Neutral atom arrays have recently emerged as a promising platform for fault-tolerant quantum computing.Based on these advances, including dynamically-reconfigurable connectivity and fast transversal operations, we present a low-overhead architecture that supports the layout and resource estimation of large-scale fault-tolerant quantum algorithms.Utilizing recent advances in fault tolerance with transversal gate operations, this architecture achieves a run time speed-up on the order of the code distance 𝑑, which we find directly translates to run time improvements of large-scale quantum algorithms.Our architecture consists of functional building blocks of key algorithmic subroutines, including magic state factories, quantum arithmetic units, and quantum look-up tables.These building blocks are implemented using efficient transversal operations, and we design space-time efficient versions of them that minimize interaction We acknowledge helpful discussions with M. Beverland, A.

Near-term quantum computers are primarily limited by errors in quantum operations (or gates) between two quantum bits (or qubits). A physical machine typically provides a set of basis gates that include primitive 2-qubit (2Q) and 1-qubit (1Q) gates that can be implemented in a given technology. 2Q entangling gates, coupled with some 1Q gates, allow for universal quantum computation. In superconducting technologies, the current state of the art is to implement the same 2Q gate between every pair of qubits (typically an XX-or XY-type gate). This strict hardware uniformity requirement for 2Q gates in a large quantum computer has made scaling up a time and resource-intensive endeavor in the lab. We propose a radical idea – allow the 2Q basis gate(s) to differ between every pair of qubits, selecting the best entangling gates that can be calibrated between given pairs of qubits. This work aims to give quantum scientists the ability to run meaningful algorithms with qubit systems that are not perfectly uniform. Scientists will also be able to use a much broader variety of novel 2Q gates for quantum computing. We develop a theoretical framework for identifying good 2Q basis gates on “nonstandard” Cartan trajectories that deviate from “standard” trajectories like XX. We then introduce practical methods for calibration and compilation with nonstandard 2Q gates, and discuss possible ways to improve the compilation. To demonstrate our methods in a case study, we simulated both standard XY-type trajectories and faster, nonstandard trajectories using an entangling gate architecture with far-detuned transmon qubits. We identify efficient 2Q basis gates on these nonstandard trajectories and use them to compile a number of standard benchmark circuits such as QFT and QAOA. Our results demonstrate an 8x improvement over the baseline 2Q gates with respect to speed and coherence-limited gate fidelity.

Current quantum computers are especially error prone and require high levels of optimization to reduce operation counts and maximize the probability the compiled program will succeed. These computers only support operations decomposed into one- and two-qubit gates and only two-qubit gates between physically connected pairs of qubits. Typical compilers first decompose operations, then route data to connected qubits. We propose a new compiler structure, Orchestrated Trios, that first decomposes to the three-qubit Toffoli, routes the inputs of the higher-level Toffoli operations to groups of nearby qubits, then finishes decomposition to hardware-supported gates.

Quantum technologies currently struggle to scale beyond moderate scale prototypes and are unable to execute even reasonably sized programs due to prohibitive gate error rates or coherence times. Many software approaches rely on heavy compiler optimization to squeeze extra value from noisy machines but are fundamentally limited by hardware. Alone, these software approaches help to maximize the use of available hardware but cannot overcome the inherent limitations posed by the underlying technology.An alternative approach is to explore the use of new, though potentially less developed, technology as a path towards scalability. In this work we evaluate the advantages and disadvantages of a Neutral Atom (NA) architecture. NA systems offer several promising advantages such as long range interactions and native multiqubit gates which reduce communication overhead, overall gate count, and depth for compiled programs. Long range interactions, however, impede parallelism with restriction zones surrounding interacting qubit pairs. We extend current compiler methods to maximize the benefit of these advantages and minimize the cost.Furthermore, atoms in an NA device have the possibility to randomly be lost over the course of program execution which is extremely detrimental to total program execution time as atom arrays are slow to load. When the compiled program is no longer compatible with the underlying topology, we need a fast and efficient coping mechanism. We propose hardware and compiler methods to increase system resilience to atom loss dramatically reducing total computation time by circumventing complete reloads or full recompilation every cycle.

