Quantum computing is something to be excited about.
a quantum computer operates directly using the unintuitive laws of quantum physics
quantum computing is a more powerful model of computation than classical computing*
if we could build a moderately-sized quantum computer, it would radically change technology: Shor's algorithm, quantum simulations
Unique features of quantum physics
a quantum system can be in a “superposition” of two or more of its allowed states
in general, we can only predict probabilities of what might happen
this is *NOT* a failure in our description -- it is an inherent aspect of quantum physics
detection/measurement irreversibly changes the state of a system
Although it may not seem believable, this is how the world really works!
Classical and quantum computation
possible states
measurement
operations
Classical computing (in a nutshell)
One classical bit
Many classical bits
A four bit machine can be in one of 16 different states.
A 300 bit machine can be in one of 2,037,035,976,334,486,086,268,445,688,409,378,161,051,468,393,665,936,250,636,140,449,354,381,299,763,336,706,183,397,376 possible states. (more than the number of atoms in the observable universe!)
Classical operations
With one bit, the only nontrivial operation is “NOT” (0 → 1, 1 → 0)
A computer works by controlling bits with other bits; e.g. “CCNOT” (if bits A and B are both 1, perform a NOT operation on bit C)
From here we could build up all of classical computing. We just need more bits.
Onward, to quantum computing!
One quantum bit (“qubit”)
But there's a catch!
Measurement (one qubit)
Measurement (one qubit)
Given one quantum bit, only one classical bit of information can be extracted.
Many quantum bits
Six quantum bits
300 quantum bits
a 300 qubit machine can be in a superposition of all 2,037,035,976,334,486,086,268,445,688,409,378,161,051,468,393,665,936,250,636,140,449,354,381,299,763,336,706,183,397,376 possible states.
as such, there's no possible way to simulate a 300-qubit machine in the universe.
Measurement (many qubits)
Measurement (many qubits)
Partial measurement
Quantum measurement: summarized
measurement of 300 qubits → 300 classical bits of classical information
but yet, it takes incredible computing power to simulate this on a classical computer
the design of quantum algorithms involves coming up with tricks for doing useful computations despite this seeming limitation
Quantum entanglement
Quantum operations
Single qubit operations
“Bloch Sphere” by “Smite-Meister.” Licensed CC-BY-SA from Wikipedia.
NOT
NOT
Phase
NOT: many qubits
Phase: many qubits
Controlled-NOT
Quantum computing must be reversible
the only irreversible step is “measurement”
quantum no clone theorem
Presumably we are working on information at the fundamental level the universe uses to operate.
How to build a quantum computer
no clone → information can be lost to anything it interacts with
low temperatures typically, or a degree of freedom that doesn't interact easily
DiVincenzo Criteria
well-defined qubits
reliable state preparation
low decoherence
accurate operations
strong measurements
Possible hardware implementations
ion traps
superconducting qubits
spin-defects in diamond and other materials
quantum dots
toplogical quantum computing
State of the art: factoring 21 = 3 * 7
Other concepts
quantum teleportation
quantum cryptography
quantum error correction
Quantum computing is something to be excited about.
a quantum computer operates directly using the unintuitive laws of quantum physics
quantum computing is a more powerful model of computation than classical computing*
if we could build a moderately-sized quantum computer, it would radically change technology: Shor's algorithm, quantum simulations
