We can therefore conveniently express the circuit sampling overhead as a quantum runtime, J: The base of this exponential, represented as γ̄, is a property of the experimentally learned noise model and its inversion. This overhead is exponential in the number of qubits n and circuit depth d. The noise inversion, however, leads to pre-factors in the measured expectation values that translate into a circuit sampling overhead. In PEC, we learn and effectively invert the noise of the circuit of interest for the computation of expectation values by averaging randomly sampled instances of noisy circuits. More recently, theoretical and experimental advances have shown that PEC can already enable noise-free estimators of quantum circuits on noisy quantum computers. 3 The ZNE method cancels subsequent orders of the noise affecting the expectation value of a noisy quantum circuit by extrapolating measurement outcomes at different noise strength.

In recent years, we developed 1 and implemented two general-purpose error mitigation methods, called zero noise extrapolation ( ZNE) 2 and probabilistic error cancellation ( PEC). Fortunately, quantum error mitigation provides a collection of tools and methods that allow us to evaluate accurate expectation values from noisy, shallow depth quantum circuits, even before the introduction of fault tolerance. However, even for shallow circuits, noise can lead to faulty estimates. These errors limit the depth of the quantum circuit that we can implement. How then do we chart a path to address the second question in practice?Ĭurrent quantum hardware is subject to different sources of noise, the most well-known being qubit decoherence, individual gate errors, and measurement errors. This is the reason we have built the world’s largest quantum ecosystem with the IBM Quantum Network, made up of Fortune 500 companies, academic institutions, national entities, start-ups, and the Qiskit Community to explore the problem space of quantum circuits to drive real application and value. It is our commitment to work with the community and industry experts to find problems that are solvable with quantum circuits that are known to be difficult to simulate classically. First, which problems can we map to quantum circuits that have solutions which are better than classical approaches? Second, how can we obtain reliable outcomes for these circuits on quantum hardware with a faster runtime?Īddressing the first question is not something we can do alone. This can only be achieved for specific kinds of problems.Īccessing a quantum advantage therefore requires us to answer two questions. For this to be possible, the algorithm should have an efficient representation as quantum circuits, and there should be no classical algorithm that can simulate these quantum circuits efficiently. Such an advantage can take many forms, the most prominent one being a substantial improvement of a quantum algorithm’s runtime over the best classical approaches. Of course, the ultimate litmus test for practical quantum computing is to provide an advantage over classical approaches for a useful problem. Along this path, advances in qubit coherence, gate fidelities, and speed immediately translate to measurable advantage in computation, akin to the steady progress historically observed with classical computers. However, recent advances in techniques we refer to broadly as quantum error mitigation allow us to lay out a smoother path towards this goal.

Building such a processor therefore is the central goal for our development. Indeed, it is widely accepted that one must first build a large fault-tolerant quantum processor before any of the quantum algorithms with proven super-polynomial speed-up can be implemented. Although quantum computers have seen tremendous improvements in their scale, quality and speed in recent years, such a gradual evolution seems to be missing from the narrative. The history of classical computing is one of advances in transistor and chip technology yielding corresponding gains in information processing performance.

Quantum error