Models for quantum computation with circuit connections subject to the quantum superposition principle have been recently proposed. There, a control quantum system can coherently determine the order in which a target quantum system undergoes
N gate operations. This process, known as the quantum
N-switch, is a resource for several information-processing tasks. In particular, it provides a computational advantage -- over fixed-gate-order quantum circuits -- for phase-estimation problems involving
N unknown unitary gates. However, the corresponding algorithm requires an experimentally unfeasible target-system dimension (super)exponential in
N. Here, we introduce a promise problem for which the quantum
N-switch gives an equivalent computational speed-up with target-system dimension as small as 2 regardless of
N. We use state-of-the-art multi-core optical-fiber technology to experimentally demonstrate the quantum
N-switch with
N=4 gates acting on a photonic-polarization qubit. This is the first observation of a quantum superposition of more than
N=2 temporal orders, demonstrating its usefulness for efficient phase-estimation.
Quantum computers achieve a speed-up by placing quantum bits (qubits) in superpositions of different states. However, it has recently been appreciated that quantum mechanics also allows one to 'superimpose different operations'. Furthermore, it has been shown that using a qubit to coherently control the gate order allows one to accomplish a task--determining if two gates commute or anti-commute--with fewer gate uses than any known quantum algorithm. Here we experimentally demonstrate this advantage, in a photonic context, using a second qubit to control the order in which two gates are applied to a first qubit. We create the required superposition of gate orders by using additional degrees of freedom of the photons encoding our qubits. The new resource we exploit can be interpreted as a superposition of causal orders, and could allow quantum algorithms to be implemented with an efficiency unlikely to be achieved on a fixed-gate-order quantum computer.
Processes with indefinite causal order (ICO), such as the quantum switch, are an emerging resource for quantum tasks and a fundamental test bed for studies of temporal correlations in quantum mechanics. A limitation of past photonic implementations of the quantum switch, however, is their inability to perform measurements inside the switch without either destroying the superposition of causal orders or delaying readout until the after the quantum switch. Measurements where the results are read out locally are needed for several applications of ICO, but also for a loophole-free verification of ICO. Here, we overcome past limitations by introducing a
local measurement scheme and coupling the photon in the switch to a
time−delocalized ancilla system. We experimentally realize this protocol using a photonic quantum switch with post-selected linear optical logic gates. Our method ensures that the measurement apparatus interacts with the system at two distinct times and yet yields a single outcome. We use a quantum eraser measurement to preserve the ICO, which we certify by measuring a causal witness and finding a negative value of
CW≈−0.305(1). Furthermore, by explicitly realizing a time-delocalized ancilla system, our protocol not only enables a new class of quantum switch protocols requiring local readout, but also provides a general method for path-coherence-preserving measurements with broad applications beyond ICO.