Low-overhead fault-tolerant implementation of quantum T Gate

At left (triangle) is a circuit diagram for the global Hadamard measurement of qubits encoded in the error-correcting code known as the color code. Such circuits are implemented using CNOT gates (circles with crosses), controlled-Hadamard gates (circles with H’s), and qubit initialization and measurement; numbers indicate the time steps at which initializations, measurements, and gates take place. At right is a blowup of one component of the circuit (blue hexagons), known as a stabilizer of the color code. Redundant ancilla encoding finds a layout such that the same architecture can be used to implement both the global Hadamard measurement and error detection (top hexagon) by swapping flag qubits with ancilla qubits, while maintaining nearest-neighbor connectivity between all qubits. CREDIT: GLYNIS CONDON, FROM A DESIGN BY CHRISTOPHER CHAMBERLAND AND KJUNGJOO NOH

Researchers at Amazon propose a new approach to reduce the number of ancillary qubits required to implement the crucial T gate by at least an order of magnitude.

Today’s qubits are still too noisy to faithfully execute the long quantum algorithms needed to solve practically important problems. Quantum error correction can compensate for noise, but it has high overhead. With existing quantum error correction schemes, a single logical qubit might require thousands of additional physical qubits to handle the error correction.

They have showed that their scheme reduces the overhead costs of implementing T gates by at least an order of magnitude, both in terms of the number of qubits and the number of required operations. Further, their scheme respects many of the hardware constraints characteristic of the most promising quantum computing architectures.

Quantum gates can be divided into two groups: the Clifford group gates and the non-Clifford gates. Gates in the Clifford group can be efficiently simulated by a classical computer; non-Clifford gates cannot be. Of the three basic gates we described above, only the T gate is a non-Clifford gate. Expressed in terms of our basic gate set, all useful quantum algorithms require many T gates. 

Instead of using the now famous magic-state distillation to prepare magic states with high fidelity, they propose a fault-tolerant method for directly preparing magic states. 

Quantum error correction requires performing measurements on some of the qubits that compose a logical circuit; the qubits that perform those measurements are known as ancilla qubits. Their scheme, which we call redundant ancilla encoding, uses the same ancilla qubits in different ways for different phases of a quantum operation.

In one part of their scheme, we use a group of ancilla qubits to detect errors; but in another part, those ancilla qubits transform into flag qubits, which can detect events where small errors grow to large uncorrectable errors. 

Using fewer ancilla qubits allows to implement a fault-tolerant protocol for preparing magic states with very few resources. It also allows all of the operations to be implemented between nearest-neighbor qubits, an important constraint in many quantum computing architectures. 

They further showed that, due to the fault tolerance of their circuits, magic states with the desired fidelities can be prepared using only physical-level Clifford operations, not the logical-level implementations required in prior work. Their scheme is thus a bottom-up approach, given that all operations can be implemented at the physical level. This is one of the main reasons they see improvement by at least an order of magnitude in their implementation of the T gate. (Amazon)

The paper has been published in npj Quantum Information.

Read more.