Many proposals to scale quantum technology rely on modular or distributed designs wherein individual quantum processors, called nodes, are linked together to form one large multinode quantum computer (MNQC). One scalable method to construct an MNQC is using superconducting quantum systems with optical interconnects. However, internode gates in these systems may be two to three orders of magnitude noisier and slower than local operations. Surmounting the limitations of internode gates will require improvements in entanglement generation, use of entanglement distillation, and optimized software and compilers. Still, it remains unclear what performance is possible with current hardware and what performance algorithms require. In this article, we employ a systems analysis approach to quantify overall MNQC performance in terms of hardware models of internode links, entanglement distillation, and local architecture. We show how to navigate tradeoffs in entanglement generation and distillation in the context of algorithm performance, lay out how compilers and software should balance between local and internode gates, and discuss when noisy quantum internode links have an advantage over purely classical links. We find that a factor of 10–100× better link performance is required and introduce a research roadmap for the co-design of hardware and software towards the realization of early MNQCs. While we focus on superconducting devices with optical interconnects, our approach is general across MNQC implementations.

We study the problem of simulating the time evolution of a system of 2nclassical coupled oscillators (e.g., 2nballs connected by springs) on a quantum computer. We map Newton’s equation for harmonic potentials to Schrödinger’s equation, such that the amplitudes of an $\mathcal{O}(n)$-qubit quantum state encode the momenta and displacements of the 2nclassical oscillators. Given oracle access to the masses and spring constants, we describe a quantum algorithm with query and time complexity poly (n) that solves this problem when certain parameters are polynomially bounded and the initial state is easy to prepare. As an example application, we apply our quantum algorithm to efficiently estimate the normalized kinetic energy of an oscillator at any time. We then show that any classical algorithm solving the same problem must make $2^{\Omega(n)}$ queries to the oracle and we also show that when the oracles are instantiated by poly (n)-size circuits, the problem is BQP-complete. Thus, our approach solves a potentially practical application with an exponential speedup over classical computers.

Quantum computing technology has grown rapidly in recent years, with new technologies being explored, error rates being reduced, and quantum processors' qubit capacity growing. However, near-term quantum algorithms are still unable to be induced without compounding consequential levels of noise, leading to non-trivial erroneous results. Quantum Error Correction (in-situ error mitigation) and Quantum Error Mitigation (post-induction error mitigation) are promising fields of research within the quantum algorithm scene, aiming to alleviate quantum errors. IBM recently published an article stating that Quantum Error Mitigation is the path to quantum computing usefulness. A recent work, namely HAMMER, demonstrated the existence of a latent structure regarding post-circuit induction errors when mapping to the Hamming spectrum. However, they assumed that errors occur solely in local clusters, whereas we observe that at higher average Hamming distances this structure falls away. In this work, we show that such a correlated structure is not only local but extends certain non-local clustering patterns which can be precisely described by a Poisson distribution model taking the input circuit, the device run time status (i.e., calibration statistics) and qubit topology into consideration. Using this quantum error characterizing model, we developed an iterative algorithm over the generated Bayesian network state-graph for post-induction error mitigation. Thanks to more precise modeling of the error distribution latent structure and the proposed iterative method, our Q-Beep approach provides state of the art performance and can boost circuit execution fidelity by up to 234.6% on Bernstein-Vazirani circuits and on average 71.0% on QAOA solution quality, using 16 practical IBMQ quantum processors. For other benchmarks such as those in QASMBench, a fidelity improvement of up to 17.8% is attained. Q-Beep is a light-weight post-processing technique that can be performed offline and remotely, making it a useful tool for quantum vendors to adopt and provide more reliable circuit induction results. Q-Beep is maintained at github.com/pnnl/qbeep

Protein design is a technique to engineer proteins by permuting amino acids in the sequence to obtain novel functionalities. However, exploring all possible combinations of amino acids is generally impossible due to the exponential growth of possibilities with the number of designable sites. The present work introduces circuits implementing a pure quantum approach, Grover's algorithm, to solve protein design problems. Our algorithms can adjust to implement any custom pair-wise energy tables and protein structure models. Moreover, the algorithm's oracle is designed to consist of only adder functions. Quantum computer simulators validate the practicality of our circuits, containing up to 234 qubits. However, a smaller circuit is implemented on real quantum devices. Our results show that using [Formula: see text] iterations, the circuits find the correct results among all N possibilities, providing the expected quadratic speed up of Grover's algorithm over classical methods (i.e., [Formula: see text]).

