Advances in quantum devices have brought scalable quantum computation closer to reality. We focus on the system-level issues of how quantum devices can be brought together to form a scalable architecture. In particular, we examine promising silicon-based proposals. We discover that communication of quantum data is a critical resource in such proposals. We find that traditional techniques using quantum SWAP gates are exponentially expensive as distances increase and propose quantum teleportation as a means to communicate data over longer distances on a chip. Furthermore, we find that realistic quantum error-correction circuits use a recursive structure that benefits from using teleportation for long-distance communication. We identify a set of important architectural building blocks necessary for constructing scalable communication and computation. Finally, we explore an actual layout scheme for recursive error correction, and demonstrate the exponential growth in communication costs with levels of recursion, and that teleportation limits those costs.
Advances in quantum devices have brought scalable quantum computation closer to reality. We focus on the system-level issues of how quantum devices can be brought together to form a scalable architecture. In particular, we examine promising silicon-based proposals. We discover that communication of quantum data is a critical resource in such proposals. We find that traditional techniques using quantum SWAP gates are exponentially expensive as distances increase and propose quantum teleportation as a means to communicate data over longer distances on a chip. Furthermore, we find that realistic quantum error-correction circuits use a recursive structure that benefits from using teleportation for long-distance communication. We identify a set of important architectural building blocks necessary for constructing scalable communication and computation. Finally, we explore an actual layout scheme for recursive error correction, and demonstrate the exponential growth in communication costs with levels of recursion, and that teleportation limits those costs.
As the complexity of quantum computers increases, typical architectural issues such as communication, layout, and efficient design need to be addressed. This document addresses some basic architectural ideas for quantum computers.
To be useful in reasonable calculations, quantum states will need constant error correction. This need guides how best to lay out physical components to minimize error-correction overhead. I propose a layout that minimizes communication overhead, and discuss the implementation of error-correction algorithms on that layout. I compare the cost overhead of purely local communication to communication by teleportation, and calculate the break-even point at which teleportation becomes efficient.
Additionally, the overhead of error correction can be reduced by using a memory hierarchy to more efficiently store data not currently being computed on. The main requirement is the same as for a classical computer's cache: temporal locality. I show that an important quantum routine can be rearranged to take advantage of a small quantum memory cache, and compute the achieved savings.
In a quantum system, complex operators are built up from the basic operators allowed by a given technology model. I show that the set of operators required to implement any complex operator in an error-corrected system can be approximated to arbitrary precision, given two elementary operators. I give results for all the operators in the set.
Finally, I examine methods to initialize a quantum system. Quantum operators are reversible, so data cannot simply be written over. Instead, initialization entails compressing the entropy of a set of quantum bits into a small subset of those bits, leaving the rest of the bits in a known, non-random state. I examine three such compression algorithms. The best of these itself requires a pool of known states, and so cannot be used directly. The other two algorithms, however, produce less-than-optimal results. I explore why they produce suboptimal results, and propose that one of the suboptimal algorithms be used to compress the entropy of a subsystem, using the resulting known state to run the optimal algorithm.
Quantum computation has become an intriguing technology with which to attack difficult problems and to enhance system security. Quantum algorithms, however, have been analyzed under idealized assumptions without important physical constraints in mind. In this paper, we analyze two key constraints: the short spatial distance of quantum interactions and the short temporal life of quantum data.In particular, quantum computations must make use of extremely robust error correction techniques to extend the life of quantum data. We present optimized spatial layouts of quantum error correction circuits for quantum bits embedded in silicon. We analyze the complexity of error correction under the constraint that interaction between these bits is near neighbor and data must be propagated via swap operations from one part of the circuit to another.We discover two interesting results from our quantum layouts. First, the recursive nature of quantum error correction circuits requires a additional communication technique more powerful than near-neighbor swaps -- too much error accumulates if we attempt to swap over long distances. We show that quantum teleportation can be used to implement recursive structures. We also show that the reliability of the quantum swap operation is the limiting factor in solid-state quantum computation.
