quantum computers

Quantum computing is attracting more and more attention in material and biological science. In the noisy intermediate-scale quantum (NISQ) computing era, the variational quantum eigensolver (VQE) is expected as an effective method to solve quantum chemistry problems which has potential quantum advantage. Classically simulating quantum algorithms plays a critical role in algorithmic development and the validation of noisy quantum devices before large-scale, fully fault-tolerant quantum computers are developed. However, most existing simulators are based on the state vector or density matrix representation of the quantum state which is faced with the memory bottleneck due to the exponential growth of memory requirement as the number of qubits increases. In this work, we present a VQE simulator based on the matrix product states (MPS) method from quantum many-body physics, and a detailed study of our MPS-VQE simulator in quantum chemistry applications. The memory requirement of MPS-VQE grows only polynomially and we demonstrate that accurate results can be obtained despite the truncation of the smallest singular values during the algorithm. A distributed parallelization scheme is also presented for massively parallel computer systems, and different implementations of the parallelization scheme based on the Julia language are benchmarked which demonstrate the efficiency and scalability of our method. Our method could open a new avenue towards large-scale classical simulation of quantum computational chemistry.

Noisy intermediate scale quantum (NISQ) systems are susceptible to errors that culminate in near-one hundred percent data loss. This is due to quantum state fragility and the incredibly high quantum communication error rates caused by decoherence, or quantum noise. As such, stabilizing qubit operational imprecision in quantum information processing is a critical area of research in quantum computing. Adaptive quantum machine learning (QML) methods, like unsupervised and fully entangled quantum generative adversarial networks is one such technology theorized to provide a breakthrough in quantum error suppression. Mechanizing the quantum error detection and correction process with QML provides a path forward from today’s monolithic quantum computers running almost exclusively single-core quantum processing unit (QPU) designs, to the next generation of federated quantum computers using multi-core QPUs. Automating the detection and correction of quantum errors in powerful NISQ devices will pave the way for fault-tolerant quantum computing, making quantum speeds at quantum scale suddenly achievable.

We introduce a new method to calculate phase shifts on noisy intermediate scale quantum (NISQ) hardware platforms using a wave packet edge time delay. The method uses the early and intermediate stages of the collision because the standard method based on the asymptotic out-state behavior is unreachable using today’s NISQ platforms. The calculation was implemented on a 4-site transverse Ising model in one spatial dimension with and without a potential interaction. A time evolution operator describing the progression of the system was constructed and transmission and reflection coefficients were calculated based on the identified quantum Fourier transformed momentum states. The detailed analysis of the phase shift calculations on both IBM superconducting transmon and University of Maryland ion trap quantum computers shows the platform independence of the methodology. This successful implementation of this wave packet preparation and projection on momentum eigenstates can now be performed with actual quantum computing hardware platforms. This method provides a procedure for calculating phase shifts and opens the possibility of using noisy intermediate scale quantum devices to perform real-time quantum mechanics and quantum field theory scattering calculations.

Classical simulations of real-space quantum dynamics are challenging due to the exponential scaling of computational cost with system dimensions. Quantum computers offer the potential to simulate quantum dynamics with polynomial complexity; however, existing quantum algorithms based on the split-operator techniques require large-scale fault-tolerant quantum computers that remain elusive in the near future. Here, we present variational simulations of real-space quantum dynamics suitable for implementation in noisy intermediate-scale quantum (NISQ) devices. The Hamiltonian is first encoded onto qubits using a discrete variable representation and binary encoding scheme. We show that direct application of a real-time variational quantum algorithm based on the McLachlan's principle is inefficient as the measurement cost grows exponentially with the qubit number for general potential energy, and an extremely small time-step size is required to achieve accurate results. Motivated by the insights that many chemical dynamics occur in the low-energy subspace, we propose a subspace expansion method by projecting the total Hamiltonian, including the time-dependent driving field, onto the system low-energy eigenstate subspace using quantum computers, and the exact quantum dynamics within the subspace can then be solved classically. We show that the measurement cost of the subspace approach grows polynomially with dimensionality for general potential energy. Our numerical examples demonstrate the capability of our approach, even under intense laser fields. Our work opens the possibility of simulating chemical dynamics with NISQ hardware.

High-quality simulated data is crucial for particle physics discoveries. Therefore, parton shower algorithms are a major building block of the data synthesis in event generator programs. However, the core algorithms used to generate parton showers have barely changed since the 1980s. With quantum computers’ rapid and continuous development, dedicated algorithms are required to exploit the potential that quantum computers provide to address problems in high-energy physics. This paper presents a novel approach to synthesising parton showers using the Discrete QCD method. The algorithm benefits from an elegant quantum walk implementation which can be embedded into the classical toolchain. We use the ibm_algiers device to sample parton shower configurations and generate data that we compare against measurements taken at the ALEPH, DELPHI and OPAL experiments. This is the first time a Noisy Intermediate-Scale Quantum (NISQ) device has been used to simulate realistic high-energy particle collision events.

State-of-the-art noisy digital quantum computers can only execute short-depth quantum circuits. Variational algorithms are a promising route to unlock the potential of noisy quantum computers since the depth of the corresponding circuits can be kept well below hardware-imposed limits. Typically, the variational parameters correspond to virtual ${R}_{Z}$ gate angles, implemented by phase changes of calibrated pulses. By encoding the variational parameters directly as hardware pulse amplitudes and durations, we succeed in further shortening the pulse schedule and overall circuit duration. This decreases the impact of qubit decoherence and gate noise. As a demonstration, we apply our pulse-based variational algorithm to the calculation of the ground state of different hydrogen-based systems (${\mathrm{H}}_{2}, {\mathrm{H}}_{3}$, and ${\mathrm{H}}_{4}$) using IBM cross-resonance-based hardware. We observe a reduction in schedule duration of up to $5\ifmmode\times\else\texttimes\fi{}$ compared to cnot-based Ans\"atze, while also reducing the measured energy. In particular, we observe a sizable improvement of the minimal energy configuration of ${\mathrm{H}}_{3}$ compared to a cnot-based variational form. Finally, we discuss possible future developments including error-mitigation schemes and schedule optimizations, which will enable further improvements of our approach, paving the way towards the simulation of larger systems on noisy quantum devices.