1,510 research outputs found
Three-dimensional surface codes: Transversal gates and fault-tolerant architectures
One of the leading quantum computing architectures is based on the
two-dimensional (2D) surface code. This code has many advantageous properties
such as a high error threshold and a planar layout of physical qubits where
each physical qubit need only interact with its nearest neighbours. However,
the transversal logical gates available in 2D surface codes are limited. This
means that an additional (resource intensive) procedure known as magic state
distillation is required to do universal quantum computing with 2D surface
codes. Here, we examine three-dimensional (3D) surface codes in the context of
quantum computation. We introduce a picture for visualizing 3D surface codes
which is useful for analysing stacks of three 3D surface codes. We use this
picture to prove that the and gates are transversal in 3D surface
codes. We also generalize the techniques of 2D surface code lattice surgery to
3D surface codes. We combine these results and propose two quantum computing
architectures based on 3D surface codes. Magic state distillation is not
required in either of our architectures. Finally, we show that a stack of three
3D surface codes can be transformed into a single 3D color code (another type
of quantum error-correcting code) using code concatenation.Comment: 23 pages, 24 figures, v2: published versio
Decoherence-Free Subspaces for Multiple-Qubit Errors: (II) Universal, Fault-Tolerant Quantum Computation
Decoherence-free subspaces (DFSs) shield quantum information from errors
induced by the interaction with an uncontrollable environment. Here we study a
model of correlated errors forming an Abelian subgroup (stabilizer) of the
Pauli group (the group of tensor products of Pauli matrices). Unlike previous
studies of DFSs, this type of errors does not involve any spatial symmetry
assumptions on the system-environment interaction. We solve the problem of
universal, fault-tolerant quantum computation on the associated class of DFSs.Comment: 22 pages, 4 figures. Sequel to quant-ph/990806
What is a quantum computer, and how do we build one?
The DiVincenzo criteria for implementing a quantum computer have been seminal
in focussing both experimental and theoretical research in quantum information
processing. These criteria were formulated specifically for the circuit model
of quantum computing. However, several new models for quantum computing
(paradigms) have been proposed that do not seem to fit the criteria well. The
question is therefore what are the general criteria for implementing quantum
computers. To this end, a formal operational definition of a quantum computer
is introduced. It is then shown that according to this definition a device is a
quantum computer if it obeys the following four criteria: Any quantum computer
must (1) have a quantum memory; (2) facilitate a controlled quantum evolution
of the quantum memory; (3) include a method for cooling the quantum memory; and
(4) provide a readout mechanism for subsets of the quantum memory. The criteria
are met when the device is scalable and operates fault-tolerantly. We discuss
various existing quantum computing paradigms, and how they fit within this
framework. Finally, we lay out a roadmap for selecting an avenue towards
building a quantum computer. This is summarized in a decision tree intended to
help experimentalists determine the most natural paradigm given a particular
physical implementation
Machine learning logical gates for quantum error correction
Quantum error correcting codes protect quantum computation from errors caused
by decoherence and other noise. Here we study the problem of designing logical
operations for quantum error correcting codes. We present an automated
procedure which generates logical operations given known encoding and
correcting procedures. Our technique is to use variational circuits for
learning both the logical gates and the physical operations implementing them.
This procedure can be implemented on near-term quantum computers via quantum
process tomography. It enables automatic discovery of logical gates from
analytically designed error correcting codes and can be extended to error
correcting codes found by numerical optimizations. We test the procedure by
simulation on classical computers on small quantum codes of four qubits to
fifteen qubits and show that it finds most logical gates known in the current
literature. Additionally, it generates logical gates not found in the current
literature for the [[5,1,2]] code, the [[6,3,2]] code, and the [[8,3,2]] code.Comment: 17 page
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