Automated Synthesis of Fault-Tolerant State Preparation Circuits for Quantum Error-Correction Codes

Abstract

A central ingredient in fault-tolerant quantum algorithms is the initialization of a logical state for a given quantum error-correcting code from a set of noisy qubits. A scheme that has demonstrated promising results for small code instances that are realizable on currently available hardware composes a non-fault-tolerant state preparation circuit with a verification circuit that checks for spreading errors. Known circuit constructions of this scheme are mostly obtained manually, and no algorithmic techniques for constructing depth- or gate-optimal circuits exist. As a consequence, the current state-of-the-art exploits this scheme only for specific code instances and mostly for the special case of distance <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>d</a:mi> <a:mo>=</a:mo> <a:mn>3</a:mn> </a:math> codes only. In this work, we propose an automated approach for synthesizing fault-tolerant state preparation circuits for arbitrary CSS codes. We utilize methods based on satisfiability solving (SAT) to construct fault-tolerant state preparation circuits consisting of depth- and gate-optimal preparation and verification circuits. We also provide heuristics that can synthesize fault-tolerant state preparation circuits for code instances where no optimal solution can be obtained in an adequate time. Moreover, we give a general construction for nondeterministic state preparation circuits for codes beyond distance 3. Numerical evaluations using <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>d</c:mi> <c:mo>=</c:mo> <c:mn>3</c:mn> </c:math> , <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>d</e:mi> <e:mo>=</e:mo> <e:mn>5</e:mn> </e:math> , and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>d</g:mi> <g:mo>=</g:mo> <g:mn>7</g:mn> </g:math> codes confirm that the generated circuits exhibit the desired scaling of the logical error rates. The resulting methods are publicly available as part of the (MQT) at . Such methods are an important step in providing fault-tolerant circuit constructions that can aid in near-term demonstrations of fault-tolerant quantum computing.

Topics & Concepts