  As quantum computers mature, quantum error correcting codes (QECs) will be
adopted in order to suppress errors to any desired level $E$ at a cost in
qubit-count $n$ that is merely poly-logarithmic in $1/E$. However in the NISQ
era, the complexity and scale required to adopt even the smallest QEC is
prohibitive. Instead, error mitigation techniques have been employed; typically
these do not require an increase in qubit-count but cannot provide exponential
error suppression. Here we show that, for the crucial case of estimating
expectation values of observables (key to almost all NISQ algorithms) one can
indeed achieve an effective exponential suppression. We introduce the Error
Suppression by Derangement (ESD) approach: by increasing the qubit count by a
factor of $n\geq 2$, the error is suppressed exponentially as $Q^n$ where $Q<1$
is a suppression factor that depends on the entropy of the errors. The ESD
approach takes $n$ independently-prepared circuit outputs and applies a
controlled derangement operator to create a state whose symmetries prevent
erroneous states from contributing to expected values. The approach is
therefore `NISQ-friendly' as it is modular in the main computation and requires
only a shallow circuit that bridges the $n$ copies immediately prior to
measurement. Imperfections in our derangement circuit do degrade performance
and therefore we propose an approach to mitigate this effect to arbitrary
precision due to the remarkable properties of derangements. a) they decompose
into a linear number of elementary gates -- limiting the impact of noise b)
they are highly resilient to noise and the effect of imperfections on them is
(almost) trivial. In numerical simulations validating our approach we confirm
error suppression below $10^{-6}$ for circuits consisting of several hundred
noisy gates (two-qubit gate error $0.5\%$) using no more than $n=4$ circuit
copies.
