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