Current quantum computer designs will not scale. To scale beyond small prototypes, quantum architectures will likely adopt a modular approach with clusters of tightly connected quantum bits and sparser connections between clusters. We exploit this clustering and the statically-known control flow of quantum programs to create tractable partitioning heuristics which map quantum circuits to modular physical machines one time slice at a time. Specifically, we create optimized mappings for each time slice, accounting for the cost to move data from the previous time slice and using a tunable lookahead scheme to reduce the cost to move to future time slices. We compare our approach to a traditional statically-mapped, owner-computes model. Our results show strict improvement over the static mapping baseline. We reduce the non-local communication overhead by 89.8% in the best case and by 60.9% on average. Our techniques, unlike many exact solver methods, are computationally tractable.

Current, near-term quantum devices have shown great progress in the last several years culminating recently with a demonstration of quantum supremacy. In the medium-term, however, quantum machines will need to transition to greater reliability through error correction, likely through promising techniques like surface codes which are well suited for near-term devices with limited qubit connectivity. We discover quantum memory, particularly resonant cavities with transmon qubits arranged in a 2.5D architecture, can efficiently implement surface codes with substantial hardware savings and performance/fidelity gains. Specifically, we virtualize logical qubits by storing them in layers of qubit memories connected to each transmon. Surprisingly, distributing each logical qubit across many memories has a minimal impact on fault tolerance and results in substantially more efficient operations. Our design permits fast transversal application of CNOT operations between logical qubits sharing the same physical address (same set of cavities) which are 6x faster than standard lattice surgery CNOTs. We develop a novel embedding which saves approximately 10x in transmons with another 2x savings from an additional optimization for compactness. Although qubit virtualization pays a 10x penalty in serialization, advantages in the transversal CNOT and in area efficiency result in fault-tolerance and performance comparable to conventional 2D transmon-only architectures. Our simulations show our system can achieve fault tolerance comparable to conventional two-dimensional grids while saving substantial hardware. Furthermore, our architecture can produce magic states at 1.22x the baseline rate given a fixed number of transmon qubits. This is a critical benchmark for future fault-tolerant quantum computers as magic states are essential and machines will spend the majority of their resources continuously producing them. This architecture substantially reduces the hardware requirements for fault-tolerant quantum computing and puts within reach a proof-of-concept experimental demonstration of around 10 logical qubits, requiring only 11 transmons and 9 attached cavities in total.

Building a quantum computer that surpasses the computational power of its classical counterpart is a great engineering challenge. Quantum software optimizations can provide an accelerated pathway to the first generation of quantum computing (QC) applications that might save years of engineering effort. Current quantum software stacks follow a layered approach similar to the stack of classical computers, which was designed to manage the complexity. In this review, we point out that greater efficiency of QC systems can be achieved by breaking the abstractions between these layers. We review several works along this line, including two hardware-aware compilation optimizations that break the quantum instruction set architecture (ISA) abstraction and two error-correction/information-processing schemes that break the qubit abstraction. Last, we discuss several possible future directions.

Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider three-level qu trits . Past work with qutrits has demonstrated only constant factor improvements, owing to the log 2 (3) binary-to-ternary compression factor. We present a novel technique, intermediate qutrits, to achieve sublinear depth decompositions of the Generalized Toffoli and other arithmetic circuits using no additional ancilla—a significant improvement over linear depth for the best qubit-only equivalents. For example, our Generalized Toffoli construction features a 70× improvement in two-qudit gate count over a qubit-only decomposition. This results in circuit cost reductions for important algorithms like quantum neurons, Grover search, and even Shor’s algorithm. Using a previously developed simulator with near-term noise models, we demonstrate for these models over 90% mean reliability (fidelity) for the Toffoli construction, versus under 30% for the qubit-only baseline. For our other constructions, such as the Incrementer, the A + B adder and the +K adder, we demonstrate the power of intermediate qutrits in producing asymptotic depth improvements with no additional ancilla. Together, these results suggest qutrits offer a promising path toward scaling quantum computation.

Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider three-level qutrits. Past work with qutrits has demonstrated only constant factor improvements, owing to the log2(3) binary-to-ternary compression factor. We present a novel technique using qutrits to achieve a logarithmic depth (runtime) decomposition of the Generalized Toffoli gate using no ancilla-a significant improvement over linear depth for the best qubit-only equivalent. Our circuit construction also features a 70x improvement in two-qudit gate count over the qubit-only equivalent decomposition. This results in circuit cost reductions for important algorithms like quantum neurons and Grover search. We develop an open-source circuit simulator for qutrits, along with realistic near-term noise models which account for the cost of operating qutrits. Simulation results for these noise models indicate over 90% mean reliability (fidelity) for our circuit construction, versus under 30% for the qubit-only baseline. These results suggest that qutrits offer a promising path towards scaling quantum computation.