of the base physical error rate on the architecture and performance, and will be discussed later.

Efficient ancilla factories. Most numeric quantum algorithms depend heavily on a three-qubit gate called a controlled-controlled NOT gate, or Toffoli gate. In most quantum error correction paradigms, direct execution of a Toffoli gate on encoded logical qubits is not possible. Instead, the Toffoli gate is performed using several operations, including one that consumes a specially prepared ancilla (temporary variable) state. The ancilla is created using distillation (a quantum error detection code), which takes noisy physical states and builds more accurate logical states. Creation of these states may dominate the workload of the machine, and recent work has assumed that 75%–90% of the machine is dedicated to their production. Isailovic et al. referred to this need as running quantum applications “at the speed of data,” that is, producing the generic ancilla states rapidly enough that they are not the performance bottleneck. 14

Balancing error management mechanisms. A functioning quantum computer almost certainly will not rely on a single type of error correction, but will incorporate different forms of error correction/detection/suppres-sion at different levels. Different error management techniques have different strengths and weaknesses, and the combinatorial space for integrating multiple types is large.

Defects. A quantum architecture must also take into account that fabrication will inevitably be an imperfect process. Qubits may be declared defective because they fail to correctly hold the correct state variable carrier (for example, to trap a single electron), because memory lifetime is short or gate control imprecise, or because they fail to couple properly to other qubits. For gate-based, error-corrected systems, calculations show that a stringent definition of declaring a device to be functional pays for itself in reduced error correction demands. 36 A system’s resilience to low yield is very microarchitecture-dependent. Alternatively, the digital quantum error correction itself can be adapted to tolerate loss. 34

ficult to execute fault tolerantly. When selecting a quantum code, the rate is important, but the demands made on the implementing hardware and the ease of logical operations are critical.

Performing error correction is not a simple task; in fact, the vast majority of the processing power of a universal quantum computer will be used to correct errors in the quantum state. Application algorithms and data processing make their appearance only at a level well above the real-time, (physical) qubit-by-qubit work of error correction. An architecture for a universal quantum computer will therefore have as its primary goal the execution of specific types of error correction.

The earliest ideas for QEC naturally took advantage of classical error correction techniques. After solving the problems of measuring error syndromes without destroying the quantum state and computing on encoded states without inadvertently spreading errors (known in QC literature as fault tolerance, referring to runtime errors rather than mid-computation failure of hardware components), application of classical error correction became relatively straightforward. 9

A promising form of error correction is surface code computation, which grew out of work by Kitaev and others on topological quantum computing. Raussendorf and collaborators created the 2D and 3D versions suitable for solid-state and photonic systems, respectively. 11, 31 Fowler, Devitt, and others have extended the practicality of these results, including implementing the real-time error processing necessary to determine that the classical half of the machine is a tractable engineering problem. 8 The code rate of surface codes is poor, but their requirement only for nearest-neighbor connections will allow them to work at a higher physical error rate than other methods on some attractive hardware platforms.

Beyond digital quantum error
correction for arbitrary states, other
approaches can be used to (partial-
ly) isolate qubits from undesirable
interactions. Decoherence-free sub-
spaces encode a logical qubit in the
phase difference of two physical qu-
bits, suppressing the effect of certain
types of noise. Techniques known as
spin echo and dynamic decoupling
similarly can be used to partially re-
verse the impact of systematic ef-
fects on memory, going with the
error for a while and against it for a
while, canceling out the effect. Puri-
fication—error detection for specific
states—will be especially useful for
communication, either system inter-
nal or external.
The implementation of error cor-
rection is perhaps the key near-term
experimental goal. As experimental
capabilities have grown, groups have
begun competing to demonstrate
quantum error correction in increas-
ingly complete forms. Blatt’s group
performed multiple rounds of an error
correction-like circuit that detects and
corrects certain types of errors using
certain simplifications. 32 Pan’s group
has recently shown an eight-photon
entangled state related to the unit cell
of 3D surface error correction. 40
Microarchitectures for error correc-
tion. As in classical computer architec-
ture, microarchitecture is the bridge
between physical device capabilities
and the architecture. Microarchitec-
ture in the quantum case can be un-
derstood to be the level dedicated to
efficient execution of quantum error
management, while the system archi-
tecture is the organization of micro-
architecture blocks into a complete
system. There are several specifically
quantum elements that must be con-
sidered for this microarchitecture.

Clock speed. The conversion factor from physical gate cycle to logical gate cycle has a strong, underappreci-ated impact on the performance of an algorithm. It depends on a number of architectural features, as well as the error correction code itself. For the ion trap-based system analyzed by Clark et al., 6, 26 a 10µsec physical gate results in a 1.6msec error correction cycle time using the basic form of Steane’s error correcting code, which encodes one logical qubit in seven physical ones. The code will need to be applied in recursive fashion, resulting in growth of the physical system by an order of magnitude and an increase in the logical clock cycle to 260msec, not far below the topmost quantum line in Figure 1. This dramatic increase illustrates the effect