Error mitigation with Clifford quantum-circuit data
Piotr Czarnik, Andrew Arrasmith, Patrick J. Coles, Łukasz Cincio
Abstract
Achieving near-term quantum advantage will require accurate estimation of quantum observables despite significant hardware noise. For this purpose, we propose a novel, scalable error-mitigation method that applies to gate-based quantum computers. The method generates training data <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo fence="false" stretchy="false">{</mml:mo><mml:msubsup><mml:mi>X</mml:mi><mml:mi>i</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mtext>noisy</mml:mtext></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mi>X</mml:mi><mml:mi>i</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mtext>exact</mml:mtext></mml:mrow></mml:msubsup><mml:mo fence="false" stretchy="false">}</mml:mo></mml:math> via quantum circuits composed largely of Clifford gates, which can be efficiently simulated classically, where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>X</mml:mi><mml:mi>i</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mtext>noisy</mml:mtext></mml:mrow></mml:msubsup></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>X</mml:mi><mml:mi>i</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mtext>exact</mml:mtext></mml:mrow></mml:msubsup></mml:math> are noisy and noiseless observables respectively. Fitting a linear ansatz to this data then allows for the prediction of noise-free observables for arbitrary circuits. We analyze the performance of our method versus the number of qubits, circuit depth, and number of non-Clifford gates. We obtain an order-of-magnitude error reduction for a ground-state energy problem on 16 qubits in an IBMQ quantum computer and on a 64-qubit noisy simulator.