To appear in the 2005 International Symposium on Microarchitecture (MICRO-38) A Quantum Logic Array Microarchitecture: Scalable Quantum Data Movement and Computation Tzvetan S. Metodi†, Darshan D. Thaker†, Andrew W. Cross‡ Frederic T. Chong§ and Isaac L. Chuang‡ †University Of California at Davis, ftsmetodiev, [email protected] §University Of California at Santa Barbara, [email protected] ‡Massachusetts Institute of Technology, fawcross, [email protected] (simply denoted as aj0i + bj1i, where a and b are proba- Abstract bility amplitudes satisfying jaj2 + jbj2 = 1). With N qubits a quantum computer can be in 2N unique states at any given Recent experimental advances have demonstrated tech- time. These states can be inter-correlated such that a single nologies capable of supporting scalable quantum computa- logic gate can act on all possible 2N states. The exponen- tion. A critical next step is how to put those technologies to- tial speedup offered by quantum computing, based on the gether into a scalable, fault-tolerant system that is also fea- ability to process quantum information through gate ma- sible. We propose a Quantum Logic Array (QLA) microar- nipulation [2], has led to several quantum algorithms with chitecture that forms the foundation of such a system. The substantial advantages over known algorithms with tradi- QLA focuses on the communication resources necessary to tional computation. The most significant is Shor’s algo- efficiently support fault-tolerant computations. We leverage rithm for factoring the product of two large primes in poly- the extensive groundwork in quantum error correction the- nomial time. Additional algorithms include Grover’s fast ory and provide analysis that shows that our system is both database search [3]; adiabatic solution of optimization prob- asymptotically and empirically fault tolerant. Specifically, lems [4]; precise clock synchronization [5]; quantum key we use the QLA to implement a hierarchical, array-based distribution [6]; and recently, Gauss sums [7] and Pell’s design and a logarithmic expense quantum-teleportation equation [8]. communication protocol. Our goal is to overcome the pri- A relevant large-scale quantum system must be capable mary scalability challenges of reliability, communication, of reaching a system size of S = KQ ¸ 1012, where K de- and quantum resource distribution that plague current pro- notes the number of computational steps and Q denotes the posals for large-scale quantum computing. Our work com- number of computational units. Quantum data is inherently plements recent work by Balenseifer et al [1], which studies very unstable, which leads to a lack of reliable operations the software tool chain necessary to simplify development that can be performed on it. Also if left idle, this quan- of quantum applications; here we focus on modeling a full- tum data will interact with its environment and lose state, a scale optimized microarchitecture for scalable computing. process called decoherence. Finally, there is the difficulty of transmitting quantum data between computational units without losing state. This implies that the greatest chal- lenge towards a large, practically useful quantum computer, 1. Introduction is designing an architecture that incorporates the required amount of fault-tolerance while minimizing overhead. Quantum computation exploits the ability for a single Previous work in large-scale quantum architecture [9, 10, quantum bit, a qubit, which can be implemented by the po- 11] has led to the consideration of several main scalability larization states of a photon or the spin of a single atom, issues that must be taken into account: reliable and realis- to exist in a superposition of the binary “0” and “1” states tic implementation technology; robust error correction and fault-tolerant structures; efficient quantum resource distri- Acknowledgements: This work is supported in part by the DARPA bution. QUIST program, in part by a NSF CAREER grant and a UC Davis Chan- cellor’s Fellowship awarded to Fred Chong, and in part by the NSF Center 1. Reliable and realistic implementation technology: for Bits and Atoms at MIT There are multiple approaches from very diverse fields of science for the realization of a full-scale quantum infor- [21, 22, 23]. Teleportation transmits a quantum state be- mation processor. Solid state technologies, trapped ions, tween two points without actually sending any quantum and superconducting quantum computation are just a small data, but rather two bits of classical information for each number of many physical implementations currently being qubit on both ends. studied. No matter the choice, any technology used to im- plement a quantum information processor must adhere to Classical Control four main requirements [12]: 1) It must allow the initial- ization of an arbitrary n-qubit quantum system to a known Q Q Q Q state. 2) A universal set of quantum operations must be available to manipulate the initialized system and bring it R RR R to a desired correlated state. 3) The technology must have Sea of the ability to reliably measure the quantum system. 