skip to main content


Title: Virtualized Logical Qubits: A 2.5D Architecture for Error-Corrected Quantum Computing
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.  more » « less
Award ID(s):
1730449
NSF-PAR ID:
10209011
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
53rd Annual IEEE/ACM International Symposium on Microarchitecture (MICRO)
Page Range / eLocation ID:
173 to 185
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Recent constructions of quantum low-density parity-check (QLDPC) codes provide optimal scaling of the number of logical qubits and the minimum distance in terms of the code length, thereby opening the door to fault-tolerant quantum systems with minimal resource overhead. However, the hardware path from nearest-neighbor-connection-based topological codes to long-range-interaction-demanding QLDPC codes is likely a challenging one. Given the practical difficulty in building a monolithic architecture for quantum systems, such as computers, based on optimal QLDPC codes, it is worth considering a distributed implementation of such codes over a network of interconnected medium-sized quantum processors. In such a setting, all syndrome measurements and logical operations must be performed through the use of high-fidelity shared entangled states between the processing nodes. Since probabilistic many-to-1 distillation schemes for purifying entanglement are inefficient, we investigate quantum error correction based entanglement purification in this work. Specifically, we employ QLDPC codes to distill GHZ states, as the resulting high-fidelity logical GHZ states can interact directly with the code used to perform distributed quantum computing (DQC), e.g. for fault-tolerant Steane syndrome extraction. This protocol is applicable beyond the application of DQC since entanglement distribution and purification is a quintessential task of any quantum network. We use the min-sum algorithm (MSA) based iterative decoder with a sequential schedule for distilling3-qubit GHZ states using a rate0.118family of lifted product QLDPC codes and obtain an input fidelity threshold of0.7974under i.i.d. single-qubit depolarizing noise. This represents the best threshold for a yield of0.118for any GHZ purification protocol. Our results apply to larger size GHZ states as well, where we extend our technical result about a measurement property of3-qubit GHZ states to construct a scalable GHZ purification protocol.

     
    more » « less
  2. Quantum computers have recently made great strides and are on a long-term path towards useful fault-tolerant computation. A dominant overhead in fault-tolerant quantum computation is the production of high-fidelity encoded qubits, called magic states, which enable reliable error-corrected computation. We present the first detailed designs of hardware functional units that implement space-time optimized magic-state factories for surface code error-corrected machines. Interactions among distant qubits require surface code braids (physical pathways on chip) which must be routed. Magic-state factories are circuits comprised of a complex set of braids that is more difficult to route than quantum circuits considered in previous work [1]. This paper explores the impact of scheduling techniques, such as gate reordering and qubit renaming, and we propose two novel mapping techniques: braid repulsion and dipole moment braid rotation. We combine these techniques with graph partitioning and community detection algorithms, and further introduce a stitching algorithm for mapping subgraphs onto a physical machine. Our results show a factor of 5.64 reduction in space-time volume compared to the best-known previous designs for magic-state factories. 
    more » « less
  3. Abstract

    Reliable qubits are difficult to engineer, but standard fault-tolerance schemes use seven or more physical qubits to encode each logical qubit, with still more qubits required for error correction. The large overhead makes it hard to experiment with fault-tolerance schemes with multiple encoded qubits. Here, we study the 15-qubit Hamming code, which protects seven encoded qubits to distance three. We give fault-tolerant procedures for applying arbitrary Clifford operations on these encoded qubits, using only two extra qubits, 17 in total. In particular, individual encoded qubits within the code block can be targeted. Fault-tolerant universal computation is possible with four extra qubits, 19 in total. The procedures could enable testing more sophisticated protected circuits in small-scale quantum devices. Our main technique is to use gadgets to protect gates against correlated faults. We also take advantage of special code symmetries, and use pieceable fault tolerance.

     
    more » « less
  4. Abstract

    We study the effectiveness of quantum error correction against coherent noise. Coherent errors (for example, unitary noise) can interfere constructively, so that in some cases the average infidelity of a quantum circuit subjected to coherent errors may increase quadratically with the circuit size; in contrast, when errors are incoherent (for example, depolarizing noise), the average infidelity increases at worst linearly with circuit size. We consider the performance of quantum stabilizer codes against a noise model in which a unitary rotation is applied to each qubit, where the axes and angles of rotation are nearly the same for all qubits. In particular, we show that for the toric code subject to such independent coherent noise, and for minimal-weight decoding, the logical channel after error correction becomes increasingly incoherent as the length of the code increases, provided the noise strength decays inversely with the code distance. A similar conclusion holds for weakly correlated coherent noise. Our methods can also be used for analyzing the performance of other codes and fault-tolerant protocols against coherent noise. However, our result does not show that the coherence of the logical channel is suppressed in the more physically relevant case where the noise strength is held constant as the code block grows, and we recount the difficulties that prevented us from extending the result to that case. Nevertheless our work supports the idea that fault-tolerant quantum computing schemes will work effectively against coherent noise, providing encouraging news for quantum hardware builders who worry about the damaging effects of control errors and coherent interactions with the environment.

     
    more » « less
  5. 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. This significantly reduces communication overhead by giving the routing pass access to the higher-level structure of the circuit instead of discarding it. A second benefit is the ability to now select an architecture-tuned Toffoli decomposition such as the 8-CNOT Toffoli for the specific hardware qubits now known after the routing pass. We perform real experiments on IBM Johannesburg showing an average 35% decrease in two-qubit gate count and 23% increase in success rate of a single Toffoli over Qiskit. We additionally compile many near-term benchmark algorithms showing an average 344% increase in (or 4.44x) simulated success rate on the Johannesburg architecture and compare with other architecture types. 
    more » « less