Variational quantum algorithm (VQA), which is comprised of a classical optimizer and a parameterized quantum circuit, emerges as one of the most promising approaches for harvesting the power of quantum computers in the noisy intermediate scale quantum (NISQ) era. However, the deployment of VQAs on contemporary NISQ devices often faces considerable system and time-dependant noise and prohibitively slow training speeds. On the other hand, the expensive supporting resources and infrastructure make quantum computers extremely keen on high utilization.

We consider a generic framework of optimization algorithms based on gradient descent. We develop a quantum algorithm that computes the gradient of a multi-variate realvalued function f : ℝd → ℝ by evaluating it at only a logarithmic number of times in superposition. Our algorithm is an improved version of Jordan's gradient computation algorithm [28], providing an approximation of the gradient ▽f with quadratically better dependence on the evaluation accuracy of f, for an important class of smooth functions. Furthermore, we show that objective functions arising from variational quantum circuits usually satisfy the necessary smoothness conditions, hence our algorithm provides a quadratic improvement in the complexity of computing their gradient. We also show that in a continuous phase-query model, our gradient computation algorithm has optimal query complexity up to poly-logarithmic factors, for a particular class of smooth functions. Moreover, we show that for low-degree multivariate polynomials our algorithm can provide exponential speedups compared to Jordan's algorithm in terms of the dimension d. One of the technical challenges in applying our gradient computation procedure for quantum optimization problems is the need to convert between a probability oracle (which is common in quantum optimization procedures) and a phase oracle (which is common in quantum algorithms) of the objective function f. We provide efficient subroutines to perform this delicate interconversion between the two types of oracles incurring only a logarithmic overhead, which might be of independent interest. Finally, using these tools we improve the runtime of prior approaches for training quantum auto-encoders, variational quantum eigensolvers (VQE), and quantum approximate optimization algorithms (QAOA).

An n-qubit quantum circuit performs a unitary operation on an exponentially large, 2n-dimensional, Hilbert space, which is a major source of quantum speed-ups. We develop a new “Quantum singular value transformation” algorithm that can directly harness the advantages of exponential dimensionality by applying polynomial transformations to the singular values of a block of a unitary operator. The transformations are realized by quantum circuits with a very simple structure - typically using only a constant number of ancilla qubits - leading to optimal algorithms with appealing constant factors. We show that our framework allows describing many quantum algorithms on a high level, and enables remarkably concise proofs for many prominent quantum algorithms, ranging from optimal Hamiltonian simulation to various quantum machine learning applications. We also devise a new singular vector transformation algorithm, describe how to exponentially improve the complexity of implementing fractional queries to unitaries with a gapped spectrum, and show how to efficiently implement principal component regression. Finally, we also prove a quantum lower bound on spectral transformations.

We present a synthesis framework to map logic networks into quantum circuits for quantum computing. The synthesis framework is based on lookup-table (LUT) networks, which play a key role in conventional logic synthesis. Establishing a connection between LUTs in an LUT network and reversible single-target gates in a reversible network allows us to bridge conventional logic synthesis with logic synthesis for quantum computing, despite several fundamental differences. We call our synthesis framework LUT-based hierarchical reversible logic synthesis (LHRS). Input to LHRS is a classical logic network representing an arbitrary Boolean combinational operation; output is a quantum network (realized in terms of Clifford+T gates). The framework allows one to account for qubit count requirements imposed by the overlying quantum algorithm or target quantum computing hardware. In a fast first step, an initial network is derived that only consists of single-target gates and already completely determines the number of qubits in the final quantum network. Different methods are then used to map each single-target gate into Clifford+T gates, while aiming at optimally using available resources. We demonstrate the versatility of our method by conducting a design space exploration using different parameters on a set of large combinational benchmarks. On the same benchmarks, we show that our approach can advance over the state-of-the-art hierarchical reversible logic synthesis algorithms.