4) It Q Q Q Q Lower Level must allow much longer qubit lifetimes than the time of a R R R R Qubits Channel quantum logic gate. The second requirement encompasses multi-qubit operations; thus, it implies that a quantum ar- Classical Control Q QQ Q Channel R chitecture must also allow for sufficient and reliable com- R R R R munication between physical qubits. 2. Robust error correction and fault tolerant struc- Figure 1. High-Level quantum computer structure, where a tures: Due to the high volatility of quantum data, ac- full-size computer consists of interconnected logical qubits tively stabilizing the system’s state through error correc- connected with programmable communication network. The tion will be one of the most vital operations through the letters R denote an integrated switch islands for redirecting course of a quantum algorithm. Fault tolerance and quan- quantum data coming from nearby logical qubits or other tum error correction constitute a significant field of research repeater islands. [13, 14, 15, 16, 17, 18] that has produced some very pow- erful quantum error correcting codes analogous, but fun- This paper introduces and evaluates the design of the damentally different from their classical counterparts. The Quantum Logic Array (QLA) architecture which takes the most important result, for our purposes, is the Threshold following approach to leveraging the three architecture re- Theorem [17], which says that an arbitrarily reliable quan- quirements described above: tum gate can be implemented using only imperfect gates, provided the imperfect gates have failure probability be- 1 At the lowest level QLA is based on the trapped ion- low a certain threshold. This remarkable result is achieved technology [24, 25, 26], which uses a single trapped through four steps: using quantum error-correction codes; atomic ion as a storage for a single unit of quantum data. performing all computations on encoded data; using fault In particular QLA is based on the highly scalable model tolerant procedures; and recursively encoding until the de- of (CCD) style ion-trap quantum information processing sired reliability is obtained. A successful architecture must architecture proposed by Kielpinski et al [27, 25]. This be carefully designed to minimize the overhead of recursive model consists of ions trapped in interconnected trap ar- error correction and be able to accommodate some of the rays and moved from trap to trap to interact [23, 22]. most efficient error correcting codes. 2 We have designed the architecture as a block structure 3. Efficient quantum resource distribution: The quantum (Figure 1), which fits naturally to quantum error correc- no-cloning theorem [19] (i.e. the inability to copy quantum tion, where each building block/tile reflects the error- data) prevents the ability to place quantum information on correction algorithm used. QLA itself is built by tiling a wire, duplicate, and transmit it to another location. Each these building blocks to form the hierarchies required for qubit must be physically transported from the source to the larger and more reliable encodings. In addition, QLA destination. This makes each qubit a physical transmitter invests area in communication channels to allow move- of quantum information, a restriction which places great ment of ions without hindering the parallelism required constraints on quantum data distribution. Particularly trou- by fault tolerant structures. blesome is moving the qubits over large distances where it 3 By structuring the large-scale model as a datapath ori- must be constantly ensured the data is safe from corrup- ented block architecture of independent, tightly compact tion. One method is to repeatedly error correct along the computational units QLA allows us to limit direct ion channel at a cost of additional error correction resources. movement to shorter, local distances within each com- Another solution is to use a purely quantum concept to im- putational unit. At larger distances (i.e. between com- plement a long-range wire [10]: teleportation [20], which putational units) we employ teleportation to avoid mov- has been experimentally demonstrated on a very small scale ing data directly over the long channels. Furthermore we couple teleportation with the concept of quantum re- Electrodes peaters [28] to avoid the exponential resource overhead. V1 V2 V3 V4 The Contributions of this Paper are: 1) We propose the QLA micro-architecture, which is designed for efficient Ballistic Channel Data Ion quantum error-correction and error-free long range commu- V1V2 V3 V4 nication of quantum states. 2) While teleportation has been proposed as a means of communication, we show the limita- Cooling Ion tions of a simplistic approach using teleportation. We then show how the QLA micro-architecture can be effectively Figure 2. A simple schematic of the basic elements neces- used to overcome these limitations. 3) To model QLA, we sary for trapped ion quantum computing. developed ARQ: a scalable quantum architectures simula- tor that maps quantum applications to fault-tolerant layouts 2.