Threshold error penalty for fault-tolerant quantum computation with nearest neighbor communication

Abstract

Abstract-The error threshold for fault-tolerant quantum computation with concatenated encoding of qubits is penalized by internal communication overhead. Many quantum computation proposals rely on nearest neighbor communication, which requires excess gate operations. For a qubit stripe with a width of + 1 physical qubits implementing levels of concatenation, we find that the error threshold of 2.1 10 5 without any communication burden is reduced to 1.2 10 7 when gate errors are the dominant source of error. This 175 penalty in error threshold translates to an 13 penalty in the amplitude and timing of gate operation control pulses.

Logical Qubit in a Linear Array of Semiconductor Quantum Dots

“…The main alternative to topological codes is code concatenation, where codes are nested inside of codes [62], which is the approach taken in this proposal. There have been encouraging results in thresholds with concatenation [6,55,76,140], as well as investigations into two-dimensional and LNN architectures [68][69][70]75,81,82,138,141]. Knill demonstrated that small quantum codes (such as the four-qubit code studied here) can be effective when concatenated [6].…”

“…Our error correction schemes are simple two-, three-, and four-qubit quantum codes that have been mapped to the linear array of qubits [68][69][70] because alternatives like the surface code [8,[71][72][73] and Bacon-Shor code [74][75][76] are not effective in a linear geometry [77][78][79]. Our logical qubit is supported with simulations of error correction that can be compared with other proposals [13,58,[69][70][71]73,75,76,[80][81][82][83][84][85][86][87]. Finally, we are careful to note that a purely linear architecture is not extensible to an arbitrary number of qubits, for the simple reason that a single defective qubit anywhere results in two noninteracting arrays.…”

Architectural implications of quantum computing technologies

“…The first and most important class of these is the Calderbank-Shor-Steane (CSS) codes [Calderbank and Shor 1996;Shor 1996;Steane 1996;Preskill 1998b]. The theory and practice (including both experimental demonstrations [Chiaverini et al 2004;Pittman et al 2005;Roos et al 2004] and system design [Svore et al 2005;Steane 2002;Copsey et al 2003;Burkard et al 1999;Devitt et al 2004;Metodiev et al 2003;Szkopek et al 2004]) of QEC and FT operation are vast; we will not cover them in any depth here. Nevertheless, a basic understanding of the pressures that QEC and FT place on architecture is critical.…”

“…Unfortunately, this syndrome calculation and measurement process may also introduce errors. Technologies that support nearest-neighbor-only interactions require swapping of qubits in order to calculate the error syndrome, with the swap gates possibly introducing errors themselves, making the threshold requirements for effective error correction more stringent; in some studies, as much as 175 times worse [Svore et al Aharonov and Ben-Or 1999;Szkopek et al 2004]. Applying two-qubit gates can result in the propagation of an error from one qubit to another, even from the target of the gate to its control.…”

Universal quantum computation with theν=5∕2fractional quantum Hall state

“…for a local architecture [5,6] to 10 −5 − 10 −2 for non-local gates [4,7]. With the present technology these rates are hardly achievable by any real device.…”