Currently, there is a large research interest and a significant economical effort to build the first practical quantum computer. Such quantum computers promise to exceed the capabilities of conventional computers in fields such as computational chemistry, machine learning and cryptanalysis. Automated methods to map logic designs to quantum networks are crucial to fully realizing this dream, however, existing methods can be expensive both in computational time as well as in the size of the resultant quantum networks. This work introduces an efficient method to map reversible single-target gates into a universal set of quantum gates (Clifford+T). This mapping method is called best-fit mapping and aims at reducing the cost of the resulting quantum network. It exploits fc-LUT mapping and the existence of clean ancilla qubits to decompose a large single-target gate into a set of smaller single-target gates. In addition this work proposes a post-synthesis optimization method to reduce the cost of the final quantum network, based on two cost-minimization properties. Results show a cost reduction for the synthesized EPFL benchmark up to 53% in the number T gates.

Today's rapid advances in the physical implementation of quantum computers demand for scalable synthesis methods in order to map practical logic designs to quantum architectures. We present a synthesis algorithm for quantum computing based on k-LUT networks, which can be derived from Verilog netlists using state-of-the-art and off-the-shelf mapping algorithms. We demonstrate the effectiveness of our method in automatically synthesizing several floating point networks up to double precision. As many quantum algorithms target scientific simulation applications, they can make rich use of floating point arithmetic components. But due to the lack of quantum circuit descriptions for those components, it is not possible to find a realistic cost estimation for the algorithms. Our synthesized benchmarks provide cost estimates that allow quantum algorithm designers to provide the first complete cost estimates for a host of quantum algorithms. This is an essential step towards the goal of understanding which quantum algorithms will be practical in the first generations of quantum computers.

We survey recent strides made towards building a software framework that is capable of compiling quantum algorithms from a high-level description down to physical gates that can be implemented on a fault-tolerant quantum computer. We discuss why compilation and design automation tools such as the ones in our framework are key for tackling the grand challenge of building a scalable quantum computer. We then describe specialized libraries that have been developed using the LIQUi|〉 programming language. This includes reversible circuits for arithmetic as well as new, truly quantum approaches that rely on quantum computer architectures that allow the probabilistic execution of gates, a model that can reduce time and space overheads in some cases. We highlight why these libraries are useful for the implementation of many quantum algorithms. Finally, we survey the tool Revs that facilitate resource efficient compilation of higher-level irreversible programs into lower-level reversible circuits while trying to optimize the memory footprint of the resulting reversible networks. This is motivated by the limited availability of qubits for the foreseeable future.

A major hurdle to the deployment of quantum linear systems algorithms and recent quantum simulation algorithms lies in the difficulty to find inexpensive reversible circuits for arithmetic using existing hand coded methods. Motivated by recent advances in reversible logic synthesis, we synthesize arithmetic circuits using classical design automation flows and tools. The combination of classical and reversible logic synthesis enables the automatic design of large components in reversible logic starting from well-known hardware description languages such as Verilog. As a prototype example for our approach we automatically generate high quality networks for the reciprocal 1/x, which is necessary for quantum linear systems algorithms.

We demonstrate how quantum computation can provide non-trivial improvements in the computational and statistical complexity of the perceptron model. We develop two quantum algorithms for perceptron learning. The first algorithm exploits quantum information processing to determine a separating hyperplane using a number of steps sublinear in the number of data points $N$, namely $O(\sqrt{N})$. The second algorithm illustrates how the classical mistake bound of $O(\frac{1}{\gamma^2})$ can be further improved to $O(\frac{1}{\sqrt{\gamma}})$ through quantum means, where $\gamma$ denotes the margin. Such improvements are achieved through the application of quantum amplitude amplification to the version space interpretation of the perceptron model.

For a mobile robot to be able to communicate usefully with others, the symbols it uses to communicate must be grounded to entities in the environment, and those groundings made consistent among agents. While it is common practice to hand-construct such groundings, this does not scale to large problems. In particular, when communicating about useful spatial references, there are a large number of potentially relevant groundings, even for a basic task such as navigation. This paper describes the development and evaluation of an approach that allows a group of robotic agents to develop consistent shared groundings for locations in an environment over time. This approach is based on local communication and interaction, and does not rely on the ability to broadcast references to all agents, and so is suitable for domains in which communication may be sporadic, such as robotic rescue. The evaluation of this approach, which compares several different grounding techniques, shows that shared groundings can be developed effectively over time, and that these improve the effectiveness of communication in a multi-robot setting.