Quantum computation has become an intriguing technology with which to attack difficult problems and to enhance system security. Quantum algorithms, however, have been analyzed under idealized assumptions without important physical constraints in mind. In this paper, we analyze two key constraints: the short spatial distance of quantum interactions and the short temporal life of quantum data.In particular, quantum computations must make use of extremely robust error correction techniques to extend the life of quantum data. We present optimized spatial layouts of quantum error correction circuits for quantum bits embedded in silicon. We analyze the complexity of error correction under the constraint that interaction between these bits is near neighbor and data must be propagated via swap operations from one part of the circuit to another.We discover two interesting results from our quantum layouts. First, the recursive nature of quantum error correction circuits requires a additional communication technique more powerful than near-neighbor swaps -- too much error accumulates if we attempt to swap over long distances. We show that quantum teleportation can be used to implement recursive structures. We also show that the reliability of the quantum swap operation is the limiting factor in solid-state quantum computation.
Recent experimental advances have demonstrated technologies capable of supporting scalable quantum computation. A critical next step is how to put those technologies together into a scalable, fault-tolerant system that is also feasible. We propose a quantum logic array (QLA) microarchitecture that forms the foundation of such a system. The QLA focuses on the communication resources necessary to efficiently support fault-tolerant computations. We leverage the extensive groundwork in quantum error correction theory and provide analysis that shows that our system is both asymptotically and empirically fault tolerant. Specifically, we use the QLA to implement a hierarchical, array-based design and a logarithmic expense quantum-teleportation communication protocol. Our goal is to overcome the primary scalability challenges of reliability, communication, and quantum resource distribution that plague current proposals for large-scale quantum computing. Our work complements recent work by Balenseifer et al. (2005), which studies the software tool chain necessary to simplify development of quantum applications; here we focus on modeling a full-scale optimized microarchitecture for scalable computing.
As quantum computing moves closer to reality the need for basic architectural studies becomes more pressing. Quantum wires, which transport quantum data, will be a fundamental component in all anticipated silicon quantum architectures. In this paper, we introduce a quantum wire architecture based upon quantum teleportation. We compare this teleportation channel with the traditional approach to transporting quantum data, which we refer to as the swapping channel. We characterize the latency and bandwidth of these two alternatives in a device-independent way and describe how the advanced architecture of the teleportation channel overcomes a basic limit to the maximum communication distance of the swapping channel. In addition, we discover a fundamental tension between the scale of quantum effects and the scale of the classical logic needed to control them. This pitch-matching problem imposes constraints on minimum wire lengths and wire intersections, which in turn imply a sparsely connected architecture of coarse-grained quantum computational elements. This is in direct contrast to the sea of gates architectures presently assumed by most quantum computing studies.
Exploiting recent advances in quantum trapped-ion technologies, we propose a scalable, fault-tolerant quantum computing architecture that overcomes the fundamental challenges of building a full-scale quantum computer and leaves the fabrication a daunting but primarily an engineering concern. Using a hierarchical array-based design and a quantum teleportation communication protocol, we are able to overcome the primary scalability challenges of reliability, communication, and quantum resource distribution. In particular, we present a reconfigurable quantum circuit substrate, or "quantum FPGA'' (qFPGA) which allows efficient implementation of universal quantum gates and error correction. We use this qFPGA as a basic building block for an array structure that scalably provides communication channels and quantum resource distribution. We exploit a hierarchical combination of ballistic transport of data ions and quantum teleportation to reduce the cost of reliable communication from exponential to polynomial in distance. By using a set of simulation tools we are able to evaluate a hypothetical design of a future general purpose quantum computer and describe the execution of a fault-tolerant Toffoli gate construction. Without considering classical control constraints and assuming best-possible ion-trap parameters our computer consists of level 2 encoded qubits with the Steane \ecc code tightly connected by the teleportation interconnect, and capable of executing a fault-tolerant Toffoli gate in roughly 2.3 seconds. This translates to factoring a 128-bit number in slightly over 40 hours in circuits dominated by Toffoli gates.