Quake Dialect¶

General Introduction¶

The quantum circuit model is the most widely used model of quantum computation. It provides a convenient tool for formulating quantum algorithms and an architecture for the physical construction of quantum computers.

A quantum circuit represents a computation as a sequence of quantum operators applied to quantum data. In our case, the quantum data is a set of quantum bits, or qubits for short. Physically, a qubit is an object with only two distinguishable states, i.e., it is a two-state quantum mechanical system such as a spin-1/2 particle.

Conceptually, a quantum operator is an effect that might modify the state of a subset of qubits. Most often, this effect is unitary evolution—in this case, we say that the operator is a unitary. The number of target qubits an operator acts upon is an intrinsic property.

A quantum instruction is the embodiment of a quantum operator when applied to a specific subset of qubits. The number of qubits must be equal to (or greater than) the number of target qubits intrinsic to the operator. If greater, the extra qubits are considered controls.

Motivation¶

The main motivation behind Quake’s value model is to directly expose quantum and classical data dependencies for optimization purposes, i.e., to represent the dataflow in quantum computations. In contrast to Quake’s memory model, which uses memory semantics (quantum operators act as side-effects on qubit references), the value model uses value semantics, that is quantum operators consume and produce values. These values are not truly SSA values, however, as operations still have side-effects on the value itself and the value cannot be copied.

Let’s see an example to clarify the distinction between the models. Take the following Quake implementation of some toy quantum computation:

func.func foo(%veq : !quake.veq<2>) {
// Boilerplate to extract each qubit from the vector
%c0 = arith.constant 0 : index
%c1 = arith.constant 1 : index
%q0 = quake.extract_ref %veq[%c0] : (!quake.veq<2>, index) -> !quake.ref
%q1 = quake.extract_ref %veq[%c1] : (!quake.veq<2>, index) -> !quake.ref

// We apply some operators to those extracted qubits
// ... bunch of operators using %q0 and %q1 ...
quake.h %q0 : (!quake.ref) -> ()

// We decide to measure the vector
%result = quake.mz %veq : (!quake.veq<2>) -> cc.stdvec<i1>

// And then apply another Hadamard to %q0
quake.h %q0 : (!quake.ref) -> ()
// ...
}

Now imagine we want to optimize this code by removing pair of adjacent adjoint operators, e.g., if we have a pair Hadamard operations next to each other on the same qubit—visually:

┌───┐ ┌───┐         ┌───┐
─┤ H ├─┤ H ├─  =  ───┤ I ├───  =  ─────────────
└───┘ └───┘         └───┘

Where I is the identity operator. Now note that a naive implementation of this optimization for Quake would optimize away both quake.h operators being applied to %q0. Such an implementation would have missed the fact that a measurement is being applied to the vector, %veq, which contains %q0.

Of course it is possible to correctly implement this optimization for Quake. However such an implementation would be quite error-prone and require complex analyses. For this reason, Quake has overloaded gates.

In the value model operators consume values and return new values:

%q0_1 = quake.op %q0_0 : (!quake.wire) -> !quake.wire

We can visualize the difference between memory and value representation as:

Memory                                   Value

┌──┐ ┌──┐     ┌──┐                  ┌──┐ %q0_1 ┌──┐     ┌──┐
%q0 ─┤  ├─┤  ├─···─┤  ├─ %q0  vs  %q0_0 ─┤  ├───────┤  ├─···─┤  ├─ %q0_Z
└──┘ └──┘     └──┘                  └──┘       └──┘     └──┘

If we look at the implementation again, we notice that the problem with the naive optimization happens because the Hadamard operators are implicitly connected by the same value %q0. In value form, all the gates are explicitly connected by distinct values, which eliminates the need to do further analysis via implicit side-effects. The following is the implementation in value form.

func.func @foo(%array : !quake.qvec<2>) {
// Boilerplate to extract each qubit
%c0 = arith.constant 0 : index
%c1 = arith.constant 1 : index
%r0 = quake.extract_ref %array[%c0] : (!quake.qvec<2>, index) -> !quake.qref
%r1 = quake.extract_ref %array[%c1] : (!quake.qvec<2>, index) -> !quake.qref

// Unwrap the quantum references to expose the wires.
%q0 = quake.unwrap %r0 : (!quake.qref) -> !quake.wire
%q1 = quake.unwrap %r1 : (!quake.qref) -> !quake.wire

// Misc. operators applied
%q0_M = quake.h %q0_L : (!quake.wire) -> !quake.wire

// Re-wrap the wire to its original source
quake.wrap %q0_M to %r0 : !quake.wire, !quake.qref
quake.wrap %q1_X to %r1 : !quake.wire, !quake.qref

// Measure the entire vector of quantum references
%result = quake.mz %array : (!quake.qvec<2>) -> !cc.stdvec<i1>

// Unwrap the wire for qubit 0 again
%q0_P = quake.unwrap %r0 : (!quake.qref) -> !quake.wire
...
%q0_Z = quake.h %q0_Y : (!quake.wire) -> !quake.wire
// Re-wrap the wire back to the original reference
quake.wrap %q0_Z to %r0 : !quake.wire, !quake.qref
return
}

In this code we can more straightforwardly see that the Hadamard operators cannot cancel each other. One way of reasoning about this is as follows: In value form we need to follow a chain of values to know the qubit operators are being applied to, in this example:

Mmeory                          Value
%q0         [%q0_0, %q0_1 ... %q0_L, %q0_M; %q0_P ... %q0_Y, %q0_Z]

We know that one Hadamard is applied to %q0_L and generates %q0_M, and the other is applied %q0_Y and generates %q0_Z. Hence, there is no connection between them—which means they cannot cancel